{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_35421/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_35421","id":"gutenberg_35421","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/35421","summary":null,"tags":["Category: Philosophy & Ethics","Category: Research Methods/Statistics/Information Sys","Knowledge, Theory of","Logic","Philosophy","Science -- Methodology"],"text":"\n\n\n\nProduced by David Clarke, Stephen H. Sentoff and the Online\nDistributed Proofreading Team at https://www.pgdp.net (This\nfile was produced from images generously made available\nby The Internet Archive/Canadian Libraries)\n\n\n\n\n\n\n\nA\nSYSTEM OF LOGIC\n\nRATIOCINATIVE AND INDUCTIVE\n\nVOL. II.\n\n\n\n\nA\nSYSTEM OF LOGIC\n\nRATIOCINATIVE AND INDUCTIVE\n\nBEING A CONNECTED VIEW OF THE\nPRINCIPLES OF EVIDENCE\nAND THE\nMETHODS OF SCIENTIFIC INVESTIGATION\n\nBY\n\nJOHN STUART MILL\n\n\nIN TWO VOLUMES\n\nVOL. II.\n\nSEVENTH EDITION\n\n\nLONDON:\nLONGMANS, GREEN, READER, AND DYER\n\nMDCCCLXVIII\n\n\n\n\nCONTENTS\nOF\nTHE SECOND VOLUME.\n\n\n BOOK III.\n\n ON INDUCTION.--(_Continued._)\n\n\n CHAPTER XIV. _Of the Limits to the Explanation of Laws of\n Nature; and of Hypotheses._\n\n \u00a7 1. Can all the sequences in nature be resolvable into one law? 3\n\n 2. Ultimate laws cannot be less numerous than the\n distinguishable feelings of our nature 4\n\n 3. In what sense ultimate facts can be explained 7\n\n 4. The proper use of scientific hypotheses 8\n\n 5. Their indispensableness 16\n\n 6. Legitimate, how distinguished from illegitimate hypotheses 18\n\n 7. Some inquiries apparently hypothetical are really inductive 25\n\n\n CHAPTER XV. _Of Progressive Effects; and of the Continued\n Action of Causes._\n\n \u00a7 1. How a progressive effect results from the simple continuance\n of the cause 29\n\n 2. --and from the progressiveness of the cause 33\n\n 3. Derivative laws generated from a single ultimate law 36\n\n\n CHAPTER XVI. _Of Empirical Laws._\n\n \u00a7 1. Definition of an empirical law 38\n\n 2. Derivative laws commonly depend on collocations 39\n\n 3. The collocations of the permanent causes are not reducible\n to any law 41\n\n 4. Hence empirical laws cannot be relied on beyond the limits\n of actual experience 41\n\n 5. Generalizations which rest only on the Method of Agreement\n can only be received as empirical laws 43\n\n 6. Signs from which an observed uniformity of sequence may be\n presumed to be resolvable 44\n\n 7. Two kinds of empirical laws 47\n\n\n CHAPTER XVII. _Of Chance, and its Elimination._\n\n \u00a7 1. The proof of empirical laws depends on the theory of chance 49\n\n 2. Chance defined and characterized 50\n\n 3. The elimination of chance 55\n\n 4. Discovery of residual phenomena by eliminating chance 57\n\n 5. The doctrine of chances 59\n\n\n CHAPTER XVIII. _Of the Calculation of Chances._\n\n \u00a7 1. Foundation of the doctrine of chances, as taught by\n mathematics 61\n\n 2. The doctrine tenable 63\n\n 3. On what foundation it really rests 64\n\n 4. Its ultimate dependence on causation 68\n\n 5. Theorem of the doctrine of chances which relates to the\n cause of a given event 72\n\n 6. How applicable to the elimination of chance 74\n\n\n CHAPTER XIX. _Of the Extension of Derivative Laws to Adjacent\n Cases._\n\n \u00a7 1. Derivative laws, when not casual, are almost always\n contingent on collocations 78\n\n 2. On what grounds they can be extended to cases beyond the\n bounds of actual experience 80\n\n 3. Those cases must be adjacent cases 82\n\n\n CHAPTER XX. _Of Analogy._\n\n \u00a7 1. Various senses of the word analogy 86\n\n 2. Nature of analogical evidence 87\n\n 3. On what circumstances its value depends 91\n\n\n CHAPTER XXI. _Of the Evidence of the Law of Universal\n Causation._\n\n \u00a7 1. The law of causality does not rest on an instinct 95\n\n 2. But on an induction by simple enumeration 100\n\n 3. In what cases such induction is allowable 102\n\n 4. The universal prevalence of the law of causality, on what\n grounds admissible 105\n\n\n CHAPTER XXII. _Of Uniformities of Coexistence not dependent\n on Causation._\n\n \u00a7 1. Uniformities of coexistence which result from laws of\n sequence 110\n\n 2. The properties of Kinds are uniformities of coexistence 111\n\n 3. Some are derivative, others ultimate 113\n\n 4. No universal axiom of coexistence 114\n\n 5. The evidence of uniformities of coexistence, how measured 117\n\n 6. When derivative, their evidence is that of empirical laws 117\n\n 7. So also when ultimate 119\n\n 8. The evidence stronger in proportion as the law is more\n general 120\n\n 9. Every distinct Kind must be examined 121\n\n\n CHAPTER XXIII. _Of Approximate Generalizations, and Probable\n Evidence._\n\n \u00a7 1. The inferences called probable, rest on approximate\n generalizations 124\n\n 2. Approximate generalizations less useful in science than\n in life 124\n\n 3. In what cases they may be resorted to 126\n\n 4. In what manner proved 127\n\n 5. With what precautions employed 130\n\n 6. The two modes of combining probabilities 131\n\n 7. How approximate generalizations may be converted into\n accurate generalizations equivalent to them 136\n\n\n CHAPTER XXIV. _Of the Remaining Laws of Nature._\n\n \u00a7 1. Propositions which assert mere existence 139\n\n 2. Resemblance, considered as a subject of science 141\n\n 3. The axioms and theorems of mathematics comprise the\n principal laws of resemblance 143\n\n 4. --and those of order in place, and rest on induction by\n simple enumeration 145\n\n 5. The propositions of arithmetic affirm the modes of formation\n of some given number 146\n\n 6. Those of algebra affirm the equivalence of different modes\n of formation of numbers generally 151\n\n 7. The propositions of geometry are laws of outward nature 154\n\n 8. Why geometry is almost entirely deductive 156\n\n 9. Function of mathematical truths in the other sciences, and\n limits of that function 158\n\n\n CHAPTER XXV. _Of the Grounds of Disbelief._\n\n \u00a7 1. Improbability and impossibility 161\n\n 2. Examination of Hume's doctrine of miracles 162\n\n 3. The degrees of improbability correspond to differences in\n the nature of the generalization with which an assertion\n conflicts 166\n\n 4. A fact is not incredible because the chances are against it 170\n\n 5. Are coincidences less credible than other facts? 172\n\n 6. An opinion of Laplace examined 175\n\n\n BOOK IV.\n\n OF OPERATIONS SUBSIDIARY TO INDUCTION.\n\n\n CHAPTER I. _Of Observation and Description._\n\n \u00a7 1. Observation, how far a subject of logic 183\n\n 2. A great part of what seems observation is really inference 184\n\n 3. The description of an observation affirms more than is\n contained in the observation 187\n\n 4. --namely an agreement among phenomena; and the comparison\n of phenomena to ascertain such agreements is a preliminary\n to induction 190\n\n\n CHAPTER II. _Of Abstraction, or the Formation of\n Conceptions._\n\n \u00a7 1. The comparison which is a preliminary to induction implies\n general conceptions 193\n\n 2. --but these need not be pre-existent 194\n\n 3. A general conception, originally the result of a comparison,\n becomes itself the type of comparison 198\n\n 4. What is meant by appropriate conceptions 200\n\n 5. --and by clear conceptions 203\n\n 6. Further illustration of the subject 205\n\n\n CHAPTER III. _Of Naming, as subsidiary to Induction._\n\n \u00a7 1. The fundamental property of names as an instrument of\n thought 209\n\n 2. Names are not indispensable to induction 210\n\n 3. In what manner subservient to it 211\n\n 4. General names not a mere contrivance to economize the\n use of language 213\n\n\n CHAPTER IV. _Of the Requisites of a Philosophical Language,\n and the Principles of Definition._\n\n \u00a7 1. First requisite of philosophical language, a steady and\n determinate meaning for every general name 215\n\n 2. Names in common use have often a loose connotation 215\n\n 3. --which the logician should fix, with as little alteration\n as possible 218\n\n 4. Why definition is often a question not of words but of\n things 220\n\n 5. How the logician should deal with the transitive\n applications of words 224\n\n 6. Evil consequences of casting off any portion of the\n customary connotation of words 229\n\n\n CHAPTER V. _On the Natural History of the Variations in\n the Meaning of Terms._\n\n \u00a7 1. How circumstances originally accidental become incorporated\n into the meaning of words 236\n\n 2. --and sometimes become the whole meaning 238\n\n 3. Tendency of words to become generalized 240\n\n 4. --and to become specialized 243\n\n\n CHAPTER VI. _The Principles of a Philosophical Language\n further considered._\n\n \u00a7 1. Second requisite of philosophical language, a name for\n every important meaning 248\n\n 2. --viz. first, an accurate descriptive terminology 248\n\n 3. --secondly, a name for each of the more important results\n of scientific abstraction 252\n\n 4. --thirdly, a nomenclature, or system of the names of\n Kinds 255\n\n 5. Peculiar nature of the connotation of names which belong\n to a nomenclature 257\n\n 6. In what cases language may, and may not, be used\n mechanically 259\n\n\n CHAPTER VII. _Of Classification, as subsidiary to\n Induction._\n\n \u00a7 1. Classification as here treated of, wherein different from\n the classification implied in naming 266\n\n 2. Theory of natural groups 267\n\n 3. Are natural groups given by type, or by definition? 271\n\n 4. Kinds are natural groups 274\n\n 5. How the names of Kinds should be constructed 280\n\n\n CHAPTER VIII. _Of Classification by Series._\n\n \u00a7 1. Natural groups should be arranged in a natural series 284\n\n 2. The arrangement should follow the degrees of the main\n phenomenon 285\n\n 3. --which implies the assumption of a type-species 287\n\n 4. How the divisions of the series should be determined 288\n\n 5. Zoology affords the completest type of scientific\n classification 289\n\n\n BOOK V.\n\n ON FALLACIES.\n\n\n CHAPTER I. _Of Fallacies in General._\n\n \u00a7 1. Theory of fallacies a necessary part of logic 295\n\n 2. Casual mistakes are not fallacies 297\n\n 3. The moral sources of erroneous opinion, how related to\n the intellectual 297\n\n\n CHAPTER II. _Classification of Fallacies._\n\n \u00a7 1. On what criteria a classification of fallacies should be\n grounded 301\n\n 2. The five classes of fallacies 302\n\n 3. The reference of a fallacy to one or another class is\n sometimes arbitrary 305\n\n\n CHAPTER III. _Fallacies of Simple Inspection, or \u00e0 priori\n Fallacies._\n\n \u00a7 1. Character of this class of Fallacies 309\n\n 2. Natural prejudice of mistaking subjective laws for\n objective, exemplified in popular superstitions 310\n\n 3. Natural prejudices, that things which we think of together\n must exist together, and that what is inconceivable\n must be false 314\n\n 4. Natural prejudice, of ascribing objective existence to\n abstractions 321\n\n 5. Fallacy of the Sufficient Reason 322\n\n 6. Natural prejudice, that the differences in nature correspond\n to the distinctions in language 325\n\n 7. Prejudice, that a phenomenon cannot have more than one\n cause 329\n\n 8. Prejudice, that the conditions of a phenomenon must\n resemble the phenomenon 332\n\n\n CHAPTER IV. _Fallacies of Observation._\n\n \u00a7 1. Non-observation, and Mal-observation 341\n\n 2. Non-observation of instances, and non-observation of\n circumstances 341\n\n 3. Examples of the former 342\n\n 4. --and of the latter 347\n\n 5. Mal-observation characterized and exemplified 352\n\n\n CHAPTER V. _Fallacies of Generalization._\n\n \u00a7 1. Character of the class 356\n\n 2. Certain kinds of generalization must always be groundless 356\n\n 3. Attempts to resolve phenomena radically different into\n the same 357\n\n 4. Fallacy of mistaking empirical for causal laws 359\n\n 5. _Post hoc, ergo propter hoc_; and the deductive fallacy\n corresponding to it 364\n\n 6. Fallacy of False Analogies 366\n\n 7. Function of metaphors in reasoning 373\n\n 8. How fallacies of generalization grow out of bad\n classification 375\n\n\n CHAPTER VI. _Fallacies of Ratiocination._\n\n \u00a7 1. Introductory Remarks 377\n\n 2. Fallacies in the conversion and \u00e6quipollency of\n propositions 377\n\n 3. Fallacies in the syllogistic process 379\n\n 4. Fallacy of changing the premises 379\n\n\n CHAPTER VII. _Fallacies of Confusion._\n\n \u00a7 1. Fallacy of Ambiguous Terms 384\n\n 2. Fallacy of Petitio Principii 396\n\n 3. Fallacy of Ignoratio Elenchi 405\n\n\n BOOK VI.\n\n ON THE LOGIC OF THE MORAL SCIENCES.\n\n\n CHAPTER I. _Introductory Remarks._\n\n \u00a7 1. The backward state of the Moral Sciences can only be\n remedied by applying to them the methods of Physical\n Science, duly extended and generalized 413\n\n 2. How far this can be attempted in the present work 415\n\n\n CHAPTER II. _Of Liberty and Necessity._\n\n \u00a7 1. Are human actions subject to the law of causality? 417\n\n 2. The doctrine commonly called Philosophical Necessity, in\n what sense true 418\n\n 3. Inappropriateness and pernicious effect of the term\n Necessity 420\n\n 4. A motive not always the anticipation of a pleasure or a\n pain 424\n\n\n CHAPTER III. _That there is, or may be, a Science of\n Human Nature._\n\n \u00a7 1. There may be sciences which are not exact sciences 426\n\n 2. To what scientific type the Science of Human Nature\n corresponds 429\n\n\n CHAPTER IV. _Of the Laws of Mind._\n\n \u00a7 1. What is meant by Laws of Mind 432\n\n 2. Is there a science of Psychology? 433\n\n 3. The principal investigations of Psychology characterized 435\n\n 4. Relation of mental facts to physical conditions 440\n\n\n CHAPTER V. _Of Ethology, or the Science of the Formation of\n Character._\n\n \u00a7 1. The Empirical Laws of Human Nature 445\n\n 2. --are merely approximate generalizations. The universal\n laws are those of the formation of character 447\n\n 3. The laws of the formation of character cannot be ascertained\n by observation and experiment 449\n\n 4. --but must be studied deductively 454\n\n 5. The Principles of Ethology are the _axiomata media_ of\n mental science 455\n\n 6. Ethology characterized 459\n\n\n CHAPTER VI. _General Considerations on the Social Science._\n\n \u00a7 1. Are Social Phenomena a subject of Science? 461\n\n 2. Of what nature the Social Science must be 463\n\n\n CHAPTER VII. _Of the Chemical, or Experimental, Method in the\n Social Science._\n\n \u00a7 1. Characters of the mode of thinking which deduces political\n doctrines from specific experience 466\n\n 2. In the Social Science experiments are impossible 468\n\n 3. --the Method of Difference inapplicable 469\n\n 4. --and the Methods of Agreement, and of Concomitant\n Variations, inconclusive 471\n\n 5. The Method of Residues also inconclusive, and presupposes\n Deduction 472\n\n\n CHAPTER VIII. _Of the Geometrical, or Abstract Method._\n\n \u00a7 1. Characters of this mode of thinking 476\n\n 2. Examples of the Geometrical Method 478\n\n 3. The interest-philosophy of the Bentham school 479\n\n\n CHAPTER IX. _Of the Physical, or Concrete Deductive Method._\n\n \u00a7 1. The Direct and Inverse Deductive Methods 486\n\n 2. Difficulties of the Direct Deductive Method in the Social\n Science 489\n\n 3. To what extent the different branches of sociological\n speculation can be studied apart. Political Economy\n characterized 492\n\n 4. Political Ethology, or the science of national character 497\n\n 5. The Empirical Laws of the Social Science 500\n\n 6. The Verification of the Social Science 502\n\n\n CHAPTER X. _Of the Inverse Deductive, or Historical Method._\n\n \u00a7 1. Distinction between the general Science of Society, and\n special sociological inquiries 506\n\n 2. What is meant by a State of Society? 506\n\n 3. The Progressiveness of Man and Society 508\n\n 4. The laws of the succession of states of society can only\n be ascertained by the Inverse Deductive Method 511\n\n 5. Social Statics, or the science of the Coexistences of\n Social Phenomena 513\n\n 6. Social Dynamics, or the science of the Successions of Social\n Phenomena 521\n\n 7. Outlines of the Historical Method 522\n\n 8. Future prospects of Sociological Inquiry 525\n\n\n CHAPTER XI. _Additional Elucidations of the Science of History._\n\n \u00a7 1. The subjection of historical facts to uniform laws is\n verified by statistics 529\n\n 2. --does not imply the insignificance of moral causes 532\n\n 3. --nor the inefficacy of the characters of individuals and\n of the acts of governments 535\n\n 4. The historical importance of eminent men and of the\n policy of governments illustrated 540\n\n\n CHAPTER XII. _Of the Logic of Practice, or Art; including\n Morality and Policy._\n\n \u00a7 1. Morality not a science, but an Art 544\n\n 2. Relation between rules of art and the theorems of the\n corresponding science 544\n\n 3. What is the proper function of rules of art? 546\n\n 4. Art cannot be Deductive 548\n\n 5. Every Art consists of truths of Science, arranged in the\n order suitable for some practical use 549\n\n 6. Teleology, or the Doctrine of Ends 550\n\n 7. Necessity of an ultimate standard, or first principle of\n Teleology 552\n\n 8. Conclusion 554\n\n\n\n\nBOOK III.\n\n_CONTINUED._\n\nOF INDUCTION.\n\n\n\"In such cases the inductive and deductive methods of inquiry may be\nsaid to go hand in hand, the one verifying the conclusions deduced by\nthe other; and the combination of experiment and theory, which may thus\nbe brought to bear in such cases, forms an engine of discovery\ninfinitely more powerful than either taken separately. This state of any\ndepartment of science is perhaps of all others the most interesting, and\nthat which promises the most to research.\"--SIR J. HERSCHEL, _Discourse\non the Study of Natural Philosophy_.\n\n\n\n\nCHAPTER XIV.\n\nOF THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE; AND OF HYPOTHESES.\n\n\n\u00a7 1. The preceding considerations have led us to recognise a distinction\nbetween two kinds of laws, or observed uniformities in nature: ultimate\nlaws, and what may be termed derivative laws. Derivative laws are such\nas are deducible from, and may, in any of the modes which we have\npointed out, be resolved into, other and more general ones. Ultimate\nlaws are those which cannot. We are not sure that any of the\nuniformities with which we are yet acquainted are ultimate laws; but we\nknow that there must be ultimate laws; and that every resolution of a\nderivative law into more general laws, brings us nearer to them.\n\nSince we are continually discovering that uniformities, not previously\nknown to be other than ultimate, are derivative, and resolvable into\nmore general laws; since (in other words) we are continually discovering\nthe explanation of some sequence which was previously known only as a\nfact; it becomes an interesting question whether there are any necessary\nlimits to this philosophical operation, or whether it may proceed until\nall the uniform sequences in nature are resolved into some one universal\nlaw. For this seems, at first sight, to be the ultimatum towards which\nthe progress of induction, by the Deductive Method resting on a basis of\nobservation and experiment, is tending. Projects of this kind were\nuniversal in the infancy of philosophy; any speculations which held out\na less brilliant prospect, being in those early times deemed not worth\npursuing. And the idea receives so much apparent countenance from the\nnature of the most remarkable achievements of modern science, that\nspeculators are even now frequently appearing, who profess either to\nhave solved the problem, or to suggest modes in which it may one day be\nsolved. Even where pretensions of this magnitude are not made, the\ncharacter of the solutions which are given or sought of particular\nclasses of phenomena, often involves such conceptions of what\nconstitutes explanation, as would render the notion of explaining all\nphenomena whatever by means of some one cause or law, perfectly\nadmissible.\n\n\n\u00a7 2. It is therefore useful to remark, that the ultimate Laws of Nature\ncannot possibly be less numerous than the distinguishable sensations or\nother feelings of our nature;--those, I mean, which are distinguishable\nfrom one another in quality, and not merely in quantity or degree. For\nexample; since there is a phenomenon _sui generis_, called colour, which\nour consciousness testifies to be not a particular degree of some other\nphenomenon, as heat or odour or motion, but intrinsically unlike all\nothers, it follows that there are ultimate laws of colour; that though\nthe facts of colour may admit of explanation, they never can be\nexplained from laws of heat or odour alone, or of motion alone, but that\nhowever far the explanation may be carried, there will always remain in\nit a law of colour. I do not mean that it might not possibly be shown\nthat some other phenomenon, some chemical or mechanical action for\nexample, invariably precedes, and is the cause of, every phenomenon of\ncolour. But though this, if proved, would be an important extension of\nour knowledge of nature, it would not explain how or why a motion, or a\nchemical action, can produce a sensation of colour; and however diligent\nmight be our scrutiny of the phenomena, whatever number of hidden links\nwe might detect in the chain of causation terminating in the colour, the\nlast link would still be a law of colour, not a law of motion, nor of\nany other phenomenon whatever. Nor does this observation apply only to\ncolour, as compared with any other of the great classes of sensations;\nit applies to every particular colour, as compared with others. White\ncolour can in no manner be explained exclusively by the laws of the\nproduction of red colour. In any attempt to explain it, we cannot but\nintroduce, as one element of the explanation, the proposition that some\nantecedent or other produces the sensation of white.\n\nThe ideal limit, therefore, of the explanation of natural phenomena\n(towards which as towards other ideal limits we are constantly tending,\nwithout the prospect of ever completely attaining it) would be to show\nthat each distinguishable variety of our sensations, or other states of\nconsciousness, has only one sort of cause; that, for example, whenever\nwe perceive a white colour, there is some one condition or set of\nconditions which is always present, and the presence of which always\nproduces in us that sensation. As long as there are several known modes\nof production of a phenomenon, (several different substances, for\ninstance, which have the property of whiteness, and between which we\ncannot trace any other resemblance,) so long it is not impossible that\none of these modes of production may be resolved into another, or that\nall of them may be resolved into some more general mode of production\nnot hitherto recognised. But when the modes of production are reduced to\none, we cannot, in point of simplification, go any further. This one may\nnot, after all, be the ultimate mode; there may be other links to be\ndiscovered between the supposed cause and the effect; but we can only\nfurther resolve the known law, by introducing some other law hitherto\nunknown; which will not diminish the number of ultimate laws.\n\nIn what cases, accordingly, has science been most successful in\nexplaining phenomena, by resolving their complex laws into laws of\ngreater simplicity and generality? Hitherto chiefly in cases of the\npropagation of various phenomena through space: and, first and\nprincipally, the most extensive and important of all facts of that\ndescription, the fact of motion. Now this is exactly what might be\nexpected from the principles here laid down. Not only is motion one of\nthe most universal of all phenomena, it is also (as might be expected\nfrom that circumstance) one of those which, apparently at least, are\nproduced in the greatest number of ways; but the phenomenon itself is\nalways, to our sensations, the same in every respect but degree.\nDifferences of duration, or of velocity, are evidently differences in\ndegree only; and differences of direction in space, which alone has any\nsemblance of being a distinction in kind, entirely disappear (so far as\nour sensations are concerned) by a change in our own position; indeed\nthe very same motion appears to us, according to our position, to take\nplace in every variety of direction, and motions in every different\ndirection to take place in the same. And again, motion in a straight\nline and in a curve are no otherwise distinct than that the one is\nmotion continuing in the same direction, the other is motion which at\neach instant changes its direction. There is, therefore, according to\nthe principles I have stated, no absurdity in supposing that all motion\nmay be produced in one and the same way; by the same kind of cause.\nAccordingly, the greatest achievements in physical science have\nconsisted in resolving one observed law of the production of motion into\nthe laws of other known modes of production, or the laws of several such\nmodes into one more general mode; as when the fall of bodies to the\nearth, and the motions of the planets, were brought under the one law of\nthe mutual attraction of all particles of matter; when the motions said\nto be produced by magnetism were shown to be produced by electricity;\nwhen the motions of fluids in a lateral direction, or even contrary to\nthe direction of gravity, were shown to be produced by gravity; and the\nlike. There is an abundance of distinct causes of motion still\nunresolved into one another; gravitation, heat, electricity, chemical\naction, nervous action, and so forth; but whether the efforts of the\npresent generation of savans to resolve all these different modes of\nproduction into one, are ultimately successful or not, the attempt so to\nresolve them is perfectly legitimate. For though these various causes\nproduce, in other respects, sensations intrinsically different, and are\nnot, therefore, capable of being resolved into one another, yet in so\nfar as they all produce motion, it is quite possible that the immediate\nantecedent of the motion may in all these different cases be the same;\nnor is it impossible that these various agencies themselves may, as the\nnew doctrines assert, all of them have for their own immediate\nantecedent, modes of molecular motion.\n\nWe need not extend our illustration to other cases, as for instance to\nthe propagation of light, sound, heat, electricity, &c. through space,\nor any of the other phenomena which have been found susceptible of\nexplanation by the resolution of their observed laws into more general\nlaws. Enough has been said to display the difference between the kind of\nexplanation and resolution of laws which is chimerical, and that of\nwhich the accomplishment is the great aim of science; and to show into\nwhat sort of elements the resolution must be effected, if at all.\n\n\n\u00a7 3. As, however, there is scarcely any one of the principles of a true\nmethod of philosophizing which does not require to be guarded against\nerrors on both sides, I must enter a caveat against another\nmisapprehension, of a kind directly contrary to the preceding. M. Comte,\namong other occasions on which he has condemned, with some asperity, any\nattempt to explain phenomena which are \"evidently primordial,\" (meaning,\napparently, no more than that every peculiar phenomenon must have at\nleast one peculiar and therefore inexplicable law,) has spoken of the\nattempt to furnish any explanation of the colour belonging to each\nsubstance, \"la couleur \u00e9l\u00e9mentaire propre \u00e0 chaque substance,\" as\nessentially illusory. \"No one,\" says he, \"in our time attempts to\nexplain the particular specific gravity of each substance or of each\nstructure. Why should it be otherwise as to the specific colour, the\nnotion of which is undoubtedly no less primordial?\"[1]\n\nNow although, as he elsewhere observes, a colour must always remain a\ndifferent thing from a weight or a sound, varieties of colour might\nnevertheless follow, or correspond to, given varieties of weight, or\nsound, or some other phenomenon as different as these are from colour\nitself. It is one question what a thing is, and another what it depends\non; and though to ascertain the conditions of an elementary phenomenon\nis not to obtain any new insight into the nature of the phenomenon\nitself, that is no reason against attempting to discover the conditions.\nThe interdict against endeavouring to reduce distinctions of colour to\nany common principle, would have held equally good against a like\nattempt on the subject of distinctions of sound; which nevertheless have\nbeen found to be immediately preceded and caused by distinguishable\nvarieties in the vibrations of elastic bodies: though a sound, no doubt,\nis quite as different as a colour is from any motion of particles,\nvibratory or otherwise. We might add, that, in the case of colours,\nthere are strong positive indications that they are not ultimate\nproperties of the different kinds of substances, but depend on\nconditions capable of being superinduced upon all substances; since\nthere is no substance which cannot, according to the kind of light\nthrown upon it, be made to assume almost any colour; and since almost\nevery change in the mode of aggregation of the particles of the same\nsubstance, is attended with alterations in its colour, and in its\noptical properties generally.\n\nThe real defect in the attempts which have been made to account for\ncolours by the vibrations of a fluid, is not that the attempt itself is\nunphilosophical, but that the existence of the fluid, and the fact of\nits vibratory motion, are not proved; but are assumed, on no other\nground than the facility they are supposed to afford of explaining the\nphenomena. And this consideration leads to the important question of the\nproper use of scientific hypotheses; the connexion of which with the\nsubject of the explanation of the phenomena of nature, and of the\nnecessary limits to that explanation, needs not be pointed out.\n\n\n\u00a7 4. An hypothesis is any supposition which we make (either without\nactual evidence, or on evidence avowedly insufficient) in order to\nendeavour to deduce from it conclusions in accordance with facts which\nare known to be real; under the idea that if the conclusions to which\nthe hypothesis leads are known truths, the hypothesis itself either must\nbe, or at least is likely to be, true. If the hypothesis relates to the\ncause, or mode of production of a phenomenon, it will serve, if\nadmitted, to explain such facts as are found capable of being deduced\nfrom it. And this explanation is the purpose of many, if not most,\nhypotheses. Since explaining, in the scientific sense, means resolving\nan uniformity which is not a law of causation, into the laws of\ncausation from which it results, or a complex law of causation into\nsimpler and more general ones from which it is capable of being\ndeductively inferred; if there do not exist any known laws which fulfil\nthis requirement, we may feign or imagine some which would fulfil it;\nand this is making an hypothesis.\n\nAn hypothesis being a mere supposition, there are no other limits to\nhypotheses than those of the human imagination; we may, if we please,\nimagine, by way of accounting for an effect, some cause of a kind\nutterly unknown, and acting according to a law altogether fictitious.\nBut as hypotheses of this sort would not have any of the plausibility\nbelonging to those which ally themselves by analogy with known laws of\nnature, and besides would not supply the want which arbitrary hypotheses\nare generally invented to satisfy, by enabling the imagination to\nrepresent to itself an obscure phenomenon in a familiar light; there is\nprobably no hypothesis in the history of science in which both the agent\nitself and the law of its operation were fictitious. Either the\nphenomenon assigned as the cause is real, but the law according to which\nit acts, merely supposed; or the cause is fictitious, but is supposed to\nproduce its effects according to laws similar to those of some known\nclass of phenomena. An instance of the first kind is afforded by the\ndifferent suppositions made respecting the law of the planetary central\nforce, anterior to the discovery of the true law, that the force varies\nas the inverse square of the distance; which also suggested itself to\nNewton, in the first instance, as an hypothesis, and was verified by\nproving that it led deductively to Kepler's laws. Hypotheses of the\nsecond kind are such as the vortices of Descartes, which were\nfictitious, but were supposed to obey the known laws of rotatory motion;\nor the two rival hypotheses respecting the nature of light, the one\nascribing the phenomena to a fluid emitted from all luminous bodies, the\nother (now generally received) attributing them to vibratory motions\namong the particles of an ether pervading all space. Of the existence of\neither fluid there is no evidence, save the explanation they are\ncalculated to afford of some of the phenomena; but they are supposed to\nproduce their effects according to known laws; the ordinary laws of\ncontinued locomotion in the one case, and in the other, those of the\npropagation of undulatory movements among the particles of an elastic\nfluid.\n\nAccording to the foregoing remarks, hypotheses are invented to enable\nthe Deductive Method to be earlier applied to phenomena. But[2] in order\nto discover the cause of any phenomenon by the Deductive Method, the\nprocess must consist of three parts; induction, ratiocination, and\nverification. Induction, (the place of which, however, may be supplied\nby a prior deduction,) to ascertain the laws of the causes;\nratiocination, to compute from those laws, how the causes will operate\nin the particular combination known to exist in the case in hand;\nverification, by comparing this calculated effect with the actual\nphenomenon. No one of these three parts of the process can be dispensed\nwith. In the deduction which proves the identity of gravity with the\ncentral force of the solar system, all the three are found. First, it is\nproved from the moon's motions, that the earth attracts her with a force\nvarying as the inverse square of the distance. This (though partly\ndependent on prior deductions) corresponds to the first, or purely\ninductive, step, the ascertainment of the law of the cause. Secondly,\nfrom this law, and from the knowledge previously obtained of the moon's\nmean distance from the earth, and of the actual amount of her deflexion\nfrom the tangent, it is ascertained with what rapidity the earth's\nattraction would cause the moon to fall, if she were no further off, and\nno more acted upon by extraneous forces, than terrestrial bodies are:\nthat is the second step, the ratiocination. Finally, this calculated\nvelocity being compared with the observed velocity with which all heavy\nbodies fall, by mere gravity, towards the surface of the earth, (sixteen\nfeet in the first second, forty-eight in the second, and so forth, in\nthe ratio of the odd numbers, 1, 3, 5, &c.,) the two quantities are\nfound to agree. The order in which the steps are here presented, was not\nthat of their discovery; but it is their correct logical order, as\nportions of the proof that the same attraction of the earth which causes\nthe moon's motion, causes also the fall of heavy bodies to the earth: a\nproof which is thus complete in all its parts.\n\nNow, the Hypothetical Method suppresses the first of the three steps,\nthe induction to ascertain the law; and contents itself with the other\ntwo operations, ratiocination and verification; the law which is\nreasoned from, being assumed, instead of proved.\n\nThis process may evidently be legitimate on one supposition, namely, if\nthe nature of the case be such that the final step, the verification,\nshall amount to, and fulfil the conditions of, a complete induction. We\nwant to be assured that the law we have hypothetically assumed is a true\none; and its leading deductively to true results will afford this\nassurance, provided the case be such that a false law cannot lead to a\ntrue result; provided no law, except the very one which we have assumed,\ncan lead deductively to the same conclusions which that leads to. And\nthis proviso is often realized. For example, in the very complete\nspecimen of deduction which we just cited, the original major premise of\nthe ratiocination, the law of the attractive force, was ascertained in\nthis mode; by this legitimate employment of the Hypothetical Method.\nNewton began by an assumption, that the force which at each instant\ndeflects a planet from its rectilineal course, and makes it describe a\ncurve round the sun, is a force tending directly towards the sun. He\nthen proved that if this be so, the planet will describe, as we know by\nKepler's first law that it does describe, equal areas in equal times;\nand, lastly, he proved that if the force acted in any other direction\nwhatever, the planet would not describe equal areas in equal times. It\nbeing thus shown that no other hypothesis would accord with the facts,\nthe assumption was proved; the hypothesis became an inductive truth. Not\nonly did Newton ascertain by this hypothetical process the direction of\nthe deflecting force; he proceeded in exactly the same manner to\nascertain the law of variation of the quantity of that force. He assumed\nthat the force varied inversely as the square of the distance; showed\nthat from this assumption the remaining two of Kepler's laws might be\ndeduced; and finally, that any other law of variation would give results\ninconsistent with those laws, and inconsistent, therefore, with the real\nmotions of the planets, of which Kepler's laws were known to be a\ncorrect expression.\n\nI have said that in this case the verification fulfils the conditions of\nan induction: but an induction of what sort? On examination we find that\nit conforms to the canon of the Method of Difference. It affords the two\ninstances, A B C, _a b c_, and B C, _b c_. A represents central force; A\nB C, the planets _plus_ a central force; B C, the planets apart from a\ncentral force. The planets with a central force give _a_, areas\nproportional to the times; the planets without a central force give _b\nc_ (a set of motions) without _a_, or with something else instead of\n_a_. This is the Method of Difference in all its strictness. It is true,\nthe two instances which the method requires are obtained in this case,\nnot by experiment, but by a prior deduction. But that is of no\nconsequence. It is immaterial what is the nature of the evidence from\nwhich we derive the assurance that A B C will produce _a b c_, and B C\nonly _b c_; it is enough that we have that assurance. In the present\ncase, a process of reasoning furnished Newton with the very instances,\nwhich, if the nature of the case had admitted of it, he would have\nsought by experiment.\n\nIt is thus perfectly possible, and indeed is a very common occurrence,\nthat what was an hypothesis at the beginning of the inquiry, becomes a\nproved law of nature before its close. But in order that this should\nhappen, we must be able, either by deduction or experiment, to obtain\n_both_ the instances which the Method of Difference requires. That we\nare able from the hypothesis to deduce the known facts, gives only the\naffirmative instance, A B C, _a b c_. It is equally necessary that we\nshould be able to obtain, as Newton did, the negative instance B C, _b\nc_; by showing that no antecedent, except the one assumed in the\nhypothesis, would in conjunction with B C produce _a_.\n\nNow it appears to me that this assurance cannot be obtained, when the\ncause assumed in the hypothesis is an unknown cause, imagined solely to\naccount for _a_. When we are only seeking to determine the precise law\nof a cause already ascertained, or to distinguish the particular agent\nwhich is in fact the cause, among several agents of the same kind, one\nor other of which it is already known to be, we may then obtain the\nnegative instance. An inquiry, which of the bodies of the solar system\ncauses by its attraction some particular irregularity in the orbit or\nperiodic time of some satellite or comet, would be a case of the second\ndescription. Newton's was a case of the first. If it had not been\npreviously known that the planets were hindered from moving in straight\nlines by some force tending towards the interior of their orbit, though\nthe exact direction was doubtful; or if it had not been known that the\nforce increased in some proportion or other as the distance diminished,\nand diminished as it increased; Newton's argument would not have proved\nhis conclusion. These facts, however, being already certain, the range\nof admissible suppositions was limited to the various possible\ndirections of a line, and the various possible numerical relations\nbetween the variations of the distance, and the variations of the\nattractive force: now among these it was easily shown that different\nsuppositions could not lead to identical consequences.\n\nAccordingly, Newton could not have performed his second great scientific\noperation, that of identifying terrestrial gravity with the central\nforce of the solar system, by the same hypothetical method. When the law\nof the moon's attraction had been proved from the data of the moon\nitself, then on finding the same law to accord with the phenomena of\nterrestrial gravity, he was warranted in adopting it as the law of those\nphenomena likewise; but it would not have been allowable for him,\nwithout any lunar data, to assume that the moon was attracted towards\nthe earth with a force as the inverse square of the distance, merely\nbecause that ratio would enable him to account for terrestrial gravity:\nfor it would have been impossible for him to prove that the observed law\nof the fall of heavy bodies to the earth could not result from any\nforce, save one extending to the moon, and proportional to the inverse\nsquare.\n\nIt appears, then, to be a condition of a genuinely scientific\nhypothesis, that it be not destined always to remain an hypothesis, but\nbe of such a nature as to be either proved or disproved by comparison\nwith observed facts. This condition is fulfilled when the effect is\nalready known to depend on the very cause supposed, and the hypothesis\nrelates only to the precise mode of dependence; the law of the variation\nof the effect according to the variations in the quantity or in the\nrelations of the cause. With these may be classed the hypotheses which\ndo not make any supposition with regard to causation, but only with\nregard to the law of correspondence between facts which accompany each\nother in their variations, though there may be no relation of cause and\neffect between them. Such were the different false hypotheses which\nKepler made respecting the law of the refraction of light. It was known\nthat the direction of the line of refraction varied with every variation\nin the direction of the line of incidence, but it was not known how;\nthat is, what changes of the one corresponded to the different changes\nof the other. In this case any law, different from the true one, must\nhave led to false results. And, lastly, we must add to these, all\nhypothetical modes of merely representing, or _describing_, phenomena;\nsuch as the hypothesis of the ancient astronomers that the heavenly\nbodies moved in circles; the various hypotheses of excentrics,\ndeferents, and epicycles, which were added to that original hypothesis;\nthe nineteen false hypotheses which Kepler made and abandoned respecting\nthe form of the planetary orbits; and even the doctrine in which he\nfinally rested, that those orbits are ellipses, which was but an\nhypothesis like the rest until verified by facts.\n\nIn all these cases, verification is proof; if the supposition accords\nwith the phenomena there needs no other evidence of it. But in order\nthat this may be the case, I conceive it to be necessary, when the\nhypothesis relates to causation, that the supposed cause should not only\nbe a real phenomenon, something actually existing in nature, but should\nbe already known to exercise, or at least to be capable of exercising,\nan influence of some sort over the effect. In any other case, it is no\nevidence of the truth of the hypothesis that we are able to deduce the\nreal phenomena from it.\n\nIs it, then, never allowable, in a scientific hypothesis, to assume a\ncause; but only to ascribe an assumed law to a known cause? I do not\nassert this. I only say, that in the latter case alone can the\nhypothesis be received as true merely because it explains the phenomena:\nin the former case it is only useful by suggesting a line of\ninvestigation which may possibly terminate in obtaining real proof. For\nthis purpose, as is justly remarked by M. Comte, it is indispensable\nthat the cause suggested by the hypothesis should be in its own nature\nsusceptible of being proved by other evidence. This seems to be the\nphilosophical import of Newton's maxim, (so often cited with approbation\nby subsequent writers,) that the cause assigned for any phenomenon must\nnot only be such as if admitted would explain the phenomenon, but must\nalso be a _vera causa_. What he meant by a _vera causa_ Newton did not\nindeed very explicitly define; and Dr. Whewell, who dissents from the\npropriety of any such restriction upon the latitude of framing\nhypotheses, has had little difficulty in showing[3] that his conception\nof it was neither precise nor consistent with itself: accordingly his\noptical theory was a signal instance of the violation of his own rule.\nIt is certainly not necessary that the cause assigned should be a cause\nalready known; else how could we ever become acquainted with any new\ncause? But what is true in the maxim is, that the cause, though not\nknown previously, should be capable of being known thereafter; that its\nexistence should be capable of being detected, and its connexion with\nthe effect ascribed to it should be susceptible of being proved, by\nindependent evidence. The hypothesis, by suggesting observations and\nexperiments, puts us on the road to that independent evidence if it be\nreally attainable; and till it be attained, the hypothesis ought not to\ncount for more than a conjecture.\n\n\n\u00a7 5. This function, however, of hypotheses, is one which must be\nreckoned absolutely indispensable in science. When Newton said,\n\"Hypotheses non fingo,\" he did not mean that he deprived himself of the\nfacilities of investigation afforded by assuming in the first instance\nwhat he hoped ultimately to be able to prove. Without such assumptions,\nscience could never have attained its present state: they are necessary\nsteps in the progress to something more certain; and nearly everything\nwhich is now theory was once hypothesis. Even in purely experimental\nscience, some inducement is necessary for trying one experiment rather\nthan another; and though it is abstractedly possible that all the\nexperiments which have been tried, might have been produced by the mere\ndesire to ascertain what would happen in certain circumstances, without\nany previous conjecture as to the result; yet, in point of fact, those\nunobvious, delicate, and often cumbrous and tedious processes of\nexperiment, which have thrown most light upon the general constitution\nof nature, would hardly ever have been undertaken by the persons or at\nthe time they were, unless it had seemed to depend on them whether some\ngeneral doctrine or theory which had been suggested, but not yet proved,\nshould be admitted or not. If this be true even of merely experimental\ninquiry, the conversion of experimental into deductive truths could\nstill less have been effected without large temporary assistance from\nhypotheses. The process of tracing regularity in any complicated, and at\nfirst sight confused set of appearances, is necessarily tentative: we\nbegin by making any supposition, even a false one, to see what\nconsequences will follow from it; and by observing how these differ from\nthe real phenomena, we learn what corrections to make in our assumption.\nThe simplest supposition which accords with the more obvious facts, is\nthe best to begin with; because its consequences are the most easily\ntraced. This rude hypothesis is then rudely corrected, and the operation\nrepeated; and the comparison of the consequences deducible from the\ncorrected hypothesis, with the observed facts, suggests still further\ncorrection, until the deductive results are at last made to tally with\nthe phenomena. \"Some fact is as yet little understood, or some law is\nunknown: we frame on the subject an hypothesis as accordant as possible\nwith the whole of the data already possessed; and the science, being\nthus enabled to move forward freely, always ends by leading to new\nconsequences capable of observation, which either confirm or refute,\nunequivocally, the first supposition.\" Neither induction nor deduction\nwould enable us to understand even the simplest phenomena, \"if we did\nnot often commence by anticipating on the results; by making a\nprovisional supposition, at first essentially conjectural, as to some of\nthe very notions which constitute the final object of the inquiry.\"[4]\nLet any one watch the manner in which he himself unravels a complicated\nmass of evidence; let him observe how, for instance, he elicits the true\nhistory of any occurrence from the involved statements of one or of many\nwitnesses: he will find that he does not take all the items of evidence\ninto his mind at once, and attempt to weave them together: he\nextemporises, from a few of the particulars, a first rude theory of the\nmode in which the facts took place, and then looks at the other\nstatements one by one, to try whether they can be reconciled with that\nprovisional theory, or what alterations or additions it requires to make\nit square with them. In this way, which has been justly compared to the\nMethods of Approximation of mathematicians, we arrive, by means of\nhypotheses, at conclusions not hypothetical.[5]\n\n\n\u00a7 6. It is perfectly consistent with the spirit of the method, to\nassume in this provisional manner not only an hypothesis respecting the\nlaw of what we already know to be the cause, but an hypothesis\nrespecting the cause itself. It is allowable, useful, and often even\nnecessary, to begin by asking ourselves what cause _may_ have produced\nthe effect, in order that we may know in what direction to look out for\nevidence to determine whether it actually _did_. The vortices of\nDescartes would have been a perfectly legitimate hypothesis, if it had\nbeen possible, by any mode of exploration which we could entertain the\nhope of ever possessing, to bring the reality of the vortices, as a fact\nin nature, conclusively to the test of observation. The hypothesis was\nvicious, simply because it could not lead to any course of investigation\ncapable of converting it from an hypothesis into a proved fact. It might\nchance to be _dis_proved, either by some want of correspondence with the\nphenomena it purported to explain, or (as actually happened) by some\nextraneous fact. \"The free passage of comets through the spaces in which\nthese vortices should have been, convinced men that these vortices did\nnot exist.\"[6] But the hypothesis would have been false, though no such\ndirect evidence of its falsity had been procurable. Direct evidence of\nits truth there could not be.\n\nThe prevailing hypothesis of a luminiferous ether, in other respects not\nwithout analogy to that of Descartes, is not in its own nature entirely\ncut off from the possibility of direct evidence in its favour. It is\nwell known that the difference between the calculated and the observed\ntimes of the periodical return of Encke's comet, has led to a conjecture\nthat a medium capable of opposing resistance to motion is diffused\nthrough space. If this surmise should be confirmed, in the course of\nages, by the gradual accumulation of a similar variance in the case of\nthe other bodies of the solar system, the luminiferous ether would have\nmade a considerable advance towards the character of a _vera causa_,\nsince the existence would have been ascertained of a great cosmical\nagent, possessing some of the attributes which the hypothesis assumes;\nthough there would still remain many difficulties, and the\nidentification of the ether with the resisting medium would even, I\nimagine, give rise to new ones. At present, however, this supposition\ncannot be looked upon as more than a conjecture; the existence of the\nether still rests on the possibility of deducing from its assumed laws a\nconsiderable number of the phenomena of light; and this evidence I\ncannot regard as conclusive, because we cannot have, in the case of such\nan hypothesis, the assurance that if the hypothesis be false it must\nlead to results at variance with the true facts.\n\nAccordingly, most thinkers of any degree of sobriety allow, that an\nhypothesis of this kind is not to be received as probably true because\nit accounts for all the known phenomena; since this is a condition\nsometimes fulfilled tolerably well by two conflicting hypotheses; while\nthere are probably a thousand more which are equally possible, but\nwhich, for want of anything analogous in our experience, our minds are\nunfitted to conceive. But it seems to be thought that an hypothesis of\nthe sort in question is entitled to a more favourable reception, if,\nbesides accounting for all the facts previously known, it has led to the\nanticipation and prediction of others which experience afterwards\nverified; as the undulatory theory of light led to the prediction,\nsubsequently realized by experiment, that two luminous rays might meet\neach other in such a manner as to produce darkness. Such predictions and\ntheir fulfilment are, indeed, well calculated to impress the uninformed,\nwhose faith in science rests solely on similar coincidences between its\nprophecies and what comes to pass. But it is strange that any\nconsiderable stress should be laid upon such a coincidence by persons of\nscientific attainments. If the laws of the propagation of light accord\nwith those of the vibrations of an elastic fluid in as many respects as\nis necessary to make the hypothesis afford a correct expression of all\nor most of the phenomena known at the time, it is nothing strange that\nthey should accord with each other in one respect more. Though twenty\nsuch coincidences should occur, they would not prove the reality of the\nundulatory ether; it would not follow that the phenomena of light were\nresults of the laws of elastic fluids, but at most that they are\ngoverned by laws partially identical with these; which, we may observe,\nis already certain, from the fact that the hypothesis in question could\nbe for a moment tenable.[7] Cases may be cited, even in our imperfect\nacquaintance with nature, where agencies that we have good reason to\nconsider as radically distinct, produce their effects, or some of their\neffects, according to laws which are identical. The law, for example, of\nthe inverse square of the distance, is the measure of the intensity not\nonly of gravitation, but (it is believed) of illumination, and of heat\ndiffused from a centre. Yet no one looks upon this identity as proving\nsimilarity in the mechanism by which the three kinds of phenomena are\nproduced.\n\nAccording to Dr. Whewell, the coincidence of results predicted from an\nhypothesis, with facts afterwards observed, amounts to a conclusive\nproof of the truth of the theory. \"If I copy a long series of letters,\nof which the last half dozen are concealed, and if I guess these aright,\nas is found to be the case when they are afterwards uncovered, this must\nbe because I have made out the import of the inscription. To say, that\nbecause I have copied all that I could see, it is nothing strange that I\nshould guess those which I cannot see, would be absurd, without\nsupposing such a ground for guessing.\"[8] If any one, from examining the\ngreater part of a long inscription, can interpret the characters so that\nthe inscription gives a rational meaning in a known language, there is a\nstrong presumption that his interpretation is correct; but I do not\nthink the presumption much increased by his being able to guess the few\nremaining letters without seeing them: for we should naturally expect\n(when the nature of the case excludes chance) that even an erroneous\ninterpretation which accorded with all the visible parts of the\ninscription would accord also with the small remainder; as would be the\ncase, for example, if the inscription had been designedly so contrived\nas to admit of a double sense. I assume that the uncovered characters\nafford an amount of coincidence too great to be merely casual: otherwise\nthe illustration is not a fair one. No one supposes the agreement with\nthe phenomena of light with the theory of undulations to be merely\nfortuitous. It must arise from the actual identity of some of the laws\nof undulations with some of those of light: and if there be that\nidentity, it is reasonable to suppose that its consequences would not\nend with the phenomena which first suggested the identification, nor be\neven confined to such phenomena as were known at the time. But it does\nnot follow, because some of the laws agree with those of undulations,\nthat there are any actual undulations; no more than it followed because\nsome (though not so many) of the same laws agreed with those of the\nprojection of particles, that there was actual emission of particles.\nEven the undulatory hypothesis does not account for all the phenomena of\nlight. The natural colours of objects, the compound nature of the solar\nray, the absorption of light, and its chemical and vital action, the\nhypothesis leaves as mysterious as it found them; and some of these\nfacts are, at least apparently, more reconcileable with the emission\ntheory than with that of Young and Fresnel. Who knows but that some\nthird hypothesis, including all these phenomena, may in time leave the\nundulatory theory as far behind as that has left the theory of Newton\nand his successors?\n\nTo the statement, that the condition of accounting for all the known\nphenomena is often fulfilled equally well by two conflicting hypotheses,\nDr. Whewell makes answer that he knows \"of no such case in the history\nof science, where the phenomena are at all numerous and complicated.\"[9]\nSuch an affirmation, by a writer of Dr. Whewell's minute acquaintance\nwith the history of science, would carry great authority, if he had\nnot, a few pages before, taken pains to refute it,[10] by maintaining\nthat even the exploded scientific hypotheses might always, or almost\nalways, have been so modified as to make them correct representations of\nthe phenomena. The hypothesis of vortices, he tells us, was, by\nsuccessive modifications, brought to coincide in its results with the\nNewtonian theory and with the facts. The vortices did not indeed explain\nall the phenomena which the Newtonian theory was ultimately found to\naccount for, such as the precession of the equinoxes; but this\nphenomenon was not, at the time, in the contemplation of either party,\nas one of the facts to be accounted for. All the facts which they did\ncontemplate, we may believe on Dr. Whewell's authority to have accorded\nas accurately with the Cartesian hypothesis, in its finally improved\nstate, as with Newton's.\n\nBut it is not, I conceive, a valid reason for accepting any given\nhypothesis, that we are unable to imagine any other which will account\nfor the facts. There is no necessity for supposing that the true\nexplanation must be one which, with only our present experience, we\ncould imagine. Among the natural agents with which we are acquainted,\nthe vibrations of an elastic fluid may be the only one whose laws bear a\nclose resemblance to those of light; but we cannot tell that there does\nnot exist an unknown cause, other than an elastic ether diffused through\nspace, yet producing effects identical in some respects with those which\nwould result from the undulations of such an ether. To assume that no\nsuch cause can exist, appears to me an extreme case of assumption\nwithout evidence.\n\nI do not mean to condemn those who employ themselves in working out into\ndetail this sort of hypotheses; it is useful to ascertain what are the\nknown phenomena, to the laws of which those of the subject of inquiry\nbear the greatest, or even a great analogy, since this may suggest (as\nin the case of the luminiferous ether it actually did) experiments to\ndetermine whether the analogy which goes so far does not extend still\nfurther. But that, in doing this, we should imagine ourselves to be\nseriously inquiring whether the hypothesis of an ether, an electric\nfluid, or the like, is true; that we should fancy it possible to obtain\nthe assurance that the phenomena are produced in that way and no other;\nseems to me, I confess, unworthy of the present improved conceptions of\nthe methods of physical science. And at the risk of being charged with\nwant of modesty, I cannot help expressing astonishment that a\nphilosopher of Dr. Whewell's abilities and attainments should have\nwritten an elaborate treatise on the philosophy of induction, in which\nhe recognises absolutely no mode of induction except that of trying\nhypothesis after hypothesis until one is found which fits the phenomena;\nwhich one, when found, is to be assumed as true, with no other\nreservation than that if on re-examination it should appear to assume\nmore than is needful for explaining the phenomena, the superfluous part\nof the assumption should be cut off. And this without the slightest\ndistinction between the cases in which it may be known beforehand that\ntwo different hypotheses cannot lead to the same result, and those in\nwhich, for aught we can ever know, the range of suppositions, all\nequally consistent with the phenomena, may be infinite.[11]\n\n\n\u00a7 7. It is necessary, before quitting the subject of hypotheses, to\nguard against the appearance of reflecting upon the scientific value of\nseveral branches of physical inquiry, which, though only in their\ninfancy, I hold to be strictly inductive. There is a great difference\nbetween inventing agencies to account for classes of phenomena, and\nendeavouring, in conformity with known laws, to conjecture what former\ncollocations of known agents may have given birth to individual facts\nstill in existence. The latter is the legitimate operation of inferring\nfrom an observed effect, the existence, in time past, of a cause similar\nto that by which we know it to be produced in all cases in which we have\nactual experience of its origin. This, for example, is the scope of the\ninquiries of geology; and they are no more illogical or visionary than\njudicial inquiries, which also aim at discovering a past event by\ninference from those of its effects which still subsist. As we can\nascertain whether a man was murdered or died a natural death, from the\nindications exhibited by the corpse, the presence or absence of signs of\nstruggling on the ground or on the adjacent objects, the marks of\nblood, the footsteps of the supposed murderers, and so on, proceeding\nthroughout on uniformities ascertained by a perfect induction without\nany mixture of hypothesis; so if we find, on and beneath the surface of\nour planet, masses exactly similar to deposits from water, or to results\nof the cooling of matter melted by fire, we may justly conclude that\nsuch has been their origin; and if the effects, though similar in kind,\nare on a far larger scale than any which are now produced, we may\nrationally, and without hypothesis, conclude either that the causes\nexisted formerly with greater intensity, or that they have operated\nduring an enormous length of time. Further than this no geologist of\nauthority has, since the rise of the present enlightened school of\ngeological speculation, attempted to go.\n\nIn many geological inquiries it doubtless happens that though the laws\nto which the phenomena are ascribed are known laws, and the agents known\nagents, those agents are not known to have been present in the\nparticular case. In the speculation respecting the igneous origin of\ntrap or granite, the fact does not admit of direct proof, that those\nsubstances have been actually subjected to intense heat. But the same\nthing might be said of all judicial inquiries which proceed on\ncircumstantial evidence. We can conclude that a man was murdered, though\nit is not proved by the testimony of eye-witnesses that some person who\nhad the intention of murdering him was present on the spot. It is\nenough, for most purposes, if no other known cause could have generated\nthe effects shown to have been produced.\n\nThe celebrated speculation of Laplace concerning the origin of the earth\nand planets, participates essentially in the inductive character of\nmodern geological theory. The speculation is, that the atmosphere of the\nsun originally extended to the present limits of the solar system; from\nwhich, by the process of cooling, it has contracted to its present\ndimensions; and since, by the general principles of mechanics, the\nrotation of the sun and of its accompanying atmosphere must increase in\nrapidity as its volume diminishes, the increased centrifugal force\ngenerated by the more rapid rotation, overbalancing the action of\ngravitation, has caused the sun to abandon successive rings of vaporous\nmatter, which are supposed to have condensed by cooling, and to have\nbecome the planets. There is in this theory no unknown substance\nintroduced on supposition, nor any unknown property or law ascribed to a\nknown substance. The known laws of matter authorize us to suppose that a\nbody which is constantly giving out so large an amount of heat as the\nsun is, must be progressively cooling, and that, by the process of\ncooling, it must contract; if, therefore, we endeavour, from the present\nstate of that luminary, to infer its state in a time long past, we must\nnecessarily suppose that its atmosphere extended much farther than at\npresent, and we are entitled to suppose that it extended as far as we\ncan trace effects such as it might naturally leave behind it on\nretiring; and such the planets are. These suppositions being made, it\nfollows from known laws that successive zones of the solar atmosphere\nmight be abandoned; that these would continue to revolve round the sun\nwith the same velocity as when they formed part of its substance; and\nthat they would cool down, long before the sun itself, to any given\ntemperature, and consequently to that at which the greater part of the\nvaporous matter of which they consisted would become liquid or solid.\nThe known law of gravitation would then cause them to agglomerate in\nmasses, which would assume the shape our planets actually exhibit; would\nacquire, each about its own axis, a rotatory movement; and would in that\nstate revolve, as the planets actually do, about the sun, in the same\ndirection with the sun's rotation, but with less velocity, because in\nthe same periodic time which the sun's rotation occupied when his\natmosphere extended to that point. There is thus, in Laplace's theory,\nnothing, strictly speaking, hypothetical: it is an example of legitimate\nreasoning from a present effect to a possible past cause, according to\nthe known laws of that cause. The theory therefore is, as I have said,\nof a similar character to the theories of geologists; but considerably\ninferior to them in point of evidence. Even if it were proved (which it\nis not) that the conditions necessary for determining the breaking off\nof successive rings would certainly occur; there would still be a much\ngreater chance of error in assuming that the existing laws of nature are\nthe same which existed at the origin of the solar system, than in merely\npresuming (with geologists) that those laws have lasted through a few\nrevolutions and transformations of a single one among the bodies of\nwhich that system is composed.\n\n\n\n\nCHAPTER XV.\n\nOF PROGRESSIVE EFFECTS; AND OF THE CONTINUED ACTION OF CAUSES.\n\n\n\u00a7 1. In the last four chapters we have traced the general outlines of\nthe theory of the generation of derivative laws from ultimate ones. In\nthe present chapter our attention will be directed to a particular case\nof the derivation of laws from other laws, but a case so general, and so\nimportant, as not only to repay, but to require, a separate examination.\nThis is, the case of a complex phenomenon resulting from one simple law,\nby the continual addition of an effect to itself.\n\nThere are some phenomena, some bodily sensations for example, which are\nessentially instantaneous, and whose existence can only be prolonged by\nthe prolongation of the existence of the cause by which they are\nproduced. But most phenomena are in their own nature permanent; having\nbegun to exist, they would exist for ever unless some cause intervened\nhaving a tendency to alter or destroy them. Such, for example, are all\nthe facts or phenomena which we call bodies. Water, once produced, will\nnot of itself relapse into a state of hydrogen and oxygen; such a change\nrequires some agent having the power of decomposing the compound. Such,\nagain, are the positions in space, and the movements, of bodies. No\nobject at rest alters its position without the intervention of some\nconditions extraneous to itself; and when once in motion, no object\nreturns to a state of rest, or alters either its direction or its\nvelocity, unless some new external conditions are superinduced. It,\ntherefore, perpetually happens that a temporary cause gives rise to a\npermanent effect. The contact of iron with moist air for a few hours,\nproduces a rust which may endure for centuries; or a projectile force\nwhich launches a cannon ball into space, produces a motion which would\ncontinue for ever unless some other force counteracted it.\n\nBetween the two examples which we have here given, there is a difference\nworth pointing out. In the former (in which the phenomenon produced is a\nsubstance, and not a motion of a substance), since the rust remains for\never and unaltered unless some new cause supervenes, we may speak of the\ncontact of air a hundred years ago as even the proximate cause of the\nrust which has existed from that time until now. But when the effect is\nmotion, which is itself a change, we must use a different language. The\npermanency of the effect is now only the permanency of a series of\nchanges. The second foot, or inch, or mile of motion, is not the mere\nprolonged duration of the first foot, or inch, or mile, but another fact\nwhich succeeds, and which may in some respects be very unlike the\nformer, since it carries the body through a different region of space.\nNow, the original projectile force which set the body moving is the\nremote cause of all its motion, however long continued, but the\nproximate cause of no motion except that which took place at the first\ninstant. The motion at any subsequent instant is proximately caused by\nthe motion which took place at the instant preceding. It is on that, and\nnot on the original moving cause, that the motion at any given moment\ndepends. For, suppose that the body passes through some resisting\nmedium, which partially counteracts the effect of the original impulse,\nand retards the motion: this counteraction (it needs scarcely here be\nrepeated) is as strict an example of obedience to the law of the\nimpulse, as if the body had gone on moving with its original velocity;\nbut the motion which results is different, being now a compound of the\neffects of two causes acting in contrary directions, instead of the\nsingle effect of one cause. Now, what cause does the body obey in its\nsubsequent motion? The original cause of motion, or the actual motion at\nthe preceding instant? The latter: for when the object issues from the\nresisting medium, it continues moving, not with its original, but with\nits retarded velocity. The motion having once been diminished, all that\nwhich follows is diminished. The effect changes, because the cause which\nit really obeys, the proximate cause, the real cause in fact, has\nchanged. This principle is recognised by mathematicians when they\nenumerate among the causes by which the motion of a body is at any\ninstant determined, the _force generated_ by the previous motion; an\nexpression which would be absurd if taken to imply that this \"force\" was\nan intermediate link between the cause and the effect, but which really\nmeans only the previous motion itself, considered as a cause of further\nmotion. We must, therefore, if we would speak with perfect precision,\nconsider each link in the succession of motions as the effect of the\nlink preceding it. But if, for the convenience of discourse, we speak of\nthe whole series as one effect, it must be as an effect produced by the\noriginal impelling force; a permanent effect produced by an\ninstantaneous cause, and possessing the property of self-perpetuation.\n\nLet us now suppose that the original agent or cause, instead of being\ninstantaneous, is permanent. Whatever effect has been produced up to a\ngiven time, would (unless prevented by the intervention of some new\ncause) subsist permanently, even if the cause were to perish. Since,\nhowever, the cause does not perish, but continues to exist and to\noperate, it must go on producing more and more of the effect; and\ninstead of an uniform effect, we have a progressive series of effects,\narising from the accumulated influence of a permanent cause. Thus, the\ncontact of iron with the atmosphere causes a portion of it to rust; and\nif the cause ceased, the effect already produced would be permanent, but\nno further effect would be added. If, however, the cause, namely,\nexposure to moist air, continues, more and more of the iron becomes\nrusted, until all which is exposed is converted into a red powder, when\none of the conditions of the production of rust, namely, the presence of\nunoxidized iron, has ceased, and the effect cannot any longer be\nproduced. Again, the earth causes bodies to fall towards it, that is,\nthe existence of the earth at a given instant, causes an unsupported\nbody to move towards it at the succeeding instant: and if the earth were\nannihilated, as much of the effect as is already produced would\ncontinue; the object would go on moving in the same direction, with its\nacquired velocity, until intercepted by some body or deflected by some\nother force. The earth, however, not being annihilated, goes on\nproducing in the second instant an effect similar and of equal amount\nwith the first, which two effects being added together, there results an\naccelerated velocity; and this operation being repeated at each\nsuccessive instant, the mere permanence of the cause, though without\nincrease, gives rise to a constant progressive increase of the effect,\nso long as all the conditions, negative and positive, of the production\nof that effect, continue to be realized.\n\nIt is obvious that this state of things is merely a case of the\nComposition of Causes. A cause which continues in action, must on a\nstrict analysis be considered as a number of causes exactly similar,\nsuccessively introduced, and producing by their combination the sum of\nthe effects which they would severally produce if they acted singly. The\nprogressive rusting of the iron is in strictness the sum of the effects\nof many particles of air acting in succession upon corresponding\nparticles of iron. The continued action of the earth upon a falling body\nis equivalent to a series of forces, applied in successive instants,\neach tending to produce a certain constant quantity of motion; and the\nmotion at each instant is the sum of the effects of the new force\napplied at the preceding instant, and the motion already acquired. In\neach instant, a fresh effect, of which gravity is the proximate cause,\nis added to the effect of which it was the remote cause: or (to express\nthe same thing in another manner) the effect produced by the earth's\ninfluence at the instant last elapsed, is added to the sum of the\neffects of which the remote causes were the influences exerted by the\nearth at all the previous instants since the motion began. The case,\ntherefore, comes under the principle of a concurrence of causes\nproducing an effect equal to the sum of their separate effects. But as\nthe causes come into play not all at once, but successively, and as the\neffect at each instant is the sum of the effects of those causes only\nwhich have come into action up to that instant, the result assumes the\nform of an ascending series; a succession of sums, each greater than\nthat which preceded it; and we have thus a progressive effect from the\ncontinued action of a cause.\n\nSince the continuance of the cause influences the effect only by adding\nto its quantity, and since the addition takes place according to a fixed\nlaw (equal quantities in equal times), the result is capable of being\ncomputed on mathematical principles. In fact, this case, being that of\ninfinitesimal increments, is precisely the case which the differential\ncalculus was invented to meet. The questions, what effect will result\nfrom the continual addition of a given cause to itself, and what amount\nof the cause, being continually added to itself, will produce a given\namount of the effect, are evidently mathematical questions, and to be\ntreated, therefore, deductively. If, as we have seen, cases of the\nComposition of Causes are seldom adapted for any other than deductive\ninvestigation, this is especially true in the case now examined, the\ncontinual composition of a cause with its own previous effects; since\nsuch a case is peculiarly amenable to the deductive method, while the\nundistinguishable manner in which the effects are blended with one\nanother and with the causes, must make the treatment of such an instance\nexperimentally, still more chimerical than in any other case.\n\n\n\u00a7 2. We shall next advert to a rather more intricate operation of the\nsame principle, namely, when the cause does not merely continue in\naction, but undergoes, during the same time, a progressive change in\nthose of its circumstances which contribute to determine the effect. In\nthis case, as in the former, the total effect goes on accumulating by\nthe continual addition of a fresh effect to that already produced, but\nit is no longer by the addition of equal quantities in equal times; the\nquantities added are unequal, and even the quality may now be different.\nIf the change in the state of the permanent cause be progressive, the\neffect will go through a double series of changes, arising partly from\nthe accumulated action of the cause, and partly from the changes in its\naction. The effect is still a progressive effect, produced however, not\nby the mere continuance of a cause, but by its continuance and its\nprogressiveness combined.\n\nA familiar example is afforded by the increase of the temperature as\nsummer advances, that is, as the sun draws nearer to a vertical\nposition, and remains a greater number of hours above the horizon. This\ninstance exemplifies in a very interesting manner the twofold operation\non the effect, arising from the continuance of the cause, and from its\nprogressive change. When once the sun has come near enough to the\nzenith, and remains above the horizon long enough, to give more warmth\nduring one diurnal rotation than the counteracting cause, the earth's\nradiation, can carry off, the mere continuance of the cause would\nprogressively increase the effect, even if the sun came no nearer and\nthe days grew no longer; but in addition to this, a change takes place\nin the accidents of the cause (its series of diurnal positions), tending\nto increase the quantity of the effect. When the summer solstice has\npassed, the progressive change in the cause begins to take place the\nreverse way; but, for some time, the accumulating effect of the mere\ncontinuance of the cause exceeds the effect of the changes in it, and\nthe temperature continues to increase.\n\nAgain, the motion of a planet is a progressive effect, produced by\ncauses at once permanent and progressive. The orbit of a planet is\ndetermined (omitting perturbations) by two causes: first, the action of\nthe central body, a permanent cause, which alternately increases and\ndiminishes as the planet draws nearer to or goes further from its\nperihelion, and which acts at every point in a different direction; and,\nsecondly, the tendency of the planet to continue moving in the direction\nand with the velocity which it has already acquired. This force also\ngrows greater as the planet draws nearer to its perihelion, because as\nit does so its velocity increases; and less, as it recedes from its\nperihelion: and this force as well as the other acts at each point in a\ndifferent direction, because at every point the action of the central\nforce, by deflecting the planet from its previous direction, alters the\nline in which it tends to continue moving. The motion at each instant is\ndetermined by the amount and direction of the motion, and the amount\nand direction of the sun's action, at the previous instant: and if we\nspeak of the entire revolution of the planet as one phenomenon (which,\nas it is periodical and similar to itself, we often find it convenient\nto do,) that phenomenon is the progressive effect of two permanent and\nprogressive causes, the central force and the acquired motion. Those\ncauses happening to be progressive in the particular way which is called\nperiodical, the effect necessarily is so too; because the quantities to\nbe added together returning in a regular order, the same sums must also\nregularly return.\n\nThis example is worthy of consideration also in another respect. Though\nthe causes themselves are permanent, and independent of all conditions\nknown to us, the changes which take place in the quantities and\nrelations of the causes are actually caused by the periodical changes in\nthe effects. The causes, as they exist at any moment, having produced a\ncertain motion, that motion, becoming itself a cause, reacts upon the\ncauses, and produces a change in them. By altering the distance and\ndirection of the central body relatively to the planet, and the\ndirection and quantity of the force in the direction of the tangent, it\nalters the elements which determine the motion at the next succeeding\ninstant. This change renders the next motion somewhat different; and\nthis difference, by a fresh reaction upon the causes, renders the next\nmotion again different, and so on. The original state of the causes\nmight have been such, that this series of actions modified by reactions\nwould not have been periodical. The sun's action, and the original\nimpelling force, might have been in such a ratio to one another, that\nthe reaction of the effect would have been such as to alter the causes\nmore and more, without ever bringing them back to what they were at any\nformer time. The planet would then have moved in a parabola, or an\nhyperbola, curves not returning into themselves. The quantities of the\ntwo forces were, however, originally such, that the successive reactions\nof the effect bring back the causes, after a certain time, to what they\nwere before; and from that time all the variations continue to recur\nagain and again in the same periodical order, and must so continue\nwhile the causes subsist and are not counteracted.\n\n\n\u00a7 3. In all cases of progressive effects, whether arising from the\naccumulation of unchanging or of changing elements, there is an\nuniformity of succession not merely between the cause and the effect,\nbut between the first stages of the effect and its subsequent stages.\nThat a body _in vacuo_ falls sixteen feet in the first second,\nforty-eight in the second, and so on in the ratio of the odd numbers, is\nas much an uniform sequence as that when the supports are removed the\nbody falls. The sequence of spring and summer is as regular and\ninvariable as that of the approach of the sun and spring: but we do not\nconsider spring to be the cause of summer; it is evident that both are\nsuccessive effects of the heat received from the sun, and that,\nconsidered merely in itself, spring might continue for ever, without\nhaving the slightest tendency to produce summer. As we have so often\nremarked, not the conditional, but the unconditional invariable\nantecedent is termed the cause. That which would not be followed by the\neffect unless something else had preceded, is not the cause, however\ninvariable the sequence may in fact be.\n\nIt is in this way that most of those uniformities of succession are\ngenerated, which are not cases of causation. When a phenomenon goes on\nincreasing, or periodically increases and diminishes, or goes through\nany continued and unceasing process of variation reducible to an uniform\nrule or law of succession, we do not on this account presume that any\ntwo successive terms of the series are cause and effect. We presume the\ncontrary; we expect to find that the whole series originates either from\nthe continued action of fixed causes, or from causes which go through a\ncorresponding process of continuous change. A tree grows from half an\ninch high to a hundred feet; and some trees will generally grow to that\nheight, unless prevented by some counteracting cause. But we do not call\nthe seedling the cause of the full-grown tree; the invariable antecedent\nit certainly is, and we know very imperfectly on what other antecedents\nthe sequence is contingent, but we are convinced that it is contingent\non something; because the homogeneousness of the antecedent with the\nconsequent, the close resemblance of the seedling to the tree in all\nrespects except magnitude, and the graduality of the growth, so exactly\nresembling the progressively accumulating effect produced by the long\naction of some one cause, leave no possibility of doubting that the\nseedling and the tree are two terms in a series of that description, the\nfirst term of which is yet to seek. The conclusion is further confirmed\nby this, that we are able to prove by strict induction the dependence of\nthe growth of the tree, and even of the continuance of its existence,\nupon the continued repetition of certain processes of nutrition, the\nrise of the sap, the absorptions and exhalations by the leaves, &c.; and\nthe same experiments would probably prove to us that the growth of the\ntree is the accumulated sum of the effects of these continued processes,\nwere we not, for want of sufficiently microscopic eyes, unable to\nobserve correctly and in detail what those effects are.\n\nThis supposition by no means requires that the effect should not, during\nits progress, undergo many modifications besides those of quantity, or\nthat it should not sometimes appear to undergo a very marked change of\ncharacter. This may be either because the unknown cause consists of\nseveral component elements or agents, whose effects, accumulating\naccording to different laws, are compounded in different proportions at\ndifferent periods in the existence of the organized being; or because,\nat certain points in its progress, fresh causes or agencies come in, or\nare evolved, which intermix their laws with those of the prime agent.\n\n\n\n\nCHAPTER XVI.\n\nOF EMPIRICAL LAWS.\n\n\n\u00a7 1. Scientific inquirers give the name of Empirical Laws to those\nuniformities which observation or experiment has shown to exist, but on\nwhich they hesitate to rely in cases varying much from those which have\nbeen actually observed, for want of seeing any reason _why_ such a law\nshould exist. It is implied, therefore, in the notion of an empirical\nlaw, that it is not an ultimate law; that if true at all, its truth is\ncapable of being, and requires to be, accounted for. It is a derivative\nlaw, the derivation of which is not yet known. To state the explanation,\nthe _why_, of the empirical law, would be to state the laws from which\nit is derived; the ultimate causes on which it is contingent. And if we\nknew these, we should also know what are its limits; under what\nconditions it would cease to be fulfilled.\n\nThe periodical return of eclipses, as originally ascertained by the\npersevering observation of the early eastern astronomers, was an\nempirical law, until the general laws of the celestial motions had\naccounted for it. The following are empirical laws still waiting to be\nresolved into the simpler laws from which they are derived. The local\nlaws of the flux and reflux of the tides in different places: the\nsuccession of certain kinds of weather to certain appearances of sky:\nthe apparent exceptions to the almost universal truth that bodies expand\nby increase of temperature: the law that breeds, both animal and\nvegetable, are improved by crossing: that gases have a strong tendency\nto permeate animal membranes: that substances containing a very high\nproportion of nitrogen (such as hydrocyanic acid and morphia) are\npowerful poisons: that when different metals are fused together, the\nalloy is harder than the various elements: that the number of atoms of\nacid required to neutralize one atom of any base, is equal to the number\nof atoms of oxygen in the base: that the solubility of substances in one\nanother, depends[12] (at least in some degree) on the similarity of\ntheir elements.\n\nAn empirical law, then, is an observed uniformity, presumed to be\nresolvable into simpler laws, but not yet resolved into them. The\nascertainment of the empirical laws of phenomena often precedes by a\nlong interval the explanation of those laws by the Deductive Method; and\nthe verification of a deduction usually consists in the comparison of\nits results with empirical laws previously ascertained.\n\n\n\u00a7 2. From a limited number of ultimate laws of causation, there are\nnecessarily generated a vast number of derivative uniformities, both of\nsuccession and of coexistence. Some are laws of succession or of\ncoexistence between different effects of the same cause: of these we had\nexamples in the last chapter. Some are laws of succession between\neffects and their remote causes; resolvable into the laws which connect\neach with the intermediate link. Thirdly, when causes act together and\ncompound their effects, the laws of those causes generate the\nfundamental law of the effect, namely, that it depends on the\ncoexistence of those causes. And, finally, the order of succession or of\ncoexistence which obtains among effects, necessarily depends on their\ncauses. If they are effects of the same cause, it depends on the laws of\nthat cause; if on different causes, it depends on the laws of those\ncauses severally, and on the circumstances which determine their\ncoexistence. If we inquire further when and how the causes will\ncoexist, that, again, depends on _their_ causes: and we may thus trace\nback the phenomena higher and higher, until the different series of\neffects meet in a point, and the whole is shown to have depended\nultimately on some common cause; or until, instead of converging to one\npoint, they terminate in different points, and the order of the effects\nis proved to have arisen from the collocation of some of the primeval\ncauses, or natural agents. For example, the order of succession and of\ncoexistence among the heavenly motions, which is expressed by Kepler's\nlaws, is derived from the coexistence of two primeval causes, the sun,\nand the original impulse or projectile force belonging to each\nplanet.[13] Kepler's laws are resolved into the laws of these causes and\nthe fact of their coexistence.\n\nDerivative laws, therefore, do not depend solely on the ultimate laws\ninto which they are resolvable: they mostly depend on those ultimate\nlaws, and an ultimate fact; namely, the mode of coexistence of some of\nthe component elements of the universe. The ultimate laws of causation\nmight be the same as at present, and yet the derivative laws completely\ndifferent, if the causes coexisted in different proportions, or with any\ndifference in those of their relations by which the effects are\ninfluenced. If, for example, the sun's attraction, and the original\nprojectile force, had existed in some other ratio to one another than\nthey did (and we know of no reason why this should not have been the\ncase), the derivative laws of the heavenly motions might have been quite\ndifferent from what they are. The proportions which exist happen to be\nsuch as to produce regular elliptical motions; any other proportions\nwould have produced different ellipses, or circular, or parabolic, or\nhyperbolic motions, but still regular ones; because the effects of each\nof the agents accumulate according to an uniform law; and two regular\nseries of quantities, when their corresponding terms are added, must\nproduce a regular series of some sort, whatever the quantities\nthemselves are.\n\n\n\u00a7 3. Now this last-mentioned element in the resolution of a derivative\nlaw, the element which is not a law of causation, but a collocation of\ncauses, cannot itself be reduced to any law. There is (as formerly\nremarked[14]) no uniformity, no _norma_, principle, or rule, perceivable\nin the distribution of the primeval natural agents through the universe.\nThe different substances composing the earth, the powers that pervade\nthe universe, stand in no constant relation to one another. One\nsubstance is more abundant than others, one power acts through a larger\nextent of space than others, without any pervading analogy that we can\ndiscover. We not only do not know of any reason why the sun's attraction\nand the force in the direction of the tangent coexist in the exact\nproportion they do, but we can trace no coincidence between it and the\nproportions in which any other elementary powers in the universe are\nintermingled. The utmost disorder is apparent in the combination of the\ncauses; which is consistent with the most regular order in their\neffects; for when each agent carries on its own operations according to\nan uniform law, even the most capricious combination of agencies will\ngenerate a regularity of some sort; as we see in the kaleidoscope, where\nany casual arrangement of coloured bits of glass produces by the laws of\nreflection a beautiful regularity in the effect.\n\n\n\u00a7 4. In the above considerations lies the justification of the limited\ndegree of reliance which scientific inquirers are accustomed to place in\nempirical laws.\n\nA derivative law which results wholly from the operation of some one\ncause, will be as universally true as the laws of the cause itself; that\nis, it will always be true except where some one of those effects of the\ncause, on which the derivative law depends, is defeated by a\ncounteracting cause. But when the derivative law results not from\ndifferent effects of one cause, but from effects of several causes, we\ncannot be certain that it will be true under any variation in the mode\nof coexistence of those causes, or of the primitive natural agents on\nwhich the causes ultimately depend. The proposition that coal beds rest\non certain descriptions of strata exclusively, though true on the earth\nso far as our observation has reached, cannot be extended to the moon or\nthe other planets, supposing coal to exist there; because we cannot be\nassured that the original constitution of any other planet was such as\nto produce the different depositions in the same order as in our globe.\nThe derivative law in this case depends not solely on laws, but on a\ncollocation; and collocations cannot be reduced to any law.\n\nNow it is the very nature of a derivative law which has not yet been\nresolved into its elements, in other words, an empirical law, that we do\nnot know whether it results from the different effects of one cause, or\nfrom effects of different causes. We cannot tell whether it depends\nwholly on laws, or partly on laws and partly on a collocation. If it\ndepends on a collocation, it will be true in all the cases in which that\nparticular collocation exists. But, since we are entirely ignorant, in\ncase of its depending on a collocation, what the collocation is, we are\nnot safe in extending the law beyond the limits of time and place in\nwhich we have actual experience of its truth. Since within those limits\nthe law has always been found true, we have evidence that the\ncollocations, whatever they are, on which it depends, do really exist\nwithin those limits. But, knowing of no rule or principle to which the\ncollocations themselves conform, we cannot conclude that because a\ncollocation is proved to exist within certain limits of place or time,\nit will exist beyond those limits. Empirical laws, therefore, can only\nbe received as true within the limits of time and place in which they\nhave been found true by observation: and not merely the limits of time\nand place, but of time, place, and circumstance: for since it is the\nvery meaning of an empirical law that we do not know the ultimate laws\nof causation on which it is dependent, we cannot foresee, without actual\ntrial, in what manner or to what extent the introduction of any new\ncircumstance may affect it.\n\n\n\u00a7 5. But how are we to know that an uniformity, ascertained by\nexperience, is only an empirical law? Since, by the supposition, we have\nnot been able to resolve it into any other laws, how do we know that it\nis not an ultimate law of causation?\n\nI answer, that no generalization amounts to more than an empirical law\nwhen the only proof on which it rests is that of the Method of\nAgreement. For it has been seen that by that method alone we never can\narrive at causes. The utmost that the Method of Agreement can do is, to\nascertain the whole of the circumstances common to all cases in which a\nphenomenon is produced: and this aggregate includes not only the cause\nof the phenomenon, but all phenomena with which it is connected by any\nderivative uniformity, whether as being collateral effects of the same\ncause, or effects of any other cause which, in all the instances we have\nbeen able to observe, coexisted with it. The method affords no means of\ndetermining which of these uniformities are laws of causation, and which\nare merely derivative laws, resulting from those laws of causation and\nfrom the collocation of the causes. None of them, therefore, can be\nreceived in any other character than that of derivative laws, the\nderivation of which has not been traced; in other words, empirical laws:\nin which light, all results obtained by the Method of Agreement (and\ntherefore almost all truths obtained by simple observation without\nexperiment) must be considered, until either confirmed by the Method of\nDifference, or explained deductively, in other words accounted for _\u00e0\npriori_.\n\nThese empirical laws may be of greater or less authority, according as\nthere is reason to presume that they are resolvable into laws only, or\ninto laws and collocations together. The sequences which we observe in\nthe production and subsequent life of an animal or a vegetable, resting\non the Method of Agreement only, are mere empirical laws; but though the\nantecedents in those sequences may not be the causes of the consequents,\nboth the one and the other are doubtless, in the main, successive stages\nof a progressive effect originating in a common cause, and therefore\nindependent of collocations. The uniformities, on the other hand, in the\norder of superposition of strata on the earth, are empirical laws of a\nmuch weaker kind, since they not only are not laws of causation, but\nthere is no reason to believe that they depend on any common cause: all\nappearances are in favour of their depending on the particular\ncollocation of natural agents which at some time or other existed on our\nglobe, and from which no inference can be drawn as to the collocation\nwhich exists or has existed in any other portion of the universe.\n\n\n\u00a7 6. Our definition of an empirical law including not only those\nuniformities which are not known to be laws of causation, but also those\nwhich are, provided there be reason to presume that they are not\nultimate laws; this is the proper place to consider by what signs we may\njudge that even if an observed uniformity be a law of causation, it is\nnot an ultimate but a derivative law.\n\nThe first sign is, if between the antecedent _a_ and the consequent _b_\nthere be evidence of some intermediate link; some phenomenon of which we\ncan surmise the existence, though from the imperfection of our senses or\nof our instruments we are unable to ascertain its precise nature and\nlaws. If there be such a phenomenon (which may be denoted by the letter\n_x_), it follows that even if _a_ be the cause of _b_, it is but the\nremote cause, and that the law, _a_ causes _b_, is resolvable into at\nleast two laws, _a_ causes _x_, and _x_ causes _b_. This is a very\nfrequent case, since the operations of nature mostly take place on so\nminute a scale, that many of the successive steps are either\nimperceptible, or very indistinctly perceived.\n\nTake, for example, the laws of the chemical composition of substances;\nas that hydrogen and oxygen being combined, water is produced. All we\nsee of the process is, that the two gases being mixed in certain\nproportions, and heat or electricity being applied, an explosion takes\nplace, the gases disappear, and water remains. There is no doubt about\nthe law, or about its being a law of causation. But between the\nantecedent (the gases in a state of mechanical mixture, heated or\nelectrified), and the consequent (the production of water), there must\nbe an intermediate process which we do not see. For if we take any\nportion whatever of the water, and subject it to analysis, we find that\nit always contains hydrogen and oxygen; nay, the very same proportions\nof them, namely, two thirds, in volume, of hydrogen, and one third\noxygen. This is true of a single drop; it is true of the minutest\nportion which our instruments are capable of appreciating. Since, then,\nthe smallest perceptible portion of the water contains both those\nsubstances, portions of hydrogen and oxygen smaller than the smallest\nperceptible must have come together in every such minute portion of\nspace; must have come closer together than when the gases were in a\nstate of mechanical mixture, since (to mention no other reasons) the\nwater occupies far less space than the gases. Now, as we cannot see this\ncontact or close approach of the minute particles, we cannot observe\nwith what circumstances it is attended, or according to what laws it\nproduces its effects. The production of water, that is, of the sensible\nphenomena which characterize the compound, may be a very remote effect\nof those laws. There may be innumerable intervening links; and we are\nsure that there must be some. Having full proof that corpuscular action\nof some kind takes place previous to any of the great transformations in\nthe sensible properties of substances, we can have no doubt that the\nlaws of chemical action, as at present known, are not ultimate but\nderivative laws; however ignorant we may be, and even though we should\nfor ever remain ignorant, of the nature of the laws of corpuscular\naction from which they are derived.\n\nIn like manner, all the processes of vegetative life, whether in the\nvegetable properly so called or in the animal body, are corpuscular\nprocesses. Nutrition is the addition of particles to one another,\nsometimes merely replacing other particles separated and excreted,\nsometimes occasioning an increase of bulk or weight, so gradual, that\nonly after a long continuance does it become perceptible. Various\norgans, by means of peculiar vessels, secrete from the blood, fluids,\nthe component particles of which must have been in the blood, but which\ndiffer from it most widely both in mechanical properties and in chemical\ncomposition. Here, then, are abundance of unknown links to be filled up;\nand there can be no doubt that the laws of the phenomena of vegetative\nor organic life are derivative laws, dependent on properties of the\ncorpuscles, and of those elementary tissues which are comparatively\nsimple combinations of corpuscles.\n\nThe first sign, then, from which a law of causation, though hitherto\nunresolved, may be inferred to be a derivative law, is any indication of\nthe existence of an intermediate link or links between the antecedent\nand the consequent. The second is, when the antecedent is an extremely\ncomplex phenomenon, and its effects therefore, probably, in part at\nleast, compounded of the effects of its different elements; since we\nknow that the case in which the effect of the whole is not made up of\nthe effects of its parts, is exceptional, the Composition of Causes\nbeing by far the more ordinary case.\n\nWe will illustrate this by two examples, in one of which the antecedent\nis the sum of many homogeneous, in the other of heterogeneous, parts.\nThe weight of a body is made up of the weights of its minute particles:\na truth which astronomers express in its most general terms, when they\nsay that bodies, at equal distances, gravitate to one another in\nproportion to their quantity of matter. All true propositions,\ntherefore, which can be made concerning gravity, are derivative laws;\nthe ultimate law into which they are all resolvable being, that every\nparticle of matter attracts every other. As our second example, we may\ntake any of the sequences observed in meteorology: for instance, a\ndiminution of the pressure of the atmosphere (indicated by a fall of the\nbarometer) is followed by rain. The antecedent is here a complex\nphenomenon, made up of heterogeneous elements; the column of the\natmosphere over any particular place consisting of two parts, a column\nof air, and a column of aqueous vapour mixed with it; and the change in\nthe two together manifested by a fall of the barometer, and followed by\nrain, must be either a change in one of these, or in the other, or in\nboth. We might, then, even in the absence of any other evidence, form a\nreasonable presumption, from the invariable presence of both these\nelements in the antecedent, that the sequence is probably not an\nultimate law, but a result of the laws of the two different agents; a\npresumption only to be destroyed when we had made ourselves so well\nacquainted with the laws of both, as to be able to affirm that those\nlaws could not by themselves produce the observed result.\n\nThere are but few known cases of succession from very complex\nantecedents, which have not either been actually accounted for from\nsimpler laws, or inferred with great probability (from the ascertained\nexistence of intermediate links of causation not yet understood) to be\ncapable of being so accounted for. It is, therefore, highly probable\nthat all sequences from complex antecedents are thus resolvable, and\nthat ultimate laws are in all cases comparatively simple. If there were\nnot the other reasons already mentioned for believing that the laws of\norganized nature are resolvable into simpler laws, it would be almost a\nsufficient reason that the antecedents in most of the sequences are so\nvery complex.\n\n\n\u00a7 7. In the preceding discussion we have recognised two kinds of\nempirical laws: those known to be laws of causation, but presumed to be\nresolvable into simpler laws; and those not known to be laws of\ncausation at all. Both these kinds of laws agree in the demand which\nthey make for being explained by deduction, and agree in being the\nappropriate means of verifying such deduction, since they represent the\nexperience with which the result of the deduction must be compared. They\nagree, further, in this, that until explained, and connected with the\nultimate laws from which they result, they have not attained the highest\ndegree of certainty of which laws are susceptible. It has been shown on\na former occasion that laws of causation which are derivative, and\ncompounded of simpler laws, are not only, as the nature of the case\nimplies, less general, but even less certain, than the simpler laws\nfrom which they result; not in the same degree to be relied on as\nuniversally true. The inferiority of evidence, however, which attaches\nto this class of laws, is trifling, compared with that which is inherent\nin uniformities not known to be laws of causation at all. So long as\nthese are unresolved, we cannot tell on how many collocations, as well\nas laws, their truth may be dependent; we can never, therefore, extend\nthem with any confidence to cases in which we have not assured\nourselves, by trial, that the necessary collocation of causes, whatever\nit may be, exists. It is to this class of laws alone that the property,\nwhich philosophers usually consider as characteristic of empirical laws,\nbelongs in all its strictness; the property of being unfit to be relied\non beyond the limits of time, place, and circumstance, in which the\nobservations have been made. These are empirical laws in a more emphatic\nsense; and when I employ that term (except where the context manifestly\nindicates the reverse) I shall generally mean to designate those\nuniformities only, whether of succession or of coexistence, which are\nnot known to be laws of causation.\n\n\n\n\nCHAPTER XVII.\n\nOF CHANCE AND ITS ELIMINATION.\n\n\n\u00a7 1. Considering then as empirical laws only those observed uniformities\nrespecting which the question whether they are laws of causation must\nremain undecided until they can be explained deductively, or until some\nmeans are found of applying the Method of Difference to the case, it has\nbeen shown in the preceding chapter, that until an uniformity can, in\none or the other of these modes, be taken out of the class of empirical\nlaws, and brought either into that of laws of causation or of the\ndemonstrated results of laws of causation, it cannot with any assurance\nbe pronounced true beyond the local and other limits within which it has\nbeen found so by actual observation. It remains to consider how we are\nto assure ourselves of its truth even within those limits; after what\nquantity of experience a generalization which rests solely on the Method\nof Agreement, can be considered sufficiently established, even as an\nempirical law. In a former chapter, when treating of the Methods of\nDirect Induction, we expressly reserved this question,[15] and the time\nis now come for endeavouring to solve it.\n\nWe found that the Method of Agreement has the defect of not proving\ncausation, and can therefore only be employed for the ascertainment of\nempirical laws. But we also found that besides this deficiency, it\nlabours under a characteristic imperfection, tending to render uncertain\neven such conclusions as it is in itself adapted to prove. This\nimperfection arises from Plurality of Causes. Although two or more cases\nin which the phenomenon _a_ has been met with, may have no common\nantecedent except A, this does not prove that there is any connexion\nbetween _a_ and A, since _a_ may have many causes, and may have been\nproduced, in these different instances, not by anything which the\ninstances had in common, but by some of those elements in them which\nwere different. We nevertheless observed, that in proportion to the\nmultiplication of instances pointing to A as the antecedent, the\ncharacteristic uncertainty of the method diminishes, and the existence\nof a law of connexion between A and _a_ more nearly approaches to\ncertainty. It is now to be determined, after what amount of experience\nthis certainty may be deemed to be practically attained, and the\nconnexion between A and _a_ may be received as an empirical law.\n\nThis question may be otherwise stated in more familiar terms:--After how\nmany and what sort of instances may it be concluded, that an observed\ncoincidence between two phenomena is not the effect of chance?\n\nIt is of the utmost importance for understanding the logic of induction,\nthat we should form a distinct conception of what is meant by chance,\nand how the phenomena which common language ascribes to that abstraction\nare really produced.\n\n\n\u00a7 2. Chance is usually spoken of in direct antithesis to law; whatever\n(it is supposed) cannot be ascribed to any law, is attributed to chance.\nIt is, however, certain, that whatever happens is the result of some\nlaw; is an effect of causes, and could have been predicted from a\nknowledge of the existence of those causes, and from their laws. If I\nturn up a particular card, that is a consequence of its place in the\npack. Its place in the pack was a consequence of the manner in which the\ncards were shuffled, or of the order in which they were played in the\nlast game; which, again, were effects of prior causes. At every stage,\nif we had possessed an accurate knowledge of the causes in existence, it\nwould have been abstractedly possible to foretell the effect.\n\nAn event occurring by chance, may be better described as a coincidence\nfrom which we have no ground to infer an uniformity: the occurrence of a\nphenomenon in certain circumstances, without our having reason on that\naccount to infer that it will happen again in those circumstances. This,\nhowever, when looked closely into, implies that the enumeration of the\ncircumstances is not complete. Whatever the fact be, since it has\noccurred once, we may be sure that if _all_ the same circumstances were\nrepeated, it would occur again; and not only if all, but there is some\nparticular portion of those circumstances, on which the phenomenon is\ninvariably consequent. With most of them, however, it is not connected\nin any permanent manner: its conjunction with those is said to be the\neffect of chance, to be merely casual. Facts casually conjoined are\nseparately the effects of causes, and therefore of laws; but of\ndifferent causes, and causes not connected by any law.\n\nIt is incorrect, then, to say that any phenomenon is produced by chance;\nbut we may say that two or more phenomena are conjoined by chance, that\nthey coexist or succeed one another only by chance: meaning that they\nare in no way related through causation; that they are neither cause and\neffect, nor effects of the same cause, nor effects of causes between\nwhich there subsists any law of coexistence, nor even effects of the\nsame collocation of primeval causes.\n\nIf the same casual coincidence never occurred a second time, we should\nhave an easy test for distinguishing such from the coincidences which\nare the results of a law. As long as the phenomena had been found\ntogether only once, so long, unless we knew some more general laws from\nwhich the coincidence might have resulted, we could not distinguish it\nfrom a casual one; but if it occurred twice, we should know that the\nphenomena so conjoined must be in some way connected through their\ncauses.\n\nThere is, however, no such test. A coincidence may occur again and\nagain, and yet be only casual. Nay, it would be inconsistent with what\nwe know of the order of nature, to doubt that every casual coincidence\nwill sooner or later be repeated, as long as the phenomena between which\nit occurred do not cease to exist, or to be reproduced. The recurrence,\ntherefore, of the same coincidence more than once, or even its frequent\nrecurrence, does not prove that it is an instance of any law; does not\nprove that it is not casual, or, in common language, the effect of\nchance.\n\nAnd yet, when a coincidence cannot be deduced from known laws, nor\nproved by experiment to be itself a case of causation, the frequency of\nits occurrence is the only evidence from which we can infer that it is\nthe result of a law. Not, however, its absolute frequency. The question\nis not whether the coincidence occurs often or seldom, in the ordinary\nsense of those terms; but whether it occurs more often than chance will\naccount for; more often than might rationally be expected if the\ncoincidence were casual. We have to decide, therefore, what degree of\nfrequency in a coincidence, chance will account for. And to this there\ncan be no general answer. We can only state the principle by which the\nanswer must be determined: the answer itself will be different in every\ndifferent case.\n\nSuppose that one of the phenomena, A, exists always, and the other\nphenomenon, B, only occasionally: it follows that every instance of B\nwill be an instance of its coincidence with A, and yet the coincidence\nwill be merely casual, not the result of any connexion between them. The\nfixed stars have been constantly in existence since the beginning of\nhuman experience, and all phenomena that have come under human\nobservation have, in every single instance, coexisted with them; yet\nthis coincidence, though equally invariable with that which exists\nbetween any of those phenomena and its own cause, does not prove that\nthe stars are its cause, nor that they are in anywise connected with it.\nAs strong a case of coincidence, therefore, as can possibly exist, and a\nmuch stronger one in point of mere frequency than most of those which\nprove laws, does not here prove a law: why? because, since the stars\nexist always, they _must_ coexist with every other phenomenon, whether\nconnected with them by causation or not. The uniformity, great though it\nbe, is no greater than would occur on the supposition that no such\nconnexion exists.\n\nOn the other hand, suppose that we were inquiring whether there be any\nconnexion between rain and any particular wind. Rain, we know,\noccasionally occurs with every wind; therefore the connexion, if it\nexists, cannot be an actual law; but still, rain may be connected with\nsome particular wind through causation; that is, though they cannot be\nalways effects of the same cause (for if so they would regularly\ncoexist), there may be some causes common to the two, so that in so far\nas either is produced by those common causes, they will, from the laws\nof the causes, be found to coexist. How, then, shall we ascertain this?\nThe obvious answer is, by observing whether rain occurs with one wind\nmore frequently than with any other. That, however, is not enough; for\nperhaps that one wind blows more frequently than any other; so that its\nblowing more frequently in rainy weather is no more than would happen,\nalthough it had no connexion with the causes of rain, provided it were\nnot connected with causes adverse to rain. In England, westerly winds\nblow during about twice as great a portion of the year as easterly. If,\ntherefore, it rains only twice as often with a westerly, as with an\neasterly wind, we have no reason to infer that any law of nature is\nconcerned in the coincidence. If it rains more than twice as often, we\nmay be sure that some law is concerned; either there is some cause in\nnature which, in this climate, tends to produce both rain and a westerly\nwind, or a westerly wind has itself some tendency to produce rain. But\nif it rains less than twice as often, we may draw a directly opposite\ninference: the one, instead of being a cause, or connected with causes,\nof the other, must be connected with causes adverse to it, or with the\nabsence of some cause which produces it; and though it may still rain\nmuch oftener with a westerly wind than with an easterly, so far would\nthis be from proving any connexion between the phenomena, that the\nconnexion proved would be between rain and an easterly wind, to which,\nin mere frequency of coincidence, it is less allied.\n\nHere, then, are two examples: in one, the greatest possible frequency of\ncoincidence, with no instance whatever to the contrary, does not prove\nthat there is any law; in the other, a much less frequency of\ncoincidence, even when non-coincidence is still more frequent, does\nprove that there is a law. In both cases the principle is the same. In\nboth we consider the positive frequency of the phenomena themselves, and\nhow great frequency of coincidence that must of itself bring about,\nwithout supposing any connexion between them, provided there be no\nrepugnance; provided neither be connected with any cause tending to\nfrustrate the other. If we find a greater frequency of coincidence than\nthis, we conclude that there is some connexion; if a less frequency,\nthat there is some repugnance. In the former case, we conclude that one\nof the phenomena can under some circumstances cause the other, or that\nthere exists something capable of causing them both; in the latter, that\none of them, or some cause which produces one of them, is capable of\ncounteracting the production of the other. We have thus to deduct from\nthe observed frequency of coincidence, as much as may be the effect of\nchance, that is, of the mere frequency of the phenomena themselves; and\nif anything remains, what does remain is the residual fact which proves\nthe existence of a law.\n\nThe frequency of the phenomena can only be ascertained within definite\nlimits of space and time; depending as it does on the quantity and\ndistribution of the primeval natural agents, of which we can know\nnothing beyond the boundaries of human observation, since no law, no\nregularity, can be traced in it, enabling us to infer the unknown from\nthe known. But for the present purpose this is no disadvantage, the\nquestion being confined within the same limits as the data. The\ncoincidences occurred in certain places and times, and within those we\ncan estimate the frequency with which such coincidences would be\nproduced by chance. If, then, we find from observation that A exists in\none case out of every two, and B in one case out of every three; then if\nthere be neither connexion nor repugnance between them, or between any\nof their causes, the instances in which A and B will both exist, that is\nto say will coexist, will be one case in every six. For A exists in\nthree cases out of six: and B, existing in one case out of every three\nwithout regard to the presence or absence of A, will exist in one case\nout of those three. There will therefore be, of the whole number of\ncases, two in which A exists without B; one case of B without A; two in\nwhich neither B nor A exists, and one case out of six in which they both\nexist. If then, in point of fact, they are found to coexist oftener than\nin one case out of six; and, consequently, A does not exist without B so\noften as twice in three times, nor B without A so often as once in every\ntwice; there is some cause in existence which tends to produce a\nconjunction between A and B.\n\nGeneralizing the result, we may say, that if A occurs in a larger\nproportion of the cases where B is, than of the cases where B is not;\nthen will B also occur in a larger proportion of the cases where A is,\nthan of the cases where A is not; and there is some connexion, through\ncausation, between A and B. If we could ascend to the causes of the two\nphenomena, we should find, at some stage, either proximate or remote,\nsome cause or causes common to both; and if we could ascertain what\nthese are, we could frame a generalization which would be true without\nrestriction of place or time: but until we can do so, the fact of a\nconnexion between the two phenomena remains an empirical law.\n\n\n\u00a7 3. Having considered in what manner it may be determined whether any\ngiven conjunction of phenomena is casual, or the result of some law; to\ncomplete the theory of chance, it is necessary that we should now\nconsider those effects which are partly the result of chance and partly\nof law, or, in other words, in which the effects of casual conjunctions\nof causes are habitually blended in one result with the effects of a\nconstant cause.\n\nThis is a case of Composition of Causes; and the peculiarity of it is,\nthat instead of two or more causes intermixing their effects in a\nregular manner with those of one another, we have now one constant\ncause, producing an effect which is successively modified by a series of\nvariable causes. Thus, as summer advances, the approach of the sun to a\nvertical position tends to produce a constant increase of temperature;\nbut with this effect of a constant cause, there are blended the effects\nof many variable causes, winds, clouds, evaporation, electric agencies\nand the like, so that the temperature of any given day depends in part\non these fleeting causes, and only in part on the constant cause. If the\neffect of the constant cause is always accompanied and disguised by\neffects of variable causes, it is impossible to ascertain the law of the\nconstant cause in the ordinary manner, by separating it from all other\ncauses and observing it apart. Hence arises the necessity of an\nadditional rule of experimental inquiry.\n\nWhen the action of a cause A is liable to be interfered with, not\nsteadily by the same cause or causes, but by different causes at\ndifferent times, and when these are so frequent, or so indeterminate,\nthat we cannot possibly exclude all of them from any experiment, though\nwe may vary them; our resource is, to endeavour to ascertain what is the\neffect of all the variable causes taken together. In order to do this,\nwe make as many trials as possible, preserving A invariable. The results\nof these different trials will naturally be different, since the\nindeterminate modifying causes are different in each: if, then, we do\nnot find these results to be progressive, but, on the contrary, to\noscillate about a certain point, one experiment giving a result a little\ngreater, another a little less, one a result tending a little more in\none direction, another a little more in the contrary direction; while\nthe average or middle point does not vary, but different sets of\nexperiments (taken in as great a variety of circumstances as possible)\nyield the same mean, provided only they be sufficiently numerous; then\nthat mean or average result, is the part, in each experiment, which is\ndue to the cause A, and is the effect which would have been obtained if\nA could have acted alone: the variable remainder is the effect of\nchance, that is, of causes the coexistence of which with the cause A was\nmerely casual. The test of the sufficiency of the induction in this case\nis, when any increase of the number of trials from which the average is\nstruck, does not materially alter the average.\n\nThis kind of elimination, in which we do not eliminate any one\nassignable cause, but the multitude of floating unassignable ones, may\nbe termed the Elimination of Chance. We afford an example of it when we\nrepeat an experiment, in order, by taking the mean of different results,\nto get rid of the effects of the unavoidable errors of each individual\nexperiment. When there is no permanent cause such as would produce a\ntendency to error peculiarly in one direction, we are warranted by\nexperience in assuming that the errors on one side will, in a certain\nnumber of experiments, about balance the errors on the contrary side. We\ntherefore repeat the experiment, until any change which is produced in\nthe average of the whole by further repetition, falls within limits of\nerror consistent with the degree of accuracy required by the purpose we\nhave in view.[16]\n\n\n\u00a7 4. In the supposition hitherto made, the effect of the constant cause\nA has been assumed to form so great and conspicuous a part of the\ngeneral result, that its existence never could be a matter of\nuncertainty, and the object of the eliminating process was only to\nascertain _how much_ is attributable to that cause; what is its exact\nlaw. Cases, however, occur in which the effect of a constant cause is so\nsmall, compared with that of some of the changeable causes with which\nit is liable to be casually conjoined, that of itself it escapes\nnotice, and the very existence of any effect arising from a constant\ncause is first learnt, by the process which in general serves only for\nascertaining the quantity of that effect. This case of induction may be\ncharacterized as follows. A given effect is known to be chiefly, and not\nknown not to be wholly, determined by changeable causes. If it be wholly\nso produced, then if the aggregate be taken of a sufficient number of\ninstances, the effects of these different causes will cancel one\nanother. If, therefore, we do not find this to be the case, but, on the\ncontrary, after such a number of trials has been made that no further\nincrease alters the average result, we find that average to be, not\nzero, but some other quantity, about which, though small in comparison\nwith the total effect, the effect nevertheless oscillates, and which is\nthe middle point in its oscillation; we may conclude this to be the\neffect of some constant cause: which cause, by some of the methods\nalready treated of, we may hope to detect. This may be called _the\ndiscovery of a residual phenomenon by eliminating the effects of\nchance_.\n\nIt is in this manner, for example, that loaded dice may be discovered.\nOf course no dice are so clumsily loaded that they must always throw\ncertain numbers; otherwise the fraud would be instantly detected. The\nloading, a constant cause, mingles with the changeable causes which\ndetermine what cast will be thrown in each individual instance. If the\ndice were not loaded, and the throw were left to depend entirely on the\nchangeable causes, these in a sufficient number of instances would\nbalance one another, and there would be no preponderant number of throws\nof any one kind. If, therefore, after such a number of trials that no\nfurther increase of their number has any material effect upon the\naverage, we find a preponderance in favour of a particular throw; we may\nconclude with assurance that there is some constant cause acting in\nfavour of that throw, or in other words, that the dice are not fair; and\nthe exact amount of the unfairness. In a similar manner, what is called\nthe diurnal variation of the barometer, which is very small compared\nwith the variations arising from the irregular changes in the state of\nthe atmosphere, was discovered by comparing the average height of the\nbarometer at different hours of the day. When this comparison was made,\nit was found that there was a small difference, which on the average was\nconstant, however the absolute quantities might vary, and which\ndifference, therefore, must be the effect of a constant cause. This\ncause was afterwards ascertained, deductively, to be the rarefaction of\nthe air, occasioned by the increase of temperature as the day advances.\n\n\n\u00a7 5. After these general remarks on the nature of chance, we are\nprepared to consider in what manner assurance may be obtained that a\nconjunction between two phenomena, which has been observed a certain\nnumber of times, is not casual, but a result of causation, and to be\nreceived therefore as one of the uniformities of nature, though (until\naccounted for _\u00e0 priori_) only as an empirical law.\n\nWe will suppose the strongest case, namely, that the phenomenon B has\nnever been observed except in conjunction with A. Even then, the\nprobability that they are connected is not measured by the total number\nof instances in which they have been found together, but by the excess\nof that number above the number due to the absolute frequency of A. If,\nfor example, A exists always, and therefore coexists with everything, no\nnumber of instances of its coexistence with B would prove a connexion;\nas in our example of the fixed stars. If A be a fact of such common\noccurrence that it may be presumed to be present in half of all the\ncases that occur, and therefore in half the cases in which B occurs, it\nis only the proportional excess above half, that is to be reckoned as\nevidence towards proving a connexion between A and B.\n\nIn addition to the question, What is the number of coincidences which,\non an average of a great multitude of trials, may be expected to arise\nfrom chance alone? there is also another question, namely, Of what\nextent of deviation from that average is the occurrence credible, from\nchance alone, in some number of instances smaller than that required\nfor striking a fair average? It is not only to be considered what is the\ngeneral result of the chances in the long run, but also what are the\nextreme limits of variation from the general result, which may\noccasionally be expected as the result of some smaller number of\ninstances.\n\nThe consideration of the latter question, and any consideration of the\nformer beyond that already given to it, belong to what mathematicians\nterm the doctrine of chances, or, in a phrase of greater pretension, the\nTheory of Probabilities.\n\n\n\n\nCHAPTER XVIII.\n\nOF THE CALCULATION OF CHANCES.\n\n\n\u00a7 1. \"Probability,\" says Laplace,[17] \"has reference partly to our\nignorance, partly to our knowledge. We know that among three or more\nevents, one, and only one, must happen; but there is nothing leading us\nto believe that any one of them will happen rather than the others. In\nthis state of indecision, it is impossible for us to pronounce with\ncertainty on their occurrence. It is, however, probable that any one of\nthese events, selected at pleasure, will not take place; because we\nperceive several cases, all equally possible, which exclude its\noccurrence, and only one which favours it.\n\n\"The theory of chances consists in reducing all events of the same kind\nto a certain number of cases equally possible, that is, such that we are\n_equally undecided_ as to their existence; and in determining the number\nof these cases which are favourable to the event of which the\nprobability is sought. The ratio of that number to the number of all the\npossible cases, is the measure of the probability; which is thus a\nfraction, having for its numerator the number of cases favourable to the\nevent, and for its denominator the number of all the cases which are\npossible.\"\n\nTo a calculation of chances, then, according to Laplace, two things are\nnecessary: we must know that of several events some one will certainly\nhappen, and no more than one; and we must not know, nor have any reason\nto expect, that it will be one of these events rather than another. It\nhas been contended that these are not the only requisites, and that\nLaplace has overlooked, in the general theoretical statement, a\nnecessary part of the foundation of the doctrine of chances. To be able\n(it has been said) to pronounce two events equally probable, it is not\nenough that we should know that one or the other must happen, and should\nhave no grounds for conjecturing which. Experience must have shown that\nthe two events are of equally frequent occurrence. Why, in tossing up a\nhalfpenny, do we reckon it equally probable that we shall throw cross or\npile? Because we know that in any great number of throws, cross and pile\nare thrown about equally often; and that the more throws we make, the\nmore nearly the equality is perfect. We may know this if we please by\nactual experiment; or by the daily experience which life affords of\nevents of the same general character; or deductively, from the effect of\nmechanical laws on a symmetrical body acted upon by forces varying\nindefinitely in quantity and direction. We may know it, in short, either\nby specific experience, or on the evidence of our general knowledge of\nnature. But, in one way or the other, we must know it, to justify us in\ncalling the two events equally probable; and if we knew it not, we\nshould proceed as much at haphazard in staking equal sums on the result,\nas in laying odds.\n\nThis view of the subject was taken in the first edition of the present\nwork: but I have since become convinced, that the theory of chances, as\nconceived by Laplace and by mathematicians generally, has not the\nfundamental fallacy which I had ascribed to it.\n\nWe must remember that the probability of an event is not a quality of\nthe event itself, but a mere name for the degree of ground which we, or\nsome one else, have for expecting it. The probability of an event to one\nperson is a different thing from the probability of the same event to\nanother, or to the same person after he has acquired additional\nevidence. The probability to me, that an individual of whom I know\nnothing but his name, will die within the year, is totally altered by my\nbeing told, the next minute, that he is in the last stage of a\nconsumption. Yet this makes no difference in the event itself, nor in\nany of the causes on which it depends. Every event is in itself certain,\nnot probable: if we knew all, we should either know positively that it\nwill happen, or positively that it will not. But its probability to us\nmeans the degree of expectation of its occurrence, which we are\nwarranted in entertaining by our present evidence.\n\nBearing this in mind, I think it must be admitted, that even when we\nhave no knowledge whatever to guide our expectations, except the\nknowledge that what happens must be some one of a certain number of\npossibilities, we may still reasonably judge, that one supposition is\nmore probable _to us_ than another supposition; and if we have any\ninterest at stake, we shall best provide for it by acting conformably to\nthat judgment.\n\n\n\u00a7 2. Suppose that we are required to take a ball from a box, of which we\nonly know that it contains balls both black and white, and none of any\nother colour. We know that the ball we select will be either a black or\na white ball; but we have no ground for expecting black rather than\nwhite, or white rather than black. In that case, if we are obliged to\nmake a choice, and to stake something on one or the other supposition,\nit will, as a question of prudence, be perfectly indifferent which; and\nwe shall act precisely as we should have acted if we had known\nbeforehand that the box contained an equal number of black and white\nballs. But though our conduct would be the same, it would not be founded\non any surmise that the balls were in fact thus equally divided; for we\nmight, on the contrary, know, by authentic information, that the box\ncontained ninety-nine balls of one colour, and only one of the other;\nstill, if we are not told which colour has only one, and which has\nninety-nine, the drawing of a white and of a black ball will be equally\nprobable to us; we shall have no reason for staking anything on the one\nevent rather than on the other; the option between the two will be a\nmatter of indifference; in other words it will be an even chance.\n\nBut let it now be supposed that instead of two there are three\ncolours--white, black, and red; and that we are entirely ignorant of the\nproportion in which they are mingled. We should then have no reason for\nexpecting one more than another, and if obliged to bet, should venture\nour stake on red, white, or black, with equal indifference. But should\nwe be indifferent whether we betted for or against some one colour, as,\nfor instance, white? Surely not. From the very fact that black and red\nare each of them separately equally probable to us with white, the two\ntogether must be twice as probable. We should in this case expect\nnot-white rather than white, and so much rather, that we would lay two\nto one upon it. It is true, there might for aught we knew be more white\nballs than black and red together; and if so, our bet would, if we knew\nmore, be seen to be a disadvantageous one. But so also, for aught we\nknew, might there be more red balls than black and white, or more black\nballs than white and red, and in such case the effect of additional\nknowledge would be to prove to us that our bet was more advantageous\nthan we had supposed it to be. There is in the existing state of our\nknowledge a rational probability of two to one against white; a\nprobability fit to be made a basis of conduct. No reasonable person\nwould lay an even wager in favour of white, against black and red;\nthough against black alone, or red alone, he might do so without\nimprudence.\n\nThe common theory, therefore, of the calculation of chances, appears to\nbe tenable. Even when we know nothing except the number of the possible\nand mutually excluding contingencies, and are entirely ignorant of their\ncomparative frequency, we may have grounds, and grounds numerically\nappreciable, for acting on one supposition rather than on another; and\nthis is the meaning of Probability.\n\n\n\u00a7 3. The principle, however, on which the reasoning proceeds, is\nsufficiently evident. It is the obvious one, that when the cases which\nexist are shared among several kinds, it is impossible that _each_ of\nthose kinds should be a majority of the whole: on the contrary, there\nmust be a majority against each kind, except one at most; and if any\nkind has more than its share in proportion to the total number, the\nothers collectively must have less. Granting this axiom, and assuming\nthat we have no ground for selecting any one kind as more likely than\nthe rest to surpass the average proportion, it follows that we cannot\nrationally presume this of any; which we should do, if we were to bet in\nfavour of it, receiving less odds than in the ratio of the number of the\nother kinds. Even, therefore, in this extreme case of the calculation of\nprobabilities, which does not rest on special experience at all, the\nlogical ground of the process is our knowledge, such knowledge as we\nthen have, of the laws governing the frequency of occurrence of the\ndifferent cases; but in this case the knowledge is limited to that\nwhich, being universal and axiomatic, does not require reference to\nspecific experience, or to any considerations arising out of the special\nnature of the problem under discussion.\n\nExcept, however, in such cases as games of chance, where the very\npurpose in view requires ignorance instead of knowledge, I can conceive\nno case in which we ought to be satisfied with such an estimate of\nchances as this; an estimate founded on the absolute minimum of\nknowledge respecting the subject. It is plain that, in the case of the\ncoloured balls, a very slight ground of surmise that the white balls\nwere really more numerous than either of the other colours, would\nsuffice to vitiate the whole of the calculations made in our previous\nstate of indifference. It would place us in that position of more\nadvanced knowledge, in which the probabilities, to us, would be\ndifferent from what they were before; and in estimating these new\nprobabilities we should have to proceed on a totally different set of\ndata, furnished no longer by mere counting of possible suppositions, but\nby specific knowledge of facts. Such data it should always be our\nendeavour to obtain; and in all inquiries, unless on subjects equally\nbeyond the range of our means of knowledge and our practical uses, they\nmay be obtained, if not good, at least better than none at all.[18]\n\nIt is obvious, too, that even when the probabilities are derived from\nobservation and experiment, a very slight improvement in the data, by\nbetter observations, or by taking into fuller consideration the special\ncircumstances of the case, is of more use than the most elaborate\napplication of the calculus to probabilities founded on the data in\ntheir previous state of inferiority. The neglect of this obvious\nreflection has given rise to misapplications of the calculus of\nprobabilities which have made it the real opprobrium of mathematics. It\nis sufficient to refer to the applications made of it to the credibility\nof witnesses, and to the correctness of the verdicts of juries. In\nregard to the first, common sense would dictate that it is impossible to\nstrike a general average of the veracity, and other qualifications for\ntrue testimony, of mankind, or of any class of them; and even if it were\npossible, the employment of it for such a purpose implies a\nmisapprehension of the use of averages: which serve indeed to protect\nthose whose interest is at stake, against mistaking the general result\nof large masses of instances, but are of extremely small value as\ngrounds of expectation in any one individual instance, unless the case\nbe one of those in which the great majority of individual instances do\nnot differ much from the average. In the case of a witness, persons of\ncommon sense would draw their conclusions from the degree of consistency\nof his statements, his conduct under cross-examination, and the relation\nof the case itself to his interests, his partialities, and his mental\ncapacity, instead of applying so rude a standard (even if it were\ncapable of being verified) as the ratio between the number of true and\nthe number of erroneous statements which he may be supposed to make in\nthe course of his life.\n\nAgain, on the subject of juries, or other tribunals, some mathematicians\nhave set out from the proposition that the judgment of any one judge, or\njuryman, is, at least in some small degree, more likely to be right than\nwrong, and have concluded that the chance of a number of persons\nconcurring in a wrong verdict is diminished, the more the number is\nincreased; so that if the judges are only made sufficiently numerous,\nthe correctness of the judgment may be reduced almost to certainty. I\nsay nothing of the disregard shown to the effect produced on the moral\nposition of the judges by multiplying their numbers; the virtual\ndestruction of their individual responsibility, and weakening of the\napplication of their minds to the subject. I remark only the fallacy of\nreasoning from a wide average, to cases necessarily differing greatly\nfrom any average. It may be true that taking all causes one with\nanother, the opinion of any one of the judges would be oftener right\nthan wrong; but the argument forgets that in all but the more simple\ncases, in all cases in which it is really of much consequence what the\ntribunal is, the proposition might probably be reversed; besides which,\nthe cause of error, whether arising from the intricacy of the case or\nfrom some common prejudice or mental infirmity, if it acted upon one\njudge, would be extremely likely to affect all the others in the same\nmanner, or at least a majority, and thus render a wrong instead of a\nright decision more probable, the more the number was increased.\n\nThese are but samples of the errors frequently committed by men who,\nhaving made themselves familiar with the difficult formul\u00e6 which algebra\naffords for the estimation of chances under suppositions of a complex\ncharacter, like better to employ those formul\u00e6 in computing what are the\nprobabilities to a person half informed about a case, than to look out\nfor means of being better informed. Before applying the doctrine of\nchances to any scientific purpose, the foundation must be laid for an\nevaluation of the chances, by possessing ourselves of the utmost\nattainable amount of positive knowledge. The knowledge required is that\nof the comparative frequency with which the different events in fact\noccur. For the purposes, therefore, of the present work, it is allowable\nto suppose, that conclusions respecting the probability of a fact of a\nparticular kind, rest on our knowledge of the proportion between the\ncases in which facts of that kind occur, and those in which they do not\noccur: this knowledge being either derived from specific experiment, or\ndeduced from our knowledge of the causes in operation which tend to\nproduce, compared with those which tend to prevent, the fact in\nquestion.\n\nSuch calculation of chances is grounded on an induction; and to render\nthe calculation legitimate, the induction must be a valid one. It is not\nless an induction, though it does not prove that the event occurs in all\ncases of a given description, but only that out of a given number of\nsuch cases, it occurs in about so many. The fraction which\nmathematicians use to designate the probability of an event, is the\nratio of these two numbers; the ascertained proportion between the\nnumber of cases in which the event occurs, and the sum of all the cases,\nthose in which it occurs and in which it does not occur taken together.\nIn playing at cross and pile, the description of cases concerned are\nthrows, and the probability of cross is one-half, because if we throw\noften enough, cross is thrown about once in every two throws. In the\ncast of a die, the probability of ace is one-sixth; not simply because\nthere are six possible throws, of which ace is one, and because we do\nnot know any reason why one should turn up rather than another; though I\nhave admitted the validity of this ground in default of a better; but\nbecause we do actually know, either by reasoning or by experience, that\nin a hundred, or a million of throws, ace is thrown about one-sixth of\nthat number, or once in six times.\n\n\n\u00a7 4. I say, \"either by reasoning or by experience;\" meaning specific\nexperience. But in estimating probabilities, it is not a matter of\nindifference from which of these two sources we derive our assurance.\nThe probability of events as calculated from their mere frequency in\npast experience, affords a less secure basis for practical guidance,\nthan their probability as deduced from an equally accurate knowledge of\nthe frequency of occurrence of their causes.\n\nThe generalization, that an event occurs in ten out of every hundred\ncases of a given description, is as real an induction as if the\ngeneralization were that it occurs in all cases. But when we arrive at\nthe conclusion by merely counting instances in actual experience, and\ncomparing the number of cases in which A has been present with the\nnumber in which it has been absent, the evidence is only that of the\nmethod of Agreement, and the conclusion amounts only to an empirical\nlaw. We can make a step beyond this when we can ascend to the causes on\nwhich the occurrence of A or its non-occurrence will depend, and form an\nestimate of the comparative frequency of the causes favourable and of\nthose unfavourable to the occurrence. These are data of a higher order,\nby which the empirical law derived from a mere numerical comparison of\naffirmative and negative instances will be either corrected or\nconfirmed, and in either case we shall obtain a more correct measure of\nprobability than is given by that numerical comparison. It has been well\nremarked that in the kind of examples by which the doctrine of chances\nis usually illustrated, that of balls in a box, the estimate of\nprobabilities is supported by reasons of causation, stronger than\nspecific experience. \"What is the reason that in a box where there are\nnine black balls and one white, we expect to draw a black ball nine\ntimes as much (in other words, nine times as often, frequency being the\ngauge of intensity in expectation) as a white? Obviously because the\nlocal conditions are nine times as favourable, because the hand may\nalight in nine places and get a black ball, while it can only alight in\none place and find a white ball; just for the same reason that we do not\nexpect to succeed in finding a friend in a crowd, the conditions in\norder that we and he should come together being many and difficult. This\nof course would not hold to the same extent were the white balls of\nsmaller size than the black, neither would the probability remain the\nsame: the larger ball would be much more likely to meet the hand.\"[19]\n\nIt is, in fact, evident, that when once causation is admitted as an\nuniversal law, our expectation of events can only be rationally grounded\non that law. To a person who recognises that every event depends on\ncauses, a thing's having happened once is a reason for expecting it to\nhappen again, only because proving that there exists, or is liable to\nexist, a cause adequate to produce it.[20] The frequency of the\nparticular event, apart from all surmise respecting its cause, can give\nrise to no other induction than that _per enumerationem simplicem_; and\nthe precarious inferences derived from this, are superseded, and\ndisappear from the field, as soon as the principle of causation makes\nits appearance there.\n\nNotwithstanding, however, the abstract superiority of an estimate of\nprobability grounded on causes, it is a fact that in almost all cases in\nwhich chances admit of estimation sufficiently precise to render their\nnumerical appreciation of any practical value, the numerical data are\nnot drawn from knowledge of the causes, but from experience of the\nevents themselves. The probabilities of life at different ages, or in\ndifferent climates; the probabilities of recovery from a particular\ndisease; the chances of the birth of male or female offspring; the\nchances of the destruction of houses or other property by fire; the\nchances of the loss of a ship in a particular voyage; are deduced from\nbills of mortality, returns from hospitals, registers of births, of\nshipwrecks, &c., that is, from the observed frequency not of the causes,\nbut of the effects. The reason is, that in all these classes of facts,\nthe causes are either not amenable to direct observation at all, or not\nwith the requisite precision, and we have no means of judging of their\nfrequency except from the empirical law afforded by the frequency of the\neffects. The inference does not the less depend on causation alone. We\nreason from an effect to a similar effect by passing through the cause.\nIf the actuary of an insurance office infers from his tables that among\na hundred persons now living, of a particular age, five on the average\nwill attain the age of seventy, his inference is legitimate, not for the\nsimple reason that this is the proportion who have lived till seventy in\ntimes past, but because the fact of their having so lived shows that\nthis is the proportion existing, at that place and time, between the\ncauses which prolong life to the age of seventy, and those tending to\nbring it to an earlier close.[21]\n\n\n\u00a7 5. From the preceding principles it is easy to deduce the\ndemonstration of that theorem of the doctrine of probabilities, which is\nthe foundation of its application to inquiries for ascertaining the\noccurrence of a given event, or the reality of an individual fact. The\nsigns or evidences by which a fact is usually proved, are some of its\nconsequences: and the inquiry hinges upon determining what cause is most\nlikely to have produced a given effect. The theorem applicable to such\ninvestigations is the Sixth Principle in Laplace's _Essai Philosophique\nsur les Probabilit\u00e9s_, which is described by him as the \"fundamental\nprinciple of that branch of the Analysis of Chances, which consists in\nascending from events to their causes.\"[22]\n\nGiven an effect to be accounted for, and there being several causes\nwhich might have produced it, but of the presence of which in the\nparticular case nothing is known; the probability that the effect was\nproduced by any one of these causes _is as the antecedent probability of\nthe cause, multiplied by the probability that the cause, if it existed,\nwould have produced the given effect_.\n\nLet M be the effect, and A, B, two causes, by either of which it might\nhave been produced. To find the probability that it was produced by the\none and not by the other, ascertain which of the two is most likely to\nhave existed, and which of them, if it did exist, was most likely to\nproduce the effect M: the probability sought is a compound of these two\nprobabilities.\n\nCASE I. Let the causes be both alike in the second respect; either A or\nB, when it exists, being supposed equally likely (or equally certain) to\nproduce M; but let A be in itself twice as likely as B to exist, that\nis, twice as frequent a phenomenon. Then it is twice as likely to have\nexisted in this case, and to have been the cause which produced M.\n\nFor, since A exists in nature twice as often as B; in any 300 cases in\nwhich one or other existed, A has existed 200 times and B 100. But\neither A or B must have existed wherever M is produced: therefore in 300\ntimes that M is produced, A was the producing cause 200 times, B only\n100, that is, in the ratio of 2 to 1. Thus, then, if the causes are\nalike in their capacity of producing the effect, the probability as to\nwhich actually produced it, is in the ratio of their antecedent\nprobabilities.\n\nCASE II. Reversing the last hypothesis, let us suppose that the causes\nare equally frequent, equally likely to have existed, but not equally\nlikely, if they did exist, to produce M: that in three times in which A\noccurs, it produces that effect twice, while B, in three times, produces\nit only once. Since the two causes are equally frequent in their\noccurrence; in every six times that either one or the other exists, A\nexists three times and B three times. A, of its three times, produces M\nin two; B, of its three times, produces M in one. Thus, in the whole six\ntimes, M is only produced thrice; but of that thrice it is produced\ntwice by A, once only by B. Consequently, when the antecedent\nprobabilities of the causes are equal, the chances that the effect was\nproduced by them are in the ratio of the probabilities that if they did\nexist they would produce the effect.\n\nCASE III. The third case, that in which the causes are unlike in both\nrespects, is solved by what has preceded. For, when a quantity depends\non two other quantities, in such a manner that while either of them\nremains constant it is proportional to the other, it must necessarily be\nproportional to the product of the two quantities, the product being the\nonly function of the two which obeys that law of variation. Therefore,\nthe probability that M was produced by either cause, is as the\nantecedent probability of the cause, multiplied by the probability that\nif it existed it would produce M. Which was to be demonstrated.\n\nOr we may prove the third case as we proved the first and second. Let A\nbe twice as frequent as B; and let them also be unequally likely, when\nthey exist, to produce M: let A produce it twice in four times, B thrice\nin four times. The antecedent probability of A is to that of B as 2 to\n1; the probabilities of their producing M are as 2 to 3; the product of\nthese ratios is the ratio of 4 to 3: and this will be the ratio of the\nprobabilities that A or B was the producing cause in the given instance.\nFor, since A is twice as frequent as B, out of twelve cases in which one\nor other exists, A exists in 8 and B in 4. But of its eight cases, A, by\nthe supposition, produces M in only 4, while B of its four cases\nproduces M in 3. M, therefore, is only produced at all in seven of the\ntwelve cases; but in four of these it is produced by A, in three by B;\nhence, the probabilities of its being produced by A and by B are as 4 to\n3, and are expressed by the fractions 4/7 and 3/7. Which was to be\ndemonstrated.\n\n\n\u00a7 6. It remains to examine the bearing of the doctrine of chances on the\npeculiar problem which occupied us in the preceding chapter, namely, how\nto distinguish coincidences which are casual from those which are the\nresult of law; from those in which the facts which accompany or follow\none another are somehow connected through causation.\n\nThe doctrine of chances affords means by which, if we knew the _average_\nnumber of coincidences to be looked for between two phenomena connected\nonly casually, we could determine how often any given deviation from\nthat average will occur by chance. If the probability of any casual\ncoincidence, considered in itself, be _1/m_, the probability that the\nsame coincidence will be repeated _n_ times in succession is _1/m^n_.\nFor example, in one throw of a die the probability of ace being 1/6; the\nprobability of throwing ace twice in succession will be 1 divided by the\nsquare of 6, or 1/36. For ace is thrown at the first throw once in six,\nor six in thirty-six times, and of those six, the die being cast again,\nace will be thrown but once; being altogether once in thirty-six times.\nThe chance of the same cast three times successively is, by a similar\nreasoning, 1/6^3 or 1/216: that is, the event will happen, on a large\naverage, only once in two hundred and sixteen throws.\n\nWe have thus a rule by which to estimate the probability that any given\nseries of coincidences arises from chance; provided we can measure\ncorrectly the probability of a single coincidence. If we can obtain an\nequally precise expression for the probability that the same series of\ncoincidences arises from causation, we should only have to compare the\nnumbers. This however, can rarely be done. Let us see what degree of\napproximation can practically be made to the necessary precision.\n\nThe question falls within Laplace's sixth principle, just demonstrated.\nThe given fact, that is to say, the series of coincidences, may have\noriginated either in a casual conjunction of causes, or in a law of\nnature. The probabilities, therefore, that the fact originated in these\ntwo modes, are as their antecedent probabilities, multiplied by the\nprobabilities that if they existed they would produce the effect. But\nthe particular combination of chances, if it occurred, or the law of\nnature if real, would certainly produce the series of coincidences. The\nprobabilities, therefore, that the coincidences are produced by the two\ncauses in question, are as the antecedent probabilities of the causes.\nOne of these, the antecedent probability of the combination of mere\nchances which would produce the given result, is an appreciable\nquantity. The antecedent probability of the other supposition may be\nsusceptible of a more or less exact estimation, according to the nature\nof the case.\n\nIn some cases, the coincidence, supposing it to be the result of\ncausation at all, must be the result of a known cause: as the succession\nof aces, if not accidental, must arise from the loading of the die. In\nsuch cases we may be able to form a conjecture as to the antecedent\nprobability of such a circumstance, from the characters of the parties\nconcerned, or other such evidence; but it would be impossible to\nestimate that probability with anything like numerical precision. The\ncounter-probability, however, that of the accidental origin of the\ncoincidence, dwindling so rapidly as it does at each new trial; the\nstage is soon reached at which the chance of unfairness in the die,\nhowever small in itself, must be greater than that of a casual\ncoincidence: and on this ground, a practical decision can generally be\ncome to without much hesitation, if there be the power of repeating the\nexperiment.\n\nWhen, however, the coincidence is one which cannot be accounted for by\nany known cause, and the connexion between the two phenomena, if\nproduced by causation, must be the result of some law of nature hitherto\nunknown; which is the case we had in view in the last chapter; then,\nthough the probability of a casual coincidence may be capable of\nappreciation, that of the counter-supposition, the existence of an\nundiscovered law of nature, is clearly unsusceptible of even an\napproximate valuation. In order to have the data which such a case would\nrequire, it would be necessary to know what proportion of all the\nindividual sequences or coexistences occurring in nature are the result\nof law, and what proportion are mere casual coincidences. It being\nevident that we cannot form any plausible conjecture as to this\nproportion, much less appreciate it numerically, we cannot attempt any\nprecise estimation of the comparative probabilities. But of this we are\nsure, that the detection of an unknown law of nature--of some previously\nunrecognised constancy of conjunction among phenomena--is no uncommon\nevent. If, therefore, the number of instances in which a coincidence is\nobserved, over and above that which would arise on the average from the\nmere concurrence of chances, be such that so great an amount of\ncoincidences from accident alone would be an extremely uncommon event;\nwe have reason to conclude that the coincidence is the effect of\ncausation, and may be received (subject to correction from further\nexperience) as an empirical law. Further than this, in point of\nprecision, we cannot go; nor, in most cases, is greater precision\nrequired, for the solution of any practical doubt.[23]\n\n\n\n\nCHAPTER XIX.\n\nOF THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.\n\n\n\u00a7 1. We have had frequent occasion to notice the inferior generality of\nderivative laws, compared with the ultimate laws from which they are\nderived. This inferiority, which affects not only the extent of the\npropositions themselves, but their degree of certainty within that\nextent, is most conspicuous in the uniformities of coexistence and\nsequence obtaining between effects which depend ultimately on different\nprimeval causes. Such uniformities will only obtain where there exists\nthe same collocation of those primeval causes. If the collocation\nvaries, though the laws themselves remain the same, a totally different\nset of derivative uniformities may, and generally will, be the result.\n\nEven where the derivative uniformity is between different effects of the\nsame cause, it will by no means obtain as universally as the law of the\ncause itself. If _a_ and _b_ accompany or succeed one another as effects\nof the cause A, it by no means follows that A is the only cause which\ncan produce them, or that if there be another cause, as B, capable of\nproducing _a_, it must produce _b_ likewise. The conjunction therefore\nof _a_ and _b_ perhaps does not hold universally, but only in the\ninstances in which _a_ arises from A. When it is produced by a cause\nother than A, _a_ and _b_ may be dissevered. Day (for example) is always\nin our experience followed by night; but day is not the cause of night;\nboth are successive effects of a common cause, the periodical passage of\nthe spectator into and out of the earth's shadow, consequent on the\nearth's rotation, and on the illuminating property of the sun. If,\ntherefore, day is ever produced by a different cause or set of causes\nfrom this, day will not, or at least may not, be followed by night. On\nthe sun's own surface, for instance, this may be the case.\n\nFinally, even when the derivative uniformity is itself a law of\ncausation (resulting from the combination of several causes), it is not\naltogether independent of collocations. If a cause supervenes, capable\nof wholly or partially counteracting the effect of any one of the\nconjoined causes, the effect will no longer conform to the derivative\nlaw. While, therefore, each ultimate law is only liable to frustration\nfrom one set of counteracting causes, the derivative law is liable to it\nfrom several. Now, the possibility of the occurrence of counteracting\ncauses which do not arise from any of the conditions involved in the law\nitself, depends on the original collocations.\n\nIt is true that (as we formerly remarked) laws of causation, whether\nultimate or derivative, are, in most cases, fulfilled even when\ncounteracted; the cause produces its effect, though that effect is\ndestroyed by something else. That the effect may be frustrated, is,\ntherefore, no objection to the universality of laws of causation. But it\nis fatal to the universality of the sequences or coexistences of\neffects, which compose the greater part of the derivative laws flowing\nfrom laws of causation. When, from the law of a certain combination of\ncauses, there results a certain order in the effects; as from the\ncombination of a single sun with the rotation of an opaque body round\nits axis, there results, on the whole surface of that opaque body, an\nalternation of day and night; then if we suppose one of the combined\ncauses counteracted, the rotation stopped, the sun extinguished, or a\nsecond sun superadded, the truth of that particular law of causation is\nin no way affected; it is still true that one sun shining on an opaque\nrevolving body will alternately produce day and night; but since the sun\nno longer does shine on such a body, the derivative uniformity, the\nsuccession of day and night on the given planet, is no longer true.\nThose derivative uniformities, therefore, which are not laws of\ncausation, are (except in the rare case of their depending on one cause\nalone, not on a combination of causes,) always more or less contingent\non collocations; and are hence subject to the characteristic infirmity\nof empirical laws, that of being admissible only where the collocations\nare known by experience to be such as are requisite for the truth of the\nlaw, that is, only within the conditions of time and place confirmed by\nactual observation.\n\n\n\u00a7 2. This principle, when stated in general terms, seems clear and\nindisputable; yet many of the ordinary judgments of mankind, the\npropriety of which is not questioned, have at least the semblance of\nbeing inconsistent with it. On what grounds, it may be asked, do we\nexpect that the sun will rise to-morrow? To-morrow is beyond the limits\nof time comprehended in our observations. They have extended over some\nthousands of years past, but they do not include the future. Yet we\ninfer with confidence that the sun will rise to-morrow; and nobody\ndoubts that we are entitled to do so. Let us consider what is the\nwarrant for this confidence.\n\nIn the example in question, we know the causes on which the derivative\nuniformity depends. They are, the sun giving out light, the earth in a\nstate of rotation and intercepting light. The induction which shows\nthese to be the real causes, and not merely prior effects of a common\ncause, being complete; the only circumstances which could defeat the\nderivative law are such as would destroy or counteract one or other of\nthe combined causes. While the causes exist, and are not counteracted,\nthe effect will continue. If they exist and are not counteracted\nto-morrow, the sun will rise to-morrow.\n\nSince the causes, namely the sun and the earth, the one in the state of\ngiving out light, the other in a state of rotation, will exist until\nsomething destroys them; all depends on the probabilities of their\ndestruction, or of their counteraction. We know by observation (omitting\nthe inferential proofs of an existence for thousands of ages anterior),\nthat these phenomena have continued for (say) five thousand years.\nWithin that time there has existed no cause sufficient to diminish them\nappreciably; nor which has counteracted their effect in any appreciable\ndegree. The chance, therefore, that the sun may not rise to-morrow,\namounts to the chance that some cause, which has not manifested itself\nin the smallest degree during five thousand years, will exist to-morrow\nin such intensity as to destroy the sun or the earth, the sun's light or\nthe earth's rotation, or to produce an immense disturbance in the effect\nresulting from those causes.\n\nNow, if such a cause will exist to-morrow, or at any future time, some\ncause, proximate or remote, of that cause must exist now, and must have\nexisted during the whole of the five thousand years. If, therefore, the\nsun do not rise to-morrow, it will be because some cause has existed,\nthe effects of which though during five thousand years they have not\namounted to a perceptible quantity, will in one day become overwhelming.\nSince this cause has not been recognised during such an interval of\ntime, by observers stationed on our earth, it must, if it exist, be\neither some agent whose effects develop themselves gradually and very\nslowly, or one which existed in regions beyond our observation, and is\nnow on the point of arriving in our part of the universe. Now all causes\nwhich we have experience of, act according to laws incompatible with the\nsupposition that their effects, after accumulating so slowly as to be\nimperceptible for five thousand years, should start into immensity in a\nsingle day. No mathematical law of proportion between an effect and the\nquantity or relations of its cause, could produce such contradictory\nresults. The sudden development of an effect of which there was no\nprevious trace, always arises from the coming together of several\ndistinct causes, not previously conjoined; but if such sudden\nconjunction is destined to take place, the causes, or _their_ causes,\nmust have existed during the entire five thousand years; and their not\nhaving once come together during that period, shows how rare that\nparticular combination is. We have, therefore, the warrant of a rigid\ninduction for considering it probable, in a degree undistinguishable\nfrom certainty, that the known conditions requisite for the sun's rising\nwill exist to-morrow.\n\n\n\u00a7 3. But this extension of derivative laws, not causative, beyond the\nlimits of observation, can only be to _adjacent_ cases. If instead of\nto-morrow we had said this day twenty thousand years, the inductions\nwould have been anything but conclusive. That a cause which, in\nopposition to very powerful causes, produced no perceptible effect\nduring five thousand years, should produce a very considerable one by\nthe end of twenty thousand, has nothing in it which is not in conformity\nwith our experience of causes. We know many agents, the effect of which\nin a short period does not amount to a perceptible quantity, but by\naccumulating for a much longer period becomes considerable. Besides,\nlooking at the immense multitude of the heavenly bodies, their vast\ndistances, and the rapidity of the motion of such of them as are known\nto move, it is a supposition not at all contradictory to experience that\nsome body may be in motion towards us, or we towards it, within the\nlimits of whose influence we have not come during five thousand years,\nbut which in twenty thousand more may be producing effects upon us of\nthe most extraordinary kind. Or the fact which is capable of preventing\nsunrise may be, not the cumulative effect of one cause, but some new\ncombination of causes; and the chances favourable to that combination,\nthough they have not produced it once in five thousand years, may\nproduce it once in twenty thousand. So that the inductions which\nauthorize us to expect future events, grow weaker and weaker the further\nwe look into the future, and at length become inappreciable.\n\nWe have considered the probabilities of the sun's rising to-morrow, as\nderived from the real laws, that is, from the laws of the causes on\nwhich that uniformity is dependent. Let us now consider how the matter\nwould have stood if the uniformity had been known only as an empirical\nlaw; if we had not been aware that the sun's light, and the earth's\nrotation (or the sun's motion), were the causes on which the periodical\noccurrence of daylight depends. We could have extended this empirical\nlaw to cases adjacent in time, though not to so great a distance of time\nas we can now. Having evidence that the effects had remained unaltered\nand been punctually conjoined for five thousand years, we could infer\nthat the unknown causes on which the conjunction is dependent had\nexisted undiminished and uncounteracted during the same period. The same\nconclusions, therefore, would follow as in the preceding case; except\nthat we should only know that during five thousand years nothing had\noccurred to defeat perceptibly this particular effect; while, when we\nknow the causes, we have the additional assurance, that during that\ninterval no such change has been noticeable in the causes themselves, as\nby any degree of multiplication or length of continuance could defeat\nthe effect.\n\nTo this must be added, that when we know the causes, we may be able to\njudge whether there exists any known cause capable of counteracting\nthem; while as long as they are unknown, we cannot be sure but that if\nwe did know them, we could predict their destruction from causes\nactually in existence. A bedridden savage, who had never seen the\ncataract of Niagara, but who lived within hearing of it, might imagine\nthat the sound he heard would endure for ever; but if he knew it to be\nthe effect of a rush of waters over a barrier of rock which is\nprogressively wearing away, he would know that within a number of ages\nwhich may be calculated, it will be heard no more. In proportion,\ntherefore, to our ignorance of the causes on which the empirical law\ndepends, we can be less assured that it will continue to hold good; and\nthe farther we look into futurity, the less improbable is it that some\none of the causes, whose coexistence gives rise to the derivative\nuniformity, may be destroyed or counteracted. With every prolongation of\ntime, the chances multiply of such an event, that is to say, its\nnon-occurrence hitherto becomes a less guarantee of its not occurring\nwithin the given time. If, then, it is only to cases which in point of\ntime are adjacent (or nearly adjacent) to those which we have actually\nobserved, that _any_ derivative law, not of causation, can be extended\nwith an assurance equivalent to certainty, much more is this true of a\nmerely empirical law. Happily, for the purposes of life it is to such\ncases alone that we can almost ever have occasion to extend them.\n\nIn respect of place, it might seem that a merely empirical law could\nnot be extended even to adjacent cases; that we could have no assurance\nof its being true in any place where it has not been specially observed.\nThe past duration of a cause is a guarantee for its future existence,\nunless something occurs to destroy it; but the existence of a cause in\none or any number of places, is no guarantee for its existence in any\nother place, since there is no uniformity in the collocations of\nprimeval causes. When, therefore, an empirical law is extended beyond\nthe local limits within which it has been found true by observation, the\ncases to which it is thus extended must be such as are presumably within\nthe influence of the same individual agents. If we discover a new planet\nwithin the known bounds of the solar system (or even beyond those\nbounds, but indicating its connexion with the system by revolving round\nthe sun), we may conclude, with great probability, that it revolves on\nits axis. For all the known planets do so; and this uniformity points to\nsome common cause, antecedent to the first records of astronomical\nobservation: and though the nature of this cause can only be matter of\nconjecture, yet if it be, as is not unlikely, and as Laplace's theory\nsupposes, not merely the same kind of cause, but the same individual\ncause (such as an impulse given to all the bodies at once), that cause,\nacting at the extreme points of the space occupied by the sun and\nplanets, is likely, unless defeated by some counteracting cause, to have\nacted at every intermediate point, and probably somewhat beyond; and\ntherefore acted, in all probability, upon the supposed newly-discovered\nplanet.\n\nWhen, therefore, effects which are always found conjoined, can be traced\nwith any probability to an identical (and not merely a similar) origin,\nwe may with the same probability extend the empirical law of their\nconjunction to all places within the extreme local boundaries within\nwhich the fact has been observed; subject to the possibility of\ncounteracting causes in some portion of the field. Still more\nconfidently may we do so when the law is not merely empirical; when the\nphenomena which we find conjoined are effects of ascertained causes,\nfrom the laws of which the conjunction of their effects is deducible. In\nthat case, we may both extend the derivative uniformity over a larger\nspace, and with less abatement for the chance of counteracting causes.\nThe first, because instead of the local boundaries of our observation of\nthe fact itself, we may include the extreme boundaries of the\nascertained influence of its causes. Thus the succession of day and\nnight, we know, holds true of all the bodies of the solar system except\nthe sun itself; but we know this only because we are acquainted with the\ncauses: if we were not, we could not extend the proposition beyond the\norbits of the earth and moon, at both extremities of which we have the\nevidence of observation for its truth. With respect to the probability\nof counteracting causes, it has been seen that this calls for a greater\nabatement of confidence, in proportion to our ignorance of the causes on\nwhich the phenomena depend. On both accounts, therefore, a derivative\nlaw which we know how to resolve, is susceptible of a greater extension\nto cases adjacent in place, than a merely empirical law.\n\n\n\n\nCHAPTER XX.\n\nOF ANALOGY.\n\n\n\u00a7 1. The word Analogy, as the name of a mode of reasoning, is generally\ntaken for some kind of argument supposed to be of an inductive nature,\nbut not amounting to a complete induction. There is no word, however,\nwhich is used more loosely, or in a greater variety of senses, than\nAnalogy. It sometimes stands for arguments which may be examples of the\nmost rigorous Induction. Archbishop Whately, for instance, following\nFerguson and other writers, defines Analogy conformably to its primitive\nacceptation, that which was given to it by mathematicians, Resemblance\nof Relations. In this sense, when a country which has sent out colonies\nis termed the mother country, the expression is analogical, signifying\nthat the colonies of a country stand in the same _relation_ to her in\nwhich children stand to their parents. And if any inference be drawn\nfrom this resemblance of relations, as, for instance, that obedience or\naffection is due from colonies to the mother country, this is called\nreasoning by analogy. Or if it be argued that a nation is most\nbeneficially governed by an assembly elected by the people, from the\nadmitted fact that other associations for a common purpose, such as\njoint-stock companies, are best managed by a committee chosen by the\nparties interested; this, too, is an argument from analogy in the\npreceding sense, because its foundation is, not that a nation is like a\njoint stock company, or Parliament like a board of directors, but that\nParliament stands in the same _relation_ to the nation in which a board\nof directors stands to a joint stock company. Now, in an argument of\nthis nature, there is no inherent inferiority of conclusiveness. Like\nother arguments from resemblance, it may amount to nothing, or it may be\na perfect and conclusive induction. The circumstance in which the two\ncases resemble, may be capable of being shown to be the _material_\ncircumstance; to be that on which all the consequences, necessary to be\ntaken into account in the particular discussion, depend. In the example\nlast given, the resemblance is one of relation; the _fundamentum\nrelationis_ being the management by a few persons, of affairs in which a\nmuch greater number are interested along with them. Now, some may\ncontend that this circumstance which is common to the two cases, and the\nvarious consequences which follow from it, have the chief share in\ndetermining all the effects which make up what we term good or bad\nadministration. If they can establish this, their argument has the force\nof a rigorous induction; if they cannot, they are said to have failed in\nproving the analogy between the two cases; a mode of speech which\nimplies that when the analogy can be proved, the argument founded on it\ncannot be resisted.\n\n\n\u00a7 2. It is on the whole more usual, however, to extend the name of\nanalogical evidence to arguments from any sort of resemblance, provided\nthey do not amount to a complete induction: without peculiarly\ndistinguishing resemblance of relations. Analogical reasoning, in this\nsense, may be reduced to the following formula:--Two things resemble\neach other in one or more respects; a certain proposition is true of the\none; therefore it is true of the other. But we have nothing here by\nwhich to discriminate analogy from induction, since this type will serve\nfor all reasoning from experience. In the strictest induction, equally\nwith the faintest analogy, we conclude because A resembles B in one or\nmore properties, that it does so in a certain other property. The\ndifference is, that in the case of a complete induction it has been\npreviously shown, by due comparison of instances, that there is an\ninvariable conjunction between the former property or properties and the\nlatter property; but in what is called analogical reasoning, no such\nconjunction has been made out. There have been no opportunities of\nputting in practice the Method of Difference, or even the Method of\nAgreement; but we conclude (and that is all which the argument of\nanalogy amounts to) that a fact _m_, known to be true of A, is more\nlikely to be true of B if B agrees with A in some of its properties\n(even though no connexion is known to exist between _m_ and those\nproperties), than if no resemblance at all could be traced between B and\nany other thing known to possess the attribute _m_.\n\nTo this argument it is of course requisite, that the properties common\nto A with B shall be merely not known to be connected with _m_; they\nmust not be properties known to be unconnected with it. If, either by\nprocesses of elimination, or by deduction from previous knowledge of the\nlaws of the properties in question, it can be concluded that they have\nnothing to do with _m_, the argument of analogy is put out of court. The\nsupposition must be that _m_ is an effect really dependent on some\nproperty of A, but we know not on which. We cannot point out any of the\nproperties of A, which is the cause of _m_, or united with it by any\nlaw. After rejecting all which we know to have nothing to do with it,\nthere remain several between which we are unable to decide: of which\nremaining properties, B possesses one or more. This accordingly, we\nconsider as affording grounds, of more or less strength, for concluding\nby analogy that B possesses the attribute _m_.\n\nThere can be no doubt that every such resemblance which can be pointed\nout between B and A, affords some degree of probability, beyond what\nwould otherwise exist, in favour of the conclusion drawn from it. If B\nresembled A in all its ultimate properties, its possessing the attribute\n_m_ would be a certainty, not a probability: and every resemblance which\ncan be shown to exist between them, places it by so much the nearer to\nthat point. If the resemblance be in an ultimate property, there will be\nresemblance in all the derivative properties dependent on that ultimate\nproperty, and of these _m_ may be one. If the resemblance be in a\nderivative property, there is reason to expect resemblance in the\nultimate property on which it depends, and in the other derivative\nproperties dependent on the same ultimate property. Every resemblance\nwhich can be shown to exist, affords ground for expecting an indefinite\nnumber of other resemblances: the particular resemblance sought will,\ntherefore, be oftener found among things thus known to resemble, than\namong things between which we know of no resemblance.[24]\n\nFor example, I might infer that there are probably inhabitants in the\nmoon, because there are inhabitants on the earth, in the sea, and in the\nair: and this is the evidence of analogy. The circumstance of having\ninhabitants is here assumed not to be an ultimate property, but (as is\nreasonable to suppose) a consequence of other properties; and depending,\ntherefore, in the case of the earth, on some of its properties as a\nportion of the universe, but on which of those properties we know not.\nNow the moon resembles the earth in being a solid, opaque, nearly\nspherical substance, appearing to contain, or to have contained, active\nvolcanoes; receiving heat and light from the sun, in about the same\nquantity as our earth; revolving on its axis; composed of materials\nwhich gravitate, and obeying all the various laws resulting from that\nproperty. And I think no one will deny that if this were all that was\nknown of the moon, the existence of inhabitants in that luminary would\nderive from these various resemblances to the earth, a greater degree of\nprobability than it would otherwise have: though the amount of the\naugmentation it would be useless to attempt to estimate.\n\nIf, however, every resemblance proved between B and A, in any point not\nknown to be immaterial with respect to _m_, forms some additional\nreason for presuming that B has the attribute _m_; it is clear, _\u00e8\ncontra_, that every dissimilarity which can be proved between them,\nfurnishes a counter-probability of the same nature on the other side. It\nis not indeed unusual that different ultimate properties should, in some\nparticular instances, produce the same derivative property; but on the\nwhole it is certain that things which differ in their ultimate\nproperties, will differ at least as much in the aggregate of their\nderivative properties, and that the differences which are unknown will\non the average of cases bear some proportion to those which are known.\nThere will, therefore, be a competition between the known points of\nagreement and the known points of difference in A and B; and according\nas the one or the other may be deemed to preponderate, the probability\nderived from analogy will be for or against B's having the property _m_.\nThe moon, for instance, agrees with the earth in the circumstances\nalready mentioned; but differs in being smaller, in having its surface\nmore unequal, and apparently volcanic throughout, in having, at least on\nthe side next the earth, no atmosphere sufficient to refract light, no\nclouds, and (it is therefore concluded) no water. These differences,\nconsidered merely as such, might perhaps balance the resemblances, so\nthat analogy would afford no presumption either way. But considering\nthat some of the circumstances which are wanting on the moon are among\nthose which, on the earth, are found to be indispensable conditions of\nanimal life, we may conclude that if that phenomenon does exist in the\nmoon, (or at all events on the nearer side,) it must be as an effect of\ncauses totally different from those on which it depends here; as a\nconsequence, therefore, of the moon's differences from the earth, not of\nthe points of agreement. Viewed in this light, all the resemblances\nwhich exist become presumptions against, not in favour of, the moon's\nbeing inhabited. Since life cannot exist there in the manner in which it\nexists here, the greater the resemblance of the lunar world to the\nterrestrial in other respects, the less reason we have to believe that\nit can contain life.\n\nThere are, however, other bodies in our system, between which and the\nearth there is a much closer resemblance; which possess an atmosphere,\nclouds, consequently water (or some fluid analogous to it), and even\ngive strong indications of snow in their polar regions; while the cold,\nor heat, though differing greatly on the average from ours, is, in some\nparts at least of those planets, possibly not more extreme than in some\nregions of our own which are habitable. To balance these agreements, the\nascertained differences are chiefly in the average light and heat,\nvelocity of rotation, density of material, intensity of gravity, and\nsimilar circumstances of a secondary kind. With regard to these planets,\ntherefore, the argument of analogy gives a decided preponderance in\nfavour of their resembling the earth in any of its derivative\nproperties, such as that of having inhabitants; though, when we consider\nhow immeasurably multitudinous are those of their properties which we\nare entirely ignorant of, compared with the few which we know, we can\nattach but trifling weight to any considerations of resemblance in which\nthe known elements bear so inconsiderable a proportion to the unknown.\n\nBesides the competition between analogy and diversity, there may be a\ncompetition of conflicting analogies. The new case may be similar in\nsome of its circumstances to cases in which the fact _m_ exists, but in\nothers to cases in which it is known not to exist. Amber has some\nproperties in common with vegetable, others with mineral products. A\npainting of unknown origin, may resemble, in certain of its characters,\nknown works of a particular master, but in others it may as strikingly\nresemble those of some other painter. A vase may bear some analogy to\nworks of Grecian, and some to those of Etruscan, or Egyptian art. We are\nof course supposing that it does not possess any quality which has been\nascertained, by a sufficient induction, to be a conclusive mark either\nof the one or of the other.\n\n\n\u00a7 3. Since the value of an analogical argument inferring one resemblance\nfrom other resemblances without any antecedent evidence of a connexion\nbetween them, depends on the extent of ascertained resemblance, compared\nfirst with the amount of ascertained difference, and next with the\nextent of the unexplored region of unascertained properties; it follows\nthat where the resemblance is very great, the ascertained difference\nvery small, and our knowledge of the subject-matter tolerably extensive,\nthe argument from analogy may approach in strength very near to a valid\ninduction. If, after much observation of B, we find that it agrees with\nA in nine out of ten of its known properties, we may conclude with a\nprobability of nine to one, that it will possess any given derivative\nproperty of A. If we discover, for example, an unknown animal or plant,\nresembling closely some known one in the greater number of the\nproperties we observe in it, but differing in some few, we may\nreasonably expect to find in the unobserved remainder of its properties,\na general agreement with those of the former; but also a difference\ncorresponding proportionately to the amount of observed diversity.\n\nIt thus appears that the conclusions derived from analogy are only of\nany considerable value, when the case to which we reason is an adjacent\ncase; adjacent, not as before, in place or time, but in circumstances.\nIn the case of effects of which the causes are imperfectly or not at all\nknown, when consequently the observed order of their occurrence amounts\nonly to an empirical law, it often happens that the conditions which\nhave coexisted whenever the effect was observed, have been very\nnumerous. Now if a new case presents itself, in which all these\nconditions do not exist, but the far greater part of them do, some one\nor a few only being wanting, the inference that the effect will occur,\nnotwithstanding this deficiency of complete resemblance to the cases in\nwhich it has been observed, may, though of the nature of analogy,\npossess a high degree of probability. It is hardly necessary to add\nthat, however considerable this probability may be, no competent\ninquirer into nature will rest satisfied with it when a complete\ninduction is attainable; but will consider the analogy as a mere\nguide-post, pointing out the direction in which more rigorous\ninvestigations should be prosecuted.\n\nIt is in this last respect that considerations of analogy have the\nhighest scientific value. The cases in which analogical evidence affords\nin itself any very high degree of probability, are, as we have observed,\nonly those in which the resemblance is very close and extensive; but\nthere is no analogy, however faint, which may not be of the utmost value\nin suggesting experiments or observations that may lead to more positive\nconclusions. When the agents and their effects are out of the reach of\nfurther observation and experiment, as in the speculations already\nalluded to respecting the moon and planets, such slight probabilities\nare no more than an interesting theme for the pleasant exercise of\nimagination; but any suspicion, however slight, that sets an ingenious\nperson at work to contrive an experiment, or affords a reason for trying\none experiment rather than another, may be of the greatest benefit to\nscience.\n\nOn this ground, though I cannot accept as positive doctrines any of\nthose scientific hypotheses which are unsusceptible of being ultimately\nbrought to the test of actual induction, such, for instance, as the two\ntheories of light, the emission theory of the last century, and the\nundulatory theory which predominates in the present, I am yet unable to\nagree with those who consider such hypotheses to be worthy of entire\ndisregard. As is well said by Hartley (and concurred in by a thinker in\ngeneral so diametrically opposed to Hartley's opinions as Dugald\nStewart), \"any hypothesis which has so much plausibility as to explain a\nconsiderable number of facts, helps us to digest these facts in proper\norder, to bring new ones to light, and make _experimenta crucis_ for the\nsake of future inquirers.\"[25] If an hypothesis both explains known\nfacts, and has led to the prediction of others previously unknown, and\nsince verified by experience, the laws of the phenomenon which is the\nsubject of inquiry must bear at least a great similarity to those of the\nclass of phenomena to which the hypothesis assimilates it; and since the\nanalogy which extends so far may probably extend farther, nothing is\nmore likely to suggest experiments tending to throw light upon the real\nproperties of the phenomenon, than the following out such an hypothesis.\nBut to this end it is by no means necessary that the hypothesis be\nmistaken for a scientific truth. On the contrary, that illusion is in\nthis respect, as in every other, an impediment to the progress of real\nknowledge, by leading inquirers to restrict themselves arbitrarily to\nthe particular hypothesis which is most accredited at the time, instead\nof looking out for every class of phenomena between the laws of which\nand those of the given phenomenon any analogy exists, and trying all\nsuch experiments as may tend to the discovery of ulterior analogies\npointing in the same direction.\n\n\n\n\nCHAPTER XXI.\n\nOF THE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION.\n\n\n\u00a7 1. We have now completed our review of the logical processes by which\nthe laws, or uniformities, of the sequence of phenomena, and those\nuniformities in their coexistence which depend on the laws of their\nsequence, are ascertained or tested. As we recognised in the\ncommencement, and have been enabled to see more clearly in the progress\nof the investigation, the basis of all these logical operations is the\nlaw of causation. The validity of all the Inductive Methods depends on\nthe assumption that every event, or the beginning of every phenomenon,\nmust have some cause; some antecedent, on the existence of which it is\ninvariably and unconditionally consequent. In the Method of Agreement\nthis is obvious; that method avowedly proceeding on the supposition that\nwe have found the true cause as soon as we have negatived every other.\nThe assertion is equally true of the Method of Difference. That method\nauthorizes us to infer a general law from two instances; one, in which A\nexists together with a multitude of other circumstances, and B follows;\nanother, in which, A being removed, and all other circumstances\nremaining the same, B is prevented. What, however, does this prove? It\nproves that B, in the particular instance, cannot have had any other\ncause than A; but to conclude from this that A was the cause, or that A\nwill on other occasions be followed by B, is only allowable on the\nassumption that B must have some cause; that among its antecedents in\nany single instance in which it occurs, there must be one which has the\ncapacity of producing it at other times. This being admitted, it is seen\nthat in the case in question that antecedent can be no other than A;\nbut, that if it be no other than A it must be A, is not proved, by these\ninstances at least, but taken for granted. There is no need to spend\ntime in proving that the same thing is true of the other Inductive\nMethods. The universality of the law of causation is assumed in them\nall.\n\nBut is this assumption warranted? Doubtless (it may be said) _most_\nphenomena are connected as effects with some antecedent or cause, that\nis, are never produced unless some assignable fact has preceded them;\nbut the very circumstance that complicated processes of induction are\nsometimes necessary, shows that cases exist in which this regular order\nof succession is not apparent to our unaided apprehension. If, then, the\nprocesses which bring these cases within the same category with the\nrest, require that we should assume the universality of the very law\nwhich they do not at first sight appear to exemplify, is not this a\n_petitio principii_? Can we prove a proposition, by an argument which\ntakes it for granted? And if not so proved, on what evidence does it\nrest?\n\nFor this difficulty, which I have purposely stated in the strongest\nterms it will admit of, the school of metaphysicians who have long\npredominated in this country find a ready salvo. They affirm, that the\nuniversality of causation is a truth which we cannot help believing;\nthat the belief in it is an instinct, one of the laws of our believing\nfaculty. As the proof of this, they say, and they have nothing else to\nsay, that everybody does believe it; and they number it among the\npropositions, rather numerous in their catalogue, which may be logically\nargued against, and perhaps cannot be logically proved, but which are of\nhigher authority than logic, and so essentially inherent in the human\nmind, that even he who denies them in speculation, shows by his habitual\npractice that his arguments make no impression upon himself.\n\nInto the merits of this question, considered as one of psychology, it\nwould be foreign to my purpose to enter here: but I must protest against\nadducing, as evidence of the truth of a fact in external nature, the\ndisposition, however strong or however general, of the human mind to\nbelieve it. Belief is not proof, and does not dispense with the\nnecessity of proof. I am aware, that to ask for evidence of a\nproposition which we are supposed to believe instinctively, is to expose\noneself to the charge of rejecting the authority of the human faculties;\nwhich of course no one can consistently do, since the human faculties\nare all which any one has to judge by: and inasmuch as the meaning of\nthe word evidence is supposed to be, something which when laid before\nthe mind, induces it to believe; to demand evidence when the belief is\nensured by the mind's own laws, is supposed to be appealing to the\nintellect against the intellect. But this, I apprehend, is a\nmisunderstanding of the nature of evidence. By evidence is not meant\nanything and everything which produces belief. There are many things\nwhich generate belief besides evidence. A mere strong association of\nideas often causes a belief so intense as to be unshakeable by\nexperience or argument. Evidence is not that which the mind does or must\nyield to, but that which it ought to yield to, namely, that, by yielding\nto which, its belief is kept conformable to fact. There is no appeal\nfrom the human faculties generally, but there is an appeal from one\nhuman faculty to another; from the judging faculty, to those which take\ncognizance of fact, the faculties of sense and consciousness. The\nlegitimacy of this appeal is admitted whenever it is allowed that our\njudgments ought to be conformable to fact. To say that belief suffices\nfor its own justification is making opinion the test of opinion; it is\ndenying the existence of any outward standard, the conformity of an\nopinion to which constitutes its truth. We call one mode of forming\nopinions right and another wrong, because the one does, and the other\ndoes not, tend to make the opinion agree with the fact--to make people\nbelieve what really is, and expect what really will be. Now a mere\ndisposition to believe, even if supposed instinctive, is no guarantee\nfor the truth of the thing believed. If, indeed, the belief ever\namounted to an irresistible necessity, there would then be no _use_ in\nappealing from it, because there would be no possibility of altering it.\nBut even then the truth of the belief would not follow; it would only\nfollow that mankind were under a permanent necessity of believing what\nmight possibly not be true; in other words, that a case might occur in\nwhich our senses or consciousness, if they could be appealed to, might\ntestify one thing, and our reason believe another. But in fact there is\nno such permanent necessity. There is no proposition of which it can be\nasserted that every human mind must eternally and irrevocably believe\nit. Many of the propositions of which this is most confidently stated,\ngreat numbers of human beings have disbelieved. The things which it has\nbeen supposed that nobody could possibly help believing, are\ninnumerable; but no two generations would make out the same catalogue of\nthem. One age or nation believes implicitly what to another seems\nincredible and inconceivable; one individual has not a vestige of a\nbelief which another deems to be absolutely inherent in humanity. There\nis not one of these supposed instinctive beliefs which is really\ninevitable. It is in the power of every one to cultivate habits of\nthought which make him independent of them. The habit of philosophical\nanalysis, (of which it is the surest effect to enable the mind to\ncommand, instead of being commanded by, the laws of the merely passive\npart of its own nature,) by showing to us that things are not\nnecessarily connected in fact because their ideas are connected in our\nminds, is able to loosen innumerable associations which reign\ndespotically over the undisciplined or early-prejudiced mind. And this\nhabit is not without power even over those associations which the school\nof which I have been speaking regard as connate and instinctive. I am\nconvinced that any one accustomed to abstraction and analysis, who will\nfairly exert his faculties for the purpose, will, when his imagination\nhas once learnt to entertain the notion, find no difficulty in\nconceiving that in some one for instance of the many firmaments into\nwhich sidereal astronomy now divides the universe, events may succeed\none another at random, without any fixed law; nor can anything in our\nexperience, or in our mental nature, constitute a sufficient, or indeed\nany, reason for believing that this is nowhere the case.\n\nWere we to suppose (what it is perfectly possible to imagine) that the\npresent order of the universe were brought to an end, and that a chaos\nsucceeded in which there was no fixed succession of events, and the past\ngave no assurance of the future; if a human being were miraculously kept\nalive to witness this change, he surely would soon cease to believe in\nany uniformity, the uniformity itself no longer existing. If this be\nadmitted, the belief in uniformity either is not an instinct, or it is\nan instinct conquerable, like all other instincts, by acquired\nknowledge.\n\nBut there is no need to speculate on what might be, when we have\npositive and certain knowledge of what has been. It is not true as a\nmatter of fact, that mankind have always believed that all the\nsuccessions of events were uniform and according to fixed laws. The\nGreek philosophers, not even excepting Aristotle, recognised Chance and\nSpontaneity ([Greek: tych\u00ea] and [Greek: to automaton]) as among the\nagents in nature; in other words, they believed that to that extent\nthere was no guarantee that the past had been similar to itself, or that\nthe future would resemble the past. Even now a full half of the\nphilosophical world, including the very same metaphysicians who contend\nmost for the instinctive character of the belief in uniformity, consider\none important class of phenomena, volitions, to be an exception to the\nuniformity, and not governed by a fixed law.[26]\n\n\n\u00a7 2. As was observed in a former place,[27] the belief we entertain in\nthe universality, throughout nature, of the law of cause and effect, is\nitself an instance of induction; and by no means one of the earliest\nwhich any of us, or which mankind in general, can have made. We arrive\nat this universal law, by generalization from many laws of inferior\ngenerality. We should never have had the notion of causation (in the\nphilosophical meaning of the term) as a condition of all phenomena,\nunless many cases of causation, or in other words, many partial\nuniformities of sequence, had previously become familiar. The more\nobvious of the particular uniformities suggest, and give evidence of,\nthe general uniformity, and the general uniformity, once established,\nenables us to prove the remainder of the particular uniformities of\nwhich it is made up. As, however, all rigorous processes of induction\npresuppose the general uniformity, our knowledge of the particular\nuniformities from which it was first inferred was not, of course,\nderived from rigorous induction, but from the loose and uncertain mode\nof induction _per enumerationem simplicem_: and the law of universal\ncausation, being collected from results so obtained, cannot itself rest\non any better foundation.\n\nIt would seem, therefore, that induction _per enumerationem simplicem_\nnot only is not necessarily an illicit logical process, but is in\nreality the only kind of induction possible; since the more elaborate\nprocess depends for its validity on a law, itself obtained in that\ninartificial mode. Is there not then an inconsistency in contrasting the\nlooseness of one method with the rigidity of another, when that other is\nindebted to the looser method for its own foundation?\n\nThe inconsistency, however, is only apparent. Assuredly, if induction by\nsimple enumeration were an invalid process, no process grounded on it\ncould be valid; just as no reliance could be placed on telescopes, if we\ncould not trust our eyes. But though a valid process, it is a fallible\none, and fallible in very different degrees: if therefore we can\nsubstitute for the more fallible forms of the process, an operation\ngrounded on the same process in a less fallible form, we shall have\neffected a very material improvement. And this is what scientific\ninduction does.\n\nA mode of concluding from experience must be pronounced untrustworthy,\nwhen subsequent experience refuses to confirm it. According to this\ncriterion, induction by simple enumeration--in other words,\ngeneralization of an observed fact from the mere absence of any known\ninstance to the contrary--affords in general a precarious and unsafe\nground of assurance; for such generalizations are incessantly\ndiscovered, on further experience, to be false. Still, however, it\naffords some assurance, sufficient, in many cases, for the ordinary\nguidance of conduct. It would be absurd to say, that the generalizations\narrived at by mankind in the outset of their experience, such as these,\nFood nourishes, Fire burns, Water drowns, were unworthy of reliance.[28]\nThere is a scale of trustworthiness in the results of the original\nunscientific Induction; and on this diversity (as observed in the fourth\nchapter of the present book) depend the rules for the improvement of the\nprocess. The improvement consists in correcting one of these\ninartificial generalizations by means of another. As has been already\npointed out, this is all that art can do. To test a generalization, by\nshowing that it either follows from, or conflicts with, some stronger\ninduction, some generalization resting on a broader foundation of\nexperience, is the beginning and end of the logic of Induction.\n\n\n\u00a7 3. Now the precariousness of the method of simple enumeration is in an\ninverse ratio to the largeness of the generalization. The process is\ndelusive and insufficient, exactly in proportion as the subject-matter\nof the observation is special and limited in extent. As the sphere\nwidens, this unscientific method becomes less and less liable to\nmislead; and the most universal class of truths, the law of causation\nfor instance, and the principles of number and of geometry, are duly and\nsatisfactorily proved by that method alone, nor are they susceptible of\nany other proof.\n\nWith respect to the whole class of generalizations of which we have\nrecently treated, the uniformities which depend on causation, the truth\nof the remark just made follows by obvious inference from the principles\nlaid down in the preceding chapters. When a fact has been observed a\ncertain number of times to be true, and is not in any instance known to\nbe false; if we at once affirm that fact as an universal truth or law of\nnature, without testing it by any of the four methods of induction, nor\ndeducing it from other known laws, we shall in general err grossly: but\nwe are perfectly justified in affirming it as an empirical law, true\nwithin certain limits of time, place, and circumstance, provided the\nnumber of coincidences be greater than can with any probability be\nascribed to chance. The reason for not extending it beyond those limits\nis, that the fact of its holding true within them may be a consequence\nof collocations, which cannot be concluded to exist in one place because\nthey exist in another; or may be dependent on the accidental absence of\ncounteracting agencies, which any variation of time, or the smallest\nchange of circumstances, may possibly bring into play. If we suppose,\nthen, the subject-matter of any generalization to be so widely diffused\nthat there is no time, no place, and no combination of circumstances,\nbut must afford an example either of its truth or of its falsity, and if\nit be never found otherwise than true, its truth cannot depend on any\ncollocations, unless such as exist at all times and places; nor can it\nbe frustrated by any counteracting agencies, unless by such as never\nactually occur. It is, therefore, an empirical law coextensive with all\nhuman experience; at which point the distinction between empirical laws\nand laws of nature vanishes, and the proposition takes its place among\nthe most firmly established as well as largest truths accessible to\nscience.\n\nNow, the most extensive in its subject-matter of all generalizations\nwhich experience warrants, respecting the sequences and coexistences of\nphenomena, is the law of causation. It stands at the head of all\nobserved uniformities, in point of universality, and therefore (if the\npreceding observations are correct) in point of certainty. And if we\nconsider, not what mankind would have been justified in believing in the\ninfancy of their knowledge, but what may rationally be believed in its\npresent more advanced state, we shall find ourselves warranted in\nconsidering this fundamental law, though itself obtained by induction\nfrom particular laws of causation, as not less certain, but on the\ncontrary, more so, than any of those from which it was drawn. It adds\nto them as much proof as it receives from them. For there is probably no\none even of the best established laws of causation which is not\nsometimes counteracted, and to which, therefore, apparent exceptions do\nnot present themselves, which would have necessarily and justly shaken\nthe confidence of mankind in the universality of those laws, if\ninductive processes founded on the universal law had not enabled us to\nrefer those exceptions to the agency of counteracting causes, and\nthereby reconcile them with the law with which they apparently conflict.\nErrors, moreover, may have slipped into the statement of any one of the\nspecial laws, through inattention to some material circumstance: and\ninstead of the true proposition, another may have been enunciated, false\nas an universal law, though leading, in all cases hitherto observed, to\nthe same result. To the law of causation, on the contrary, we not only\ndo not know of any exception, but the exceptions which limit or\napparently invalidate the special laws, are so far from contradicting\nthe universal one, that they confirm it; since in all cases which are\nsufficiently open to our observation, we are able to trace the\ndifference of result, either to the absence of a cause which had been\npresent in ordinary cases, or to the presence of one which had been\nabsent.\n\nThe law of cause and effect, being thus certain, is capable of imparting\nits certainty to all other inductive propositions which can be deduced\nfrom it; and the narrower inductions may be regarded as receiving their\nultimate sanction from that law, since there is no one of them which is\nnot rendered more certain than it was before, when we are able to\nconnect it with that larger induction, and to show that it cannot be\ndenied, consistently with the law that everything which begins to exist\nhas a cause. And hence we are justified in the seeming inconsistency, of\nholding induction by simple enumeration to be good for proving this\ngeneral truth, the foundation of scientific induction, and yet refusing\nto rely on it for any of the narrower inductions. I fully admit that if\nthe law of causation were unknown, generalization in the more obvious\ncases of uniformity in phenomena would nevertheless be possible, and\nthough in all cases more or less precarious, and in some extremely so,\nwould suffice to constitute a certain measure of probability: but what\nthe amount of this probability might be, we are dispensed from\nestimating, since it never could amount to the degree of assurance which\nthe proposition acquires, when, by the application to it of the Four\nMethods, the supposition of its falsity is shown to be inconsistent with\nthe Law of Causation. We are therefore logically entitled, and, by the\nnecessities of scientific Induction, required, to disregard the\nprobabilities derived from the early rude method of generalizing, and to\nconsider no minor generalization as proved except so far as the law of\ncausation confirms it, nor probable except so far as it may reasonably\nbe expected to be so confirmed.\n\n\n\u00a7 4. The assertion, that our inductive processes assume the law of\ncausation, while the law of causation is itself a case of induction, is\na paradox, only on the old theory of reasoning, which supposes the\nuniversal truth, or major premise, in a ratiocination, to be the real\nproof of the particular truths which are ostensibly inferred from it.\nAccording to the doctrine maintained in the present treatise,[29] the\nmajor premise is not the proof of the conclusion, but is itself proved,\nalong with the conclusion from the same evidence. \"All men are mortal\"\nis not the proof that Lord Palmerston is mortal; but our past experience\nof mortality authorizes us to infer _both_ the general truth and the\nparticular fact, and the one with exactly the same degree of assurance\nas the other. The mortality of Lord Palmerston is not an inference from\nthe mortality of all men, but from the experience which proves the\nmortality of all men; and is a correct inference from experience, if\nthat general truth is so too. This relation between our general beliefs\nand their particular applications holds equally true in the more\ncomprehensive case which we are now discussing. Any new fact of\ncausation inferred by induction, is rightly inferred, if no other\nobjection can be made to the inference than can be made to the general\ntruth that every event has a cause. The utmost certainty which can be\ngiven to a conclusion arrived at in the way of inference, stops at this\npoint. When we have ascertained that the particular conclusion must\nstand or fall with the general uniformity of the laws of nature--that it\nis liable to no doubt except the doubt whether every event has a\ncause--we have done all that can be done for it. The strongest assurance\nwe can obtain of any theory respecting the cause of a given phenomenon,\nis that the phenomenon has either that cause or none.\n\nThe latter supposition might have been an admissible one in a very early\nperiod of our study of nature. But we have been able to perceive that in\nthe stage which mankind have now reached, the generalization which gives\nthe Law of Universal Causation has grown into a stronger and better\ninduction, one deserving of greater reliance, than any of the\nsubordinate generalizations. We may even, I think, go a step further\nthan this, and regard the certainty of that great induction as not\nmerely comparative, but, for all practical purposes, absolute.\n\nThe considerations which, as I apprehend, give, at the present day, to\nthe proof of the law of uniformity of succession as true of all\nphenomena without exception, this character of completeness and\nconclusiveness, are the following:--First, that we now know it directly\nto be true of far the greatest number of phenomena; that there are none\nof which we know it not to be true, the utmost that can be said being,\nthat of some we cannot positively from direct evidence affirm its truth;\nwhile phenomenon after phenomenon, as they become better known to us,\nare constantly passing from the latter class into the former; and in all\ncases in which that transition has not yet taken place, the absence of\ndirect proof is accounted for by the rarity or the obscurity of the\nphenomena, our deficient means of observing them, or the logical\ndifficulties arising from the complication of the circumstances in which\nthey occur; insomuch that, notwithstanding as rigid a dependence on\ngiven conditions as exists in the case of any other phenomenon, it was\nnot likely that we should be better acquainted with those conditions\nthan we are. Besides this first class of considerations, there is a\nsecond, which still further corroborates the conclusion. Although there\nare phenomena the production and changes of which elude all our attempts\nto reduce them universally to any ascertained law; yet in every such\ncase, the phenomenon, or the objects concerned in it, are found in some\ninstances to obey the known laws of nature. The wind, for example, is\nthe type of uncertainty and caprice, yet we find it in some cases\nobeying with as much constancy as any phenomenon in nature the law of\nthe tendency of fluids to distribute themselves so as to equalize the\npressure on every side of each of their particles; as in the case of the\ntrade winds, and the monsoons. Lightning might once have been supposed\nto obey no laws; but since it has been ascertained to be identical with\nelectricity, we know that the very same phenomenon in some of its\nmanifestations is implicitly obedient to the action of fixed causes. I\ndo not believe that there is now one object or event in all our\nexperience of nature, within the bounds of the solar system at least,\nwhich has not either been ascertained by direct observation to follow\nlaws of its own, or been proved to be closely similar to objects and\nevents which, in more familiar manifestations, or on a more limited\nscale, follow strict laws: our inability to trace the same laws on a\nlarger scale and in the more recondite instances, being accounted for by\nthe number and complication of the modifying causes, or by their\ninaccessibility to observation.\n\nThe progress of experience, therefore, has dissipated the doubt which\nmust have rested on the universality of the law of causation while there\nwere phenomena which seemed to be _sui generis_, not subject to the same\nlaws with any other class of phenomena, and not as yet ascertained to\nhave peculiar laws of their own. This great generalization, however,\nmight reasonably have been, as it in fact was, acted on as a probability\nof the highest order, before there were sufficient grounds for receiving\nit as a certainty. For, whatever has been found true in innumerable\ninstances, and never found to be false after due examination in any, we\nare safe in acting on as universal provisionally, until an undoubted\nexception appears; provided the nature of the case be such that a real\nexception could scarcely have escaped our notice. When every phenomenon\nthat we ever knew sufficiently well to be able to answer the question,\nhad a cause on which it was invariably consequent, it was more rational\nto suppose that our inability to assign the causes of other phenomena\narose from our ignorance, than that there were phenomena which were\nuncaused, and which happened to be exactly those which we had hitherto\nhad no sufficient opportunity of studying.\n\nIt must, at the same time, be remarked, that the reasons for this\nreliance do not hold in circumstances unknown to us, and beyond the\npossible range of our experience. In distant parts of the stellar\nregions, where the phenomena may be entirely unlike those with which we\nare acquainted, it would be folly to affirm confidently that this\ngeneral law prevails, any more than those special ones which we have\nfound to hold universally on our own planet. The uniformity in the\nsuccession of events, otherwise called the law of causation, must be\nreceived not as a law of the universe, but of that portion of it only\nwhich is within the range of our means of sure observation, with a\nreasonable degree of extension to adjacent cases. To extend it further\nis to make a supposition without evidence, and to which, in the absence\nof any ground from experience for estimating its degree of probability,\nit would be idle to attempt to assign any.[30]\n\n\n\n\nCHAPTER XXII.\n\nOF UNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION.\n\n\n\u00a7 1. The order of the occurrence of phenomena in time, is either\nsuccessive or simultaneous; the uniformities, therefore, which obtain in\ntheir occurrence, are either uniformities of succession or of\ncoexistence. Uniformities of succession are all comprehended under the\nlaw of causation and its consequences. Every phenomenon has a cause,\nwhich it invariably follows; and from this are derived other invariable\nsequences among the successive stages of the same effect, as well as\nbetween the effects resulting from causes which invariably succeed one\nanother.\n\nIn the same manner with these derivative uniformities of succession, a\ngreat variety of uniformities of coexistence also take their rise.\nCoordinate effects of the same cause naturally coexist with one another.\nHigh water at any point on the earth's surface, and high water at the\npoint diametrically opposite to it, are effects uniformly simultaneous,\nresulting from the direction in which the combined attractions of the\nsun and moon act upon the waters of the ocean. An eclipse of the sun to\nus, and an eclipse of the earth to a spectator situated in the moon, are\nin like manner phenomena invariably coexistent; and their coexistence\ncan equally be deduced from the laws of their production.\n\nIt is an obvious question, therefore, whether all the uniformities of\ncoexistence among phenomena may not be accounted for in this manner. And\nit cannot be doubted that between phenomena which are themselves\neffects, the coexistences must necessarily depend on the causes of those\nphenomena. If they are effects immediately or remotely of the same\ncause, they cannot coexist except by virtue of some laws or properties\nof that cause: if they are effects of different causes, they cannot\ncoexist unless it be because their causes coexist; and the uniformity of\ncoexistence, if such there be, between the effects, proves that those\nparticular causes, within the limits of our observation, have uniformly\nbeen coexistent.\n\n\n\u00a7 2. But these same considerations compel us to recognise that there\nmust be one class of coexistences which cannot depend on causation; the\ncoexistences between the ultimate properties of things--those properties\nwhich are the causes of all phenomena, but are not themselves caused by\nany phenomenon, and a cause for which could only be sought by ascending\nto the origin of all things. Yet among these ultimate properties there\nare not only coexistences, but uniformities of coexistence. General\npropositions may be, and are, formed, which assert that whenever certain\nproperties are found, certain others are found along with them. We\nperceive an object; say, for instance, water. We recognise it to be\nwater, of course by certain of its properties. Having recognised it, we\nare able to affirm of it innumerable other properties; which we could\nnot do unless it were a general truth, a law or uniformity in nature,\nthat the set of properties by which we identify the substance as water,\nalways have those other properties conjoined with them.\n\nIn a former place,[31] it has been explained in some detail what is\nmeant by the Kinds of objects; those classes which differ from one\nanother not by a limited and definite, but by an indefinite and unknown,\nnumber of distinctions. To this we have now to add, that every\nproposition by which anything is asserted of a Kind, affirms an\nuniformity of coexistence. Since we know nothing of Kinds but their\nproperties, the Kind, to us, _is_ the set of properties by which it is\nidentified, and which must of course be sufficient to distinguish it\nfrom every other kind.[32] In affirming anything, therefore, of a Kind,\nwe are affirming something to be uniformly coexistent with the\nproperties by which the kind is recognised; and that is the sole meaning\nof the assertion.\n\nAmong the uniformities of coexistence which exist in nature, may hence\nbe numbered all the properties of Kinds. The whole of these, however,\nare not independent of causation, but only a portion of them. Some are\nultimate properties, others derivative; of some, no cause can be\nassigned, but others are manifestly dependent on causes. Thus, pure\natmospheric air is a Kind, and one of its most unequivocal properties is\nits gaseous form: this property, however, has for its cause the presence\nof a certain quantity of latent heat; and if that heat could be taken\naway (as has been done from so many gases in Faraday's experiments), the\ngaseous form would doubtless disappear, together with numerous other\nproperties which depend on, or are caused by, that property.\n\nIn regard to all substances which are chemical compounds, and which\ntherefore may be regarded as products of the juxtaposition of substances\ndifferent in Kind from themselves, there is considerable reason to\npresume that the specific properties of the compound are consequent, as\neffects, on some of the properties of the elements, though little\nprogress has yet been made in tracing any invariable relation between\nthe latter and the former. Still more strongly will a similar\npresumption exist, when the object itself, as in the case of organized\nbeings, is no primeval agent, but an effect, which depends on a cause or\ncauses for its very existence. The Kinds therefore which are called in\nchemistry simple substances, or elementary natural agents, are the only\nones, any of whose properties can with certainty be considered\nultimate; and of these the ultimate properties are probably much more\nnumerous that we at present recognise, since every successful instance\nof the resolution of the properties of their compounds into simpler\nlaws, generally leads to the recognition of properties in the elements\ndistinct from any previously known. The resolution of the laws of the\nheavenly motions, established the previously unknown ultimate property\nof a mutual attraction between all bodies: the resolution, so far as it\nhas yet proceeded, of the laws of crystallization, of chemical\ncomposition, electricity, magnetism, &c., points to various polarities,\nultimately inherent in the particles of which bodies are composed; the\ncomparative atomic weights of different kinds of bodies were ascertained\nby resolving, into more general laws, the uniformities observed in the\nproportions in which substances combine with one another; and so forth.\nThus although every resolution of a complex uniformity into simpler and\nmore elementary laws has an apparent tendency to diminish the number of\nthe ultimate properties, and really does remove many properties from the\nlist; yet, (since the result of this simplifying process is to trace up\nan ever greater variety of different effects to the same agents,) the\nfurther we advance in this direction, the greater number of distinct\nproperties we are forced to recognise in one and the same object: the\ncoexistences of which properties must accordingly be ranked among the\nultimate generalities of nature.\n\n\n\u00a7 3. There are, therefore, only two kinds of propositions which assert\nuniformity of coexistence between properties. Either the properties\ndepend on causes, or they do not. If they do, the proposition which\naffirms them to be coexistent is a derivative law of coexistence between\neffects, and until resolved into the laws of causation on which it\ndepends, is an empirical law, and to be tried by the principles of\ninduction to which such laws are amenable. If, on the other hand, the\nproperties do not depend on causes, but are ultimate properties; then if\nit be true that they invariably coexist, they must all be ultimate\nproperties of one and the same Kind; and it is of these only that the\ncoexistences can be classed as a peculiar sort of laws of nature.\n\nWhen we affirm that all crows are black, or that all negroes have woolly\nhair, we assert an uniformity of coexistence. We assert that the\nproperty of blackness, or of having woolly hair, invariably coexists\nwith the properties which, in common language, or in the scientific\nclassification that we adopt, are taken to constitute the class crow, or\nthe class negro. Now, supposing blackness to be an ultimate property of\nblack objects, or woolly hair an ultimate property of the animals which\npossess it; supposing that these properties are not results of\ncausation, are not connected with antecedent phenomena by any law; then\nif all crows are black, and all negroes have woolly hair, these must be\nultimate properties of the Kind _crow_, or _negro_, or of some Kind\nwhich includes them. If, on the contrary, blackness or woolly hair be an\neffect depending on causes, these general propositions are manifestly\nempirical laws; and all that has already been said respecting that class\nof generalizations may be applied without modification to these.\n\nNow, we have seen that in the case of all compounds--of all things, in\nshort, except the elementary substances and primary powers of\nnature--the presumption is, that the properties do really depend upon\ncauses; and it is impossible in any case whatever to be certain that\nthey do not. We therefore should not be safe in claiming for any\ngeneralization respecting the coexistence of properties, a degree of\ncertainty to which, if the properties should happen to be the result of\ncauses, it would have no claim. A generalization respecting coexistence,\nor in other words respecting the properties of Kinds, may be an ultimate\ntruth, but it may, also, be merely a derivative one; and since, if so,\nit is one of those derivative laws which are neither laws of causation,\nnor have been resolved into the laws of causation on which they depend,\nit can possess no higher degree of evidence than belongs to an empirical\nlaw.\n\n\n\u00a7 4. This conclusion will be confirmed by the consideration of one\ngreat deficiency, which precludes the application to the ultimate\nuniformities of coexistence, of a system of rigorous scientific\ninduction, such as the uniformities in the succession of phenomena have\nbeen found to admit of. The basis of such a system is wanting: there is\nno general axiom, standing in the same relation to the uniformities of\ncoexistence as the law of causation does to those of succession. The\nMethods of Induction applicable to the ascertainment of causes and\neffects, are grounded on the principle that everything which has a\nbeginning must have some cause or other; that among the circumstances\nwhich actually existed at the time of its commencement, there is\ncertainly some one combination, on which the effect in question is\nunconditionally consequent, and on the repetition of which it would\ncertainly again recur. But in an inquiry whether some kind (as crow)\nuniversally possesses a certain property (as blackness), there is no\nroom for any assumption analogous to this. We have no previous certainty\nthat the property must have something which constantly coexists with it;\nmust have an invariable coexistent, in the same manner as an event must\nhave an invariable antecedent. When we feel pain, we must be in some\ncircumstances under which if exactly repeated we should always feel\npain. But when we are conscious of blackness, it does not follow that\nthere is something else present of which blackness is a constant\naccompaniment. There is, therefore, no room for elimination; no Method\nof Agreement or Difference, or of Concomitant Variations (which is but a\nmodification either of the Method of Agreement or of the Method of\nDifference). We cannot conclude that the blackness we see in crows must\nbe an invariable property of crows, merely because there is nothing else\npresent of which it can be an invariable property. We therefore inquire\ninto the truth of a proposition like \"All crows are black,\" under the\nsame disadvantage as if, in our inquiries into causation, we were\ncompelled to let in, as one of the possibilities, that the effect may in\nthat particular instance have arisen without any cause at all.\n\nTo overlook this grand distinction was, as it seems to me, the capital\nerror in Bacon's view of inductive philosophy. The principle of\nelimination, that great logical instrument which he had the immense\nmerit of first bringing into general use, he deemed applicable in the\nsame sense, and in as unqualified a manner, to the investigation of the\ncoexistences, as to that of the successions of phenomena. He seems to\nhave thought that as every event has a cause, or invariable antecedent,\nso every property of an object has an invariable coexistent, which he\ncalled its Form: and the examples he chiefly selected for the\napplication and illustration of his method, were inquiries into such\nForms; attempts to determine in what else all those objects resembled,\nwhich agreed in some one general property, as hardness or softness,\ndryness or moistness, heat or coldness. Such inquiries could lead to no\nresult. The objects seldom have any such circumstances in common. They\nusually agree in the one point inquired into, and in nothing else. A\ngreat proportion of the properties which, so far as we can conjecture,\nare the likeliest to be really ultimate, would seem to be inherently\nproperties of many different Kinds of things, not allied in any other\nrespect. And as for the properties which, being effects of causes, we\nare able to give some account of, they have generally nothing to do with\nthe ultimate resemblances or diversities in the objects themselves, but\ndepend on some outward circumstances, under the influence of which any\nobjects whatever are capable of manifesting those properties; as is\nemphatically the case with those favourite subjects of Bacon's\nscientific inquiries, hotness and coldness; as well as with hardness and\nsoftness, solidity and fluidity, and many other conspicuous qualities.\n\nIn the absence, then, of any universal law of coexistence, similar to\nthe universal law of causation which regulates sequence, we are thrown\nback upon the unscientific induction of the ancients, _per enumerationem\nsimplicem, ubi non reperitur instantia contradictoria_. The reason we\nhave for believing that all crows are black, is simply that we have seen\nand heard of many black crows, and never one of any other colour. It\nremains to be considered how far this evidence can reach, and how we are\nto measure its strength in any given case.\n\n\n\u00a7 5. It sometimes happens that a mere change in the mode of verbally\nenunciating a question, though nothing is really added to the meaning\nexpressed, is of itself a considerable step towards its solution. This,\nI think, happens in the present instance. The degree of certainty of any\ngeneralization which rests on no other evidence than the agreement, so\nfar as it goes, of all past observation, is but another phrase for the\ndegree of improbability that an exception, if any existed, could have\nhitherto remained unobserved. The reason for believing that all crows\nare black, is measured by the improbability that crows of any other\ncolour should have existed to the present time without our being aware\nof it. Let us state the question in this last mode, and consider what is\nimplied in the supposition that there may be crows which are not black,\nand under what conditions we can be justified in regarding this as\nincredible.\n\nIf there really exist crows which are not black, one of two things must\nbe the fact. Either the circumstance of blackness, in all crows hitherto\nobserved, must be, as it were, an accident, not connected with any\ndistinction of Kind; or if it be a property of Kind, the crows which are\nnot black must be a new Kind, a Kind hitherto overlooked, though coming\nunder the same general description by which crows have hitherto been\ncharacterized. The first supposition would be proved true if we were to\ndiscover casually a white crow among black ones, or if it were found\nthat black crows sometimes turn white. The second would be shown to be\nthe fact if in Australia or Central Africa a species or a race of white\nor grey crows were found to exist.\n\n\n\u00a7 6. The former of these suppositions necessarily implies that the\ncolour is an effect of causation. If blackness, in the crows in which it\nhas been observed, be not a property of Kind, but can be present or\nabsent without any difference generally in the properties of the object;\nthen it is not an ultimate fact in the individuals themselves, but is\ncertainly dependent on a cause. There are, no doubt, many properties\nwhich vary from individual to individual of the same Kind, even the\nsame _infima species_, or lowest Kind. Some flowers may be either white\nor red, without differing in any other respect. But these properties are\nnot ultimate; they depend on causes. So far as the properties of a thing\nbelong to its own nature, and do not arise from some cause extrinsic to\nit, they are always the same in the same Kind. Take, for instance, all\nsimple substances and elementary powers; the only things of which we are\ncertain that some at least of their properties are really ultimate.\nColour is generally esteemed the most variable of all properties: yet we\ndo not find that sulphur is sometimes yellow and sometimes white, or\nthat it varies in colour at all, except so far as colour is the effect\nof some extrinsic cause, as of the sort of light thrown upon it, the\nmechanical arrangement of the particles, (as after fusion) &c. We do not\nfind that iron is sometimes fluid and sometimes solid at the same\ntemperature; gold sometimes malleable and sometimes brittle; that\nhydrogen will sometimes combine with oxygen and sometimes not; or the\nlike. If from simple substances we pass to any of their definite\ncompounds, as water, lime, or sulphuric acid, there is the same\nconstancy in their properties. When properties vary from individual to\nindividual, it is either in the case of miscellaneous aggregations, such\nas atmospheric air or rock, composed of heterogeneous substances, and\nnot constituting or belonging to any real Kind,[33] or it is in the case\nof organic beings. In them, indeed, there is variability in a high\ndegree. Animals of the same species and race, human beings of the same\nage, sex, and country, will be most different, for example, in face and\nfigure. But organized beings (from the extreme complication of the laws\nby which they are regulated) being more eminently modifiable, that is,\nliable to be influenced by a greater number and variety of causes, than\nany other phenomena whatever; having also themselves had a beginning,\nand therefore a cause; there is reason to believe that none of their\nproperties are ultimate, but all of them derivative, and produced by\ncausation. And the presumption is confirmed, by the fact that the\nproperties which vary from one individual to another, also generally\nvary more or less at different times in the same individual; which\nvariation, like any other event, supposes a cause, and implies,\nconsequently, that the properties are not independent of causation.\n\nIf, therefore, blackness be merely accidental in crows, and capable of\nvarying while the Kind remains the same, its presence or absence is\ndoubtless no ultimate fact, but the effect of some unknown cause: and in\nthat case the universality of the experience that all crows are black is\nsufficient proof of a common cause, and establishes the generalization\nas an empirical law. Since there are innumerable instances in the\naffirmative, and hitherto none at all in the negative, the causes on\nwhich the property depends must exist everywhere in the limits of the\nobservations which have been made; and the proposition may be received\nas universal within those limits, and with the allowable degree of\nextension to adjacent cases.\n\n\n\u00a7 7. If, in the second place, the property, in the instances in which it\nhas been observed, is not an effect of causation, it is a property of\nKind; and in that case the generalization can only be set aside by the\ndiscovery of a new Kind of crow. That, however, a peculiar Kind, not\nhitherto discovered, should exist in nature, is a supposition so often\nrealized, that it cannot be considered at all improbable. We have\nnothing to authorize us in attempting to limit the Kinds of things which\nexist in nature. The only unlikelihood would be that a new Kind should\nbe discovered in localities which there was previously reason to believe\nhad been thoroughly explored; and even this improbability depends on the\ndegree of conspicuousness of the difference between the newly-discovered\nKind and all others, since new Kinds of minerals, plants, and even\nanimals, previously overlooked or confounded with known species, are\nstill continually detected in the most frequented situations. On this\nsecond ground, therefore, as well as on the first, the observed\nuniformity of coexistence can only hold good as an empirical law, within\nthe limits not only of actual observation, but of an observation as\naccurate as the nature of the case required. And hence it is that (as\nremarked in an early chapter of the present Book) we so often give up\ngeneralizations of this class at the first summons. If any credible\nwitness stated that he had seen a white crow, under circumstances which\nmade it not incredible that it should have escaped notice previously, we\nshould give full credence to the statement.\n\nIt appears, then, that the uniformities which obtain in the coexistence\nof phenomena,--those which we have reason to consider as ultimate, no\nless than those which arise from the laws of causes yet undetected--are\nentitled to reception only as empirical laws; are not to be presumed\ntrue except within the limits of time, place, and circumstance, in which\nthe observations were made, or except in cases strictly adjacent.\n\n\n\u00a7 8. We have seen in the last chapter that there is a point of\ngenerality at which empirical laws become as certain as laws of nature,\nor rather, at which there is no longer any distinction between empirical\nlaws and laws of nature. As empirical laws approach this point, in other\nwords, as they rise in their degree of generality, they become more\ncertain; their universality may be more strongly relied on. For, in the\nfirst place, if they are results of causation (which, even in the class\nof uniformities treated of in the present chapter, we never can be\ncertain that they are not) the more general they are, the greater is\nproved to be the space over which the necessary collocations prevail,\nand within which no causes exist capable of counteracting the unknown\ncauses on which the empirical law depends. To say that anything is an\ninvariable property of some very limited class of objects, is to say\nthat it invariably accompanies some very numerous and complex group of\ndistinguishing properties; which, if causation be at all concerned in\nthe matter, argues a combination of many causes, and therefore a great\nliability to counteraction; while the comparatively narrow range of the\nobservations renders it impossible to predict to what extent unknown\ncounteracting causes may be distributed throughout nature. But when a\ngeneralization has been found to hold good of a very large proportion of\nall things whatever, it is already proved that nearly all the causes\nwhich exist in nature have no power over it; that very few changes in\nthe combination of causes can effect it; since the greater number of\npossible combinations must have already existed in some one or other of\nthe instances in which it has been found true. If, therefore, any\nempirical law is a result of causation, the more general it is, the more\nit may be depended on. And even if it be no result of causation, but an\nultimate coexistence, the more general it is, the greater amount of\nexperience it is derived from, and the greater therefore is the\nprobability that if exceptions had existed, some would already have\npresented themselves.\n\nFor these reasons, it requires much more evidence to establish an\nexception to one of the more general empirical laws than to the more\nspecial ones. We should not have any difficulty in believing that there\nmight be a new Kind of crow; or a new kind of bird resembling a crow in\nthe properties hitherto considered distinctive of that Kind. But it\nwould require stronger proof to convince us of the existence of a Kind\nof crow having properties at variance with any generally recognised\nuniversal property of birds; and a still higher degree if the properties\nconflict with any recognised universal property of animals. And this is\nconformable to the mode of judgment recommended by the common sense and\ngeneral practice of mankind, who are more incredulous as to any\nnovelties in nature, according to the degree of generality of the\nexperience which these novelties seem to contradict.\n\n\n\u00a7 9. Still, however, even these greater generalizations, which embrace\ncomprehensive Kinds, containing under them a great number and variety of\n_infim\u00e6 species_, are only empirical laws, resting on induction by\nsimple enumeration merely, and not on any process of elimination, a\nprocess wholly inapplicable to this sort of case. Such generalizations,\ntherefore, ought to be grounded on an examination of all the _infim\u00e6\nspecies_ comprehended in them, and not of a portion only. We cannot\nconclude (where causation is not concerned), because a proposition is\ntrue of a number of things resembling one another only in being animals,\nthat it is therefore true of all animals. If, indeed, anything be true\nof species which differ more from one another than either differs from a\nthird, (especially if that third species occupies in most of its known\nproperties a position between the two former,) there is some probability\nthat the same thing will also be true of that intermediate species; for\nit is often, though by no means universally, found, that there is a sort\nof parallelism in the properties of different Kinds, and that their\ndegree of unlikeness in one respect bears some proportion to their\nunlikeness in others. We see this parallelism in the properties of the\ndifferent metals; in those of sulphur, phosphorus, and carbon; of\nchlorine, iodine, and bromine; in the natural orders of plants and\nanimals, &c. But there are innumerable anomalies and exceptions to this\nsort of conformity; if indeed the conformity itself be anything but an\nanomaly and an exception in nature.\n\nUniversal propositions, therefore, respecting the properties of superior\nKinds, unless grounded on proved or presumed connexion by causation,\nought not to be hazarded except after separately examining every known\nsub-kind included in the larger Kind. And even then such generalizations\nmust be held in readiness to be given up on the occurrence of some new\nanomaly, which, when the uniformity is not derived from causation, can\nnever, even in the case of the most general of these empirical laws, be\nconsidered very improbable. Thus all the universal propositions which it\nhas been attempted to lay down respecting simple substances, or\nconcerning any of the classes which have been formed among simple\nsubstances, (and the attempt has been often made,) have, with the\nprogress of experience, either faded into inanity, or been proved to be\nerroneous; and each Kind of simple substance remains with its own\ncollection of properties apart from the rest, saving a certain\nparallelism with a few other Kinds, the most similar to itself. In\norganized beings, indeed, there are abundance of propositions\nascertained to be universally true of superior genera, to many of which\nthe discovery hereafter of any exceptions must be regarded as extremely\nimprobable. But these, as already observed, are, we have every reason to\nbelieve, properties dependent on causation.\n\nUniformities of coexistence, then, not only when they are consequences\nof laws of succession, but also when they are ultimate truths, must be\nranked, for the purpose of logic, among empirical laws; and are amenable\nin every respect to the same rules with those unresolved uniformities\nwhich are known to be dependent on causation.\n\n\n\n\nCHAPTER XXIII.\n\nOF APPROXIMATE GENERALIZATIONS, AND PROBABLE EVIDENCE.\n\n\n\u00a7 1. In our inquiries into the nature of the inductive process, we must\nnot confine our notice to such generalizations from experience as\nprofess to be universally true. There is a class of inductive truths\navowedly not universal; in which it is not pretended that the predicate\nis always true of the subject; but the value of which, as\ngeneralizations, is nevertheless extremely great. An important portion\nof the field of inductive knowledge does not consist of universal\ntruths, but of approximations to such truths; and when a conclusion is\nsaid to rest on probable evidence, the premises it is drawn from are\nusually generalizations of this sort.\n\nAs every certain inference respecting a particular case, implies that\nthere is ground for a general proposition, of the form, Every A is B; so\ndoes every probable inference suppose that there is ground for a\nproposition of the form, Most A are B: and the degree of probability of\nthe inference in an average case, will depend on the proportion between\nthe number of instances existing in nature which accord with the\ngeneralization, and the number of those which conflict with it.\n\n\n\u00a7 2. Propositions in the form, Most A are B, are of a very different\ndegree of importance in science, and in the practice of life. To the\nscientific inquirer they are valuable chiefly as materials for, and\nsteps towards, universal truths. The discovery of these is the proper\nend of science: its work is not done if it stops at the proposition that\na majority of A are B, without circumscribing that majority by some\ncommon character, fitted to distinguish them from the minority.\nIndependently of the inferior precision of such imperfect\ngeneralizations, and the inferior assurance with which they can be\napplied to individual cases, it is plain that, compared with exact\ngeneralizations, they are almost useless as means of discovering\nulterior truths by way of deduction. We may, it is true, by combining\nthe proposition Most A are B, with an universal proposition, Every B is\nC, arrive at the conclusion that Most A are C. But when a second\nproposition of the approximate kind is introduced,--or even when there\nis but one, if that one be the major premise,--nothing can in general be\npositively concluded. When the major is Most B are D, then, even if the\nminor be Every A is B, we cannot infer that most A are D, or with any\ncertainty that even some A are D. Though the majority of the class B\nhave the attribute signified by D, the whole of the sub-class A may\nbelong to the minority.[34]\n\nThough so little use can be made, in science, of approximate\ngeneralizations, except as a stage on the road to something better, for\npractical guidance they are often all we have to rely on. Even when\nscience has really determined the universal laws of any phenomenon, not\nonly are those laws generally too much encumbered with conditions to be\nadapted for every-day use, but the cases which present themselves in\nlife are too complicated, and our decisions require to be taken too\nrapidly, to admit of waiting till the existence of a phenomenon can be\nproved by what have been scientifically ascertained to be universal\nmarks of it. To be indecisive and reluctant to act, because we have not\nevidence of a perfectly conclusive character to act on, is a defect\nsometimes incident to scientific minds, but which, wherever it exists,\nrenders them unfit for practical emergencies. If we would succeed in\naction, we must judge by indications which, though they do not\ngenerally mislead us, sometimes do; and must make up, as far as\npossible, for the incomplete conclusiveness of any one indication, by\nobtaining others to corroborate it. The principles of induction\napplicable to approximate generalization are therefore a not less\nimportant subject of inquiry, than the rules for the investigation of\nuniversal truths; and might reasonably be expected to detain us almost\nas long, were it not that these principles are mere corollaries from\nthose which have been already treated of.\n\n\n\u00a7 3. There are two sorts of cases in which we are forced to guide\nourselves by generalizations of the imperfect form, Most A are B. The\nfirst is, when we have no others; when we have not been able to carry\nour investigation of the laws of the phenomena any farther; as in the\nfollowing propositions: Most dark-eyed persons have dark hair; Most\nsprings contain mineral substances; Most stratified formations contain\nfossils. The importance of this class of generalizations is not very\ngreat; for, though it frequently happens that we see no reason why that\nwhich is true of most individuals of a class is not true of the\nremainder, nor are able to bring the former under any general\ndescription which can distinguish them from the latter, yet if we are\nwilling to be satisfied with propositions of a less degree of\ngenerality, and to break down the class A into subclasses, we may\ngenerally obtain a collection of propositions exactly true. We do not\nknow why most wood is lighter than water, nor can we point out any\ngeneral property which discriminates wood that is lighter than water\nfrom that which is heavier. But we know exactly what species are the one\nand what the other. And if we meet with a specimen not conformable to\nany known species (the only case in which our previous knowledge affords\nno other guidance than the approximate generalization), we can generally\nmake a specific experiment, which is a surer resource.\n\nIt often happens, however, that the proposition, Most A are B, is not\nthe ultimatum of our scientific progress, though the knowledge we\npossess beyond it cannot conveniently be brought to bear upon the\nparticular instance. In such a case we know well enough what\ncircumstances distinguish the portion of A which has the attribute B\nfrom the portion which has it not, but have no means, or have not time,\nto examine whether those characteristic circumstances exist or not in\nthe individual case. This is the situation we are generally in when the\ninquiry is of the kind called moral, that is, of the kind which has in\nview to predict human actions. To enable us to affirm anything\nuniversally concerning the actions of classes of human beings, the\nclassification must be grounded on the circumstances of their mental\nculture and habits, which in an individual case are seldom exactly\nknown; and classes grounded on these distinctions would never precisely\naccord with those into which mankind are divided for social purposes.\nAll propositions which can be framed respecting the actions of human\nbeings as ordinarily classified, or as classified according to any kind\nof outward indications, are merely approximate. We can only say, Most\npersons of a particular age, profession, country, or rank in society,\nhave such and such qualities; or, Most persons when placed in certain\ncircumstances act in such and such a way. Not that we do not often know\nwell enough on what causes the qualities depend, or what sort of persons\nthey are who act in that particular way; but we have seldom the means of\nknowing whether any individual person has been under the influence of\nthose causes, or is a person of that particular sort. We could replace\nthe approximate generalizations by propositions universally true; but\nthese would hardly ever be capable of being applied to practice. We\nshould be sure of our majors, but we should not be able to get minors to\nfit: we are forced, therefore, to draw our conclusions from coarser and\nmore fallible indications.\n\n\n\u00a7 4. Proceeding now to consider, what is to be regarded as sufficient\nevidence of an approximate generalization; we can have no difficulty in\nat once recognising that when admissible at all, it is admissible only\nas an empirical law. Propositions of the form, Every A is B, are not\nnecessarily laws of causation, or ultimate uniformities of coexistence;\npropositions like Most A are B _cannot_ be so. Propositions hitherto\nfound true in every observed instance, may yet be no necessary\nconsequence of laws of causation, or of ultimate uniformities, and\nunless they are so, may, for aught we know, be false beyond the limits\nof actual observation: still more evidently must this be the case with\npropositions which are only true in a mere majority of the observed\ninstances.\n\nThere is some difference, however, in the degree of certainty of the\nproposition, Most A are B, according as that approximate generalization\ncomposes the whole of our knowledge of the subject, or not. Suppose,\nfirst, that the former is the case. We know only that most A are B, not\nwhy they are so, nor in what respect those which are, differ from those\nwhich are not. How then did we learn that most A are B? Precisely in the\nmanner in which we should have learnt, had such happened to be the fact,\nthat all A are B. We collected a number of instances sufficient to\neliminate chance, and having done so, compared the number of instances\nin the affirmative with the number in the negative. The result, like\nother unresolved derivative laws, can be relied on solely within the\nlimits not only of place and time, but also of circumstance, under which\nits truth has been actually observed; for as we are supposed to be\nignorant of the causes which make the proposition true, we cannot tell\nin what manner any new circumstance might perhaps affect it. The\nproposition, Most judges are inaccessible to bribes, would be found true\nof Englishmen, Frenchmen, Germans, North Americans, and so forth; but if\non this evidence alone we extended the assertion to Orientals, we should\nstep beyond the limits, not only of place but of circumstance, within\nwhich the fact had been observed, and should let in possibilities of the\nabsence of the determining causes, or the presence of counteracting\nones, which might be fatal to the approximate generalization.\n\nIn the case where the approximate proposition is not the ultimatum of\nour scientific knowledge, but only the most available form of it for\npractical guidance; where we know, not only that most A have the\nattribute B, but also the causes of B, or some properties by which the\nportion of A which has that attribute is distinguished from the portion\nwhich has it not; we are rather more favourably situated than in the\npreceding case. For we have now a double mode of ascertaining whether it\nbe true that most A are B; the direct mode, as before, and an indirect\none, that of examining whether the proposition admits of being deduced\nfrom the known cause, or from any known criterion, of B. Let the\nquestion, for example, be whether most Scotchmen can read? We may not\nhave observed, or received the testimony of others respecting, a\nsufficient number and variety of Scotchmen to ascertain this fact; but\nwhen we consider that the cause of being able to read is the having been\ntaught it, another mode of determining the question presents itself,\nnamely, by inquiring whether most Scotchmen have been sent to schools\nwhere reading is effectually taught. Of these two modes, sometimes one\nand sometimes the other is the more available. In some cases, the\nfrequency of the effect is the more accessible to that extensive and\nvaried observation which is indispensable to the establishment of an\nempirical law; at other times, the frequency of the causes, or of some\ncollateral indications. It commonly happens that neither is susceptible\nof so satisfactory an induction as could be desired, and that the\ngrounds on which the conclusion is received are compounded of both. Thus\na person may believe that most Scotchmen can read, because, so far as\nhis information extends, most Scotchmen have been sent to school, and\nmost Scotch schools teach reading effectually; and also because most of\nthe Scotchmen whom he has known or heard of, could read; though neither\nof these two sets of observations may by itself fulfil the necessary\nconditions of extent and variety.\n\nAlthough the approximate generalization may in most cases be\nindispensable for our guidance, even when we know the cause, or some\ncertain mark, of the attribute predicated; it needs hardly be observed\nthat we may always replace the uncertain indication by a certain one, in\nany case in which we can actually recognise the existence of the cause\nor mark. For example, an assertion is made by a witness, and the\nquestion is, whether to believe it. If we do not look to any of the\nindividual circumstances of the case, we have nothing to direct us but\nthe approximate generalization, that truth is more common than\nfalsehood, or, in other words, that most persons, on most occasions,\nspeak truth. But if we consider in what circumstances the cases where\ntruth is spoken differ from those in which it is not, we find, for\ninstance, the following: the witness's being an honest person or not;\nhis being an accurate observer or not; his having an interest to serve\nin the matter or not. Now, not only may we be able to obtain other\napproximate generalizations respecting the degree of frequency of these\nvarious possibilities, but we may know which of them is positively\nrealized in the individual case. That the witness has or has not an\ninterest to serve, we perhaps know directly; and the other two points\nindirectly, by means of marks; as, for example, from his conduct on some\nformer occasion; or from his reputation, which, though a very uncertain\nmark, affords an approximate generalization (as, for instance, Most\npersons who are believed to be honest by those with whom they have had\nfrequent dealings, are really so) which approaches nearer to an\nuniversal truth than the approximate general proposition with which we\nset out, viz. Most persons on most occasions speak truth.\n\nAs it seems unnecessary to dwell further on the question of the evidence\nof approximate generalizations, we shall proceed to a not less important\ntopic, that of the cautions to be observed in arguing from these\nincompletely universal propositions to particular cases.\n\n\n\u00a7 5. So far as regards the direct application of an approximate\ngeneralization to an individual instance, this question presents no\ndifficulty. If the proposition, Most A are B, has been established, by a\nsufficient induction, as an empirical law, we may conclude that any\nparticular A is B with a probability proportioned to the preponderance\nof the number of affirmative instances over the number of exceptions. If\nit has been found practicable to attain numerical precision in the data,\na corresponding degree of precision may be given to the evaluation of\nthe chances of error in the conclusion. If it can be established as an\nempirical law that nine out of every ten A are B, there will be one\nchance in ten of error in assuming that any A, not individually known to\nus, is a B: but this of course holds only within the limits of time,\nplace, and circumstance, embraced in the observations, and therefore\ncannot be counted on for any sub-class or variety of A (or for A in any\nset of external circumstances) which were not included in the average.\nIt must be added, that we can guide ourselves by the proposition, Nine\nout of every ten A are B, only in cases of which we know nothing except\nthat they fall within the class A. For if we know, of any particular\ninstance _i_, not only that it falls under A, but to what species or\nvariety of A it belongs, we shall generally err in applying to _i_ the\naverage struck for the whole genus, from which the average corresponding\nto that species alone would, in all probability, materially differ. And\nso if _i_, instead of being a particular sort of instance, is an\ninstance known to be under the influence of a particular set of\ncircumstances. The presumption drawn from the numerical proportions in\nthe whole genus would probably, in such a case, only mislead. A general\naverage should only be applied to cases which are neither known, nor can\nbe presumed, to be other than average cases. Such averages, therefore,\nare commonly of little use for the practical guidance of any affairs but\nthose which concern large numbers. Tables of the chances of life are\nuseful to insurance offices, but they go a very little way towards\ninforming any one of the chances of his own life, or any other life in\nwhich he is interested, since almost every life is either better or\nworse than the average. Such averages can only be considered as\nsupplying the first term in a series of approximations; the subsequent\nterms proceeding on an appreciation of the circumstances belonging to\nthe particular case.\n\n\n\u00a7 6. From the application of a single approximate generalization to\nindividual cases, we proceed to the application of two or more of them\ntogether to the same case.\n\nWhen a judgment applied to an individual instance is grounded on two\napproximate generalizations taken in conjunction, the propositions may\nco-operate towards the result in two different ways. In the one, each\nproposition is separately applicable to the case in hand, and our object\nin combining them is to give to the conclusion in that particular case\nthe double probability arising from the two propositions separately.\nThis may be called joining two probabilities by way of Addition; and the\nresult is a probability greater than either. The other mode is, when\nonly one of the propositions is directly applicable to the case, the\nsecond being only applicable to it by virtue of the application of the\nfirst. This is joining two probabilities by way of Ratiocination or\nDeduction; the result of which is a less probability than either. The\ntype of the first argument is, Most A are B; most C are B; this thing is\nboth an A and a C; therefore it is probably a B. The type of the second\nis, Most A are B; most C are A; this is a C; therefore it is probably an\nA, therefore it is probably a B. The first is exemplified when we prove\na fact by the testimony of two unconnected witnesses; the second, when\nwe adduce only the testimony of one witness that he has heard the thing\nasserted by another. Or again, in the first mode it may be argued that\nthe accused committed the crime, because he concealed himself, and\nbecause his clothes were stained with blood; in the second, that he\ncommitted it because he washed or destroyed his clothes, which is\nsupposed to render it probable that they were stained with blood.\nInstead of only two links, as in these instances, we may suppose chains\nof any length. A chain of the former kind was termed by Bentham[35] a\nself-corroborative chain of evidence; the second, a self-infirmative\nchain.\n\nWhen approximate generalizations are joined by way of addition, we may\ndeduce from the theory of probabilities laid down in a former chapter,\nin what manner each of them adds to the probability of a conclusion\nwhich has the warrant of them all.\n\nIn the early editions of this treatise, the joint probability arising\nfrom the sum of two independent probabilities was estimated in the\nfollowing manner. If, on an average, two of every three As are Bs, and\nthree of every four Cs are Bs, the probability that something which is\nboth an A and a C is a B, will be more than two in three, or than three\nin four. Of every twelve things which are As, all except four are Bs by\nthe supposition; and if the whole twelve, and consequently those four,\nhave the characters of C likewise, three of these will be Bs on that\nground. Therefore, out of twelve which are both As and Cs, eleven are\nBs. To state the argument in another way; a thing which is both an A and\na C, but which is not a B, is found in only one of three sections of the\nclass A, and in only one of four sections of the class C; but this\nfourth of C being spread over the whole of A indiscriminately, only\none-third part of it (or one-twelfth of the whole number) belongs to the\nthird section of A; therefore a thing which is not a B occurs only once,\namong twelve things which are both As and Cs. The argument would in the\nlanguage of the doctrine of chances, be thus expressed: the chance that\nan A is not a B is 1/3, the chance that a C is not a B is 1/4; hence if\nthe thing be both an A and a C, the chance is 1/3 of 1/4 = 1/12.\n\nIt has, however, been pointed out to me by a mathematical friend, that\nin this statement the evaluation of the chances is erroneous. The\ncorrect mode of setting out the possibilities is as follows. If the\nthing (let us call it T) which is both an A and a C, is a B, something\nis true which is only true twice in every thrice, and something else\nwhich is only true thrice in every four times. The first fact being true\neight times in twelve, and the second being true six times in every\neight, and consequently six times in those eight; both facts will be\ntrue only six times in twelve. On the other hand if T, although it is\nboth an A and a C, is not a B, something is true which is only true once\nin every thrice, and something else which is only true once in every\nfour times. The former being true four times out of twelve, and the\nlatter once in every four, and therefore once in those four; both are\nonly true in one case out of twelve. So that T is a B six times in\ntwelve, and T is not a B, only once: making the comparative\nprobabilities, not eleven to one, as I had previously made them, but six\nto one.\n\nIt may be asked, what happens in the remaining cases? since in this\ncalculation seven out of twelve cases seem to have exhausted the\npossibilities. If T is a B in only six cases of every twelve, and a\nnot-B in only one, what is it in the other five? The only supposition\nremaining for those cases is that it is neither a B nor not a B, which\nis impossible. But this impossibility merely proves that the state of\nthings supposed in the hypothesis does not exist in those cases. They\nare cases that do not furnish anything which is both an A and a C.\n\nTo make this intelligible, we will substitute for our symbols a concrete\ncase. Let there be two witnesses, M and N, whose probabilities of\nveracity correspond with the ratios of the preceding example: M speaks\ntruth twice in every thrice, N thrice in every four times. The question\nis, what is the probability that a statement, in which they both concur,\nwill be true. The cases may be classed as follows. Both the witnesses\nwill speak truly six in every twelve times; both falsely once in twelve\ntimes. Therefore, if they both agree in an assertion, it will be true\nsix times, for once that it will be false. What happens in the remaining\ncases is here evident; there will be five cases in every twelve in which\nthe witnesses will not agree. M will speak truth and N falsehood in two\ncases of every twelve; N will speak truth and M falsehood in three\ncases, making in all five. In these cases, however, the witnesses will\nnot agree in their testimony. But disagreement between them is excluded\nby the supposition. There are, therefore, only seven cases which are\nwithin the conditions of the hypothesis; of which seven, veracity exists\nin six, and falsehood in one. Resuming our former symbols, in five cases\nout of twelve T is not both an A and a C, but an A only, or a C only.\nThe cases in which it is both are only seven, in six of which it is a B,\nin one not a B, making the chance six to one, or 6/7 and 1/7\nrespectively.\n\nIn this correct, as in the former incorrect computation, it is of course\npresupposed that the probabilities arising from A and C are independent\nof each other. There must not be any such connexion between A and C,\nthat when a thing belongs to the one class it will therefore belong to\nthe other, or even have a greater chance of doing so. Otherwise the\nnot-Bs which are Cs may be, most or even all of them, identical with the\nnot-Bs which are As; in which last case the probability arising from A\nand C together will be no greater than that arising from A alone.\n\nWhen approximate generalizations are joined together in the other mode,\nthat of deduction, the degree of probability of the inference, instead\nof increasing, diminishes at each step. From two such premises as Most A\nare B, Most B are C, we cannot with certainty conclude that even a\nsingle A is C; for the whole of the portion of A which in any way falls\nunder B, may perhaps be comprised in the exceptional part of it. Still,\nthe two propositions in question afford an appreciable probability that\nany given A is C, provided the average on which the second proposition\nis grounded, was taken fairly with reference to the first; provided the\nproposition, Most B are C, was arrived at in a manner leaving no\nsuspicion that the probability arising from it is otherwise than fairly\ndistributed over the section of B which belongs to A. For though the\ninstances which are A _may_ be all in the minority, they may, also, be\nall in the majority; and the one possibility is to be set against the\nother. On the whole, the probability arising from the two propositions\ntaken together, will be correctly measured by the probability arising\nfrom the one, abated in the ratio of that arising from the other. If\nnine out of ten Swedes have light hair, and eight out of nine\ninhabitants of Stockholm are Swedes, the probability arising from these\ntwo propositions, that any given inhabitant of Stockholm is\nlight-haired, will amount to eight in ten; though it is rigorously\npossible that the whole Swedish population of Stockholm might belong to\nthat tenth section of the people of Sweden who are an exception to the\nrest.\n\nIf the premises are known to be true not of a bare majority, but of\nnearly the whole, of their respective subjects, we may go on joining one\nsuch proposition to another for several steps, before we reach a\nconclusion not presumably true even of a majority. The error of the\nconclusion will amount to the aggregate of the errors of all the\npremises. Let the proposition, Most A are B, be true of nine in ten;\nMost B are C, of eight in nine: then not only will one A in ten not be\nC, because not B, but even of the nine-tenths which are B, only\neight-ninths will be C: that is, the cases of A which are C will be only\n8/9 of 9/10, or four-fifths. Let us now add Most C are D, and suppose\nthis to be true of seven cases out of eight; the proportion of A which\nis D will be only 7/8 of 8/9 of 9/10, or 7/10. Thus the probability\nprogressively dwindles. The experience, however, on which our\napproximate generalizations are grounded, has so rarely been subjected\nto, or admits of, accurate numerical estimation, that we cannot in\ngeneral apply any measurement to the diminution of probability which\ntakes place at each illation; but must be content with remembering that\nit does diminish at every step, and that unless the premises approach\nvery nearly indeed to being universally true, the conclusion after a\nvery few steps is worth nothing. A hearsay of a hearsay, or an argument\nfrom presumptive evidence depending not on immediate marks but on marks\nof marks, is worthless at a very few removes from the first stage.\n\n\n\u00a7 7. There are, however, two cases in which reasonings depending on\napproximate generalizations may be carried to any length we please with\nas much assurance, and are as strictly scientific, as if they were\ncomposed of universal laws of nature. But these cases are exceptions of\nthe sort which are currently said to prove the rule. The approximate\ngeneralizations are as suitable, in the cases in question, for purposes\nof ratiocination, as if they were complete generalizations, because they\nare capable of being transformed into complete generalizations exactly\nequivalent.\n\nFirst: If the approximate generalization is of the class in which our\nreason for stopping at the approximation is not the impossibility, but\nonly the inconvenience, of going further; if we are cognizant of the\ncharacter which distinguishes the cases that accord with the\ngeneralization from those which are exceptions to it; we may then\nsubstitute for the approximate proposition, an universal proposition\nwith a proviso. The proposition, Most persons who have uncontrolled\npower employ it ill, is a generalization of this class, and may be\ntransformed into the following:--All persons who have uncontrolled power\nemploy it ill, provided they are not persons of unusual strength of\njudgment and rectitude of purpose. The proposition, carrying the\nhypothesis or proviso with it, may then be dealt with no longer as an\napproximate, but as an universal proposition; and to whatever number of\nsteps the reasoning may reach, the hypothesis, being carried forward to\nthe conclusion, will exactly indicate how far that conclusion is from\nbeing applicable universally. If in the course of the argument other\napproximate generalizations are introduced, each of them being in like\nmanner expressed as an universal proposition with a condition annexed,\nthe sum of all the conditions will appear at the end as the sum of all\nthe errors which affect the conclusion. Thus, to the proposition last\ncited, let us add the following:--All absolute monarchs have\nuncontrolled power, unless their position is such that they need the\nactive support of their subjects (as was the case with Queen Elizabeth,\nFrederick of Prussia, and others). Combining these two propositions, we\ncan deduce from them an universal conclusion, which will be subject to\nboth the hypotheses in the premises; All absolute monarchs employ their\npower ill, unless their position makes them need the active support of\ntheir subjects, or unless they are persons of unusual strength of\njudgment and rectitude of purpose. It is of no consequence how rapidly\nthe errors in our premises accumulate, if we are able in this manner to\nrecord each error, and keep an account of the aggregate as it swells up.\n\nSecondly: there is a case in which approximate propositions, even\nwithout our taking note of the conditions under which they are not true\nof individual cases, are yet, for the purposes of science, universal\nones; namely, in the inquiries which relate to the properties not of\nindividuals, but of multitudes. The principal of these is the science of\npolitics, or of human society. This science is principally concerned\nwith the actions not of solitary individuals, but of masses; with the\nfortunes not of single persons, but of communities.\n\nFor the statesman, therefore, it is generally enough to know that\n_most_ persons act or are acted upon in a particular way; since his\nspeculations and his practical arrangements refer almost exclusively to\ncases in which the whole community, or some large portion of it, is\nacted upon at once, and in which, therefore, what is done or felt by\n_most_ persons determines the result produced by or upon the body at\nlarge. He can get on well enough with approximate generalizations on\nhuman nature, since what is true approximately of all individuals is\ntrue absolutely of all masses. And even when the operations of\nindividual men have a part to play in his deductions, as when he is\nreasoning of kings, or other single rulers, still, as he is providing\nfor indefinite duration, involving an indefinite succession of such\nindividuals, he must in general both reason and act as if what is true\nof most persons were true of all.\n\nThe two kinds of considerations above adduced are a sufficient\nrefutation of the popular error, that speculations on society and\ngovernment, as resting on merely probable evidence, must be inferior in\ncertainty and scientific accuracy to the conclusions of what are called\nthe exact sciences, and less to be relied on in practice. There are\nreasons enough why the moral sciences must remain inferior to at least\nthe more perfect of the physical: why the laws of their more complicated\nphenomena cannot be so completely deciphered, nor the phenomena\npredicted with the same degree of assurance. But though we cannot attain\nto so many truths, there is no reason that those we can attain should\ndeserve less reliance, or have less of a scientific character. Of this\ntopic, however, I shall treat more systematically in the concluding\nBook, to which place any further consideration of it must be deferred.\n\n\n\n\nCHAPTER XXIV.\n\nOF THE REMAINING LAWS OF NATURE.\n\n\n\u00a7 1. In the First Book, we found that all the assertions which can be\nconveyed by language, express some one or more of five different things:\nExistence; Order in Place; Order in Time; Causation; and\nResemblance.[36] Of these, Causation, in our view of the subject, not\nbeing fundamentally different from Order in Time, the five species of\npossible assertions are reduced to four. The propositions which affirm\nOrder in Time, in either of its two modes, Coexistence and Succession,\nhave formed, thus far, the subject of the present Book. And we have now\nconcluded the exposition, so far as it falls within the limits assigned\nto this work, of the nature of the evidence on which these propositions\nrest, and the processes of investigation by which they are ascertained\nand proved. There remain three classes of facts: Existence, Order in\nPlace, and Resemblance; in regard to which the same questions are now to\nbe resolved.\n\nRegarding the first of these, very little needs be said. Existence in\ngeneral, is a subject not for our science, but for metaphysics. To\ndetermine what things can be recognised as really existing,\nindependently of our own sensible or other impressions, and in what\nmeaning the term is, in that case, predicated of them, belongs to the\nconsideration of \"Things in themselves,\" from which, throughout this\nwork, we have as much as possible kept aloof. Existence, so far as Logic\nis concerned about it, has reference only to phenomena; to actual, or\npossible, states of external or internal consciousness, in ourselves or\nothers. Feelings of sensitive beings, or possibilities of having such\nfeelings, are the only things the existence of which can be a subject\nof logical induction, because the only things of which the existence in\nindividual cases can be a subject of experience.\n\nIt is true that a thing is said by us to exist, even when it is absent,\nand therefore is not and cannot be perceived. But even then, its\nexistence is to us only another word for our conviction that we should\nperceive it on a certain supposition; namely, if we were in the needful\ncircumstances of time and place, and endowed with the needful perfection\nof organs. My belief that the Emperor of China exists, is simply my\nbelief that if I were transported to the imperial palace or some other\nlocality in Pekin, I should see him. My belief that Julius C\u00e6sar\nexisted, is my belief that I should have seen him if I had been present\nin the field of Pharsalia, or in the senate-house at Rome. When I\nbelieve that stars exist beyond the utmost range of my vision, though\nassisted by the most powerful telescopes yet invented, my belief,\nphilosophically expressed, is, that with still better telescopes, if\nsuch existed, I could see them, or that they may be perceived by beings\nless remote from them in space, or whose capacities of perception are\nsuperior to mine.\n\nThe existence, therefore, of a phenomenon, is but another word for its\nbeing perceived, or for the inferred possibility of perceiving it. When\nthe phenomenon is within the range of present observation, by present\nobservation we assure ourselves of its existence; when it is beyond that\nrange, and is therefore said to be absent, we infer its existence from\nmarks or evidences. But what can these evidences be? Other phenomena;\nascertained by induction to be connected with the given phenomenon,\neither in the way of succession or of coexistence. The simple existence,\ntherefore, of an individual phenomenon, when not directly perceived, is\ninferred from some inductive law of succession or coexistence: and is\nconsequently not amenable to any peculiar inductive principles. We prove\nthe existence of a thing, by proving that it is connected by succession\nor coexistence with some known thing.\n\nWith respect to _general_ propositions of this class, that is, which\naffirm the bare fact of existence, they have a peculiarity which renders\nthe logical treatment of them a very easy matter; they are\ngeneralizations which are sufficiently proved by a single instance. That\nghosts, or unicorns, or sea-serpents exist, would be fully established\nif it could be ascertained positively that such things had been even\nonce seen. Whatever has once happened, is capable of happening again;\nthe only question relates to the conditions under which it happens.\n\nSo far, therefore, as relates to simple existence, the Inductive Logic\nhas no knots to untie. And we may proceed to the remaining two of the\ngreat classes into which facts have been divided; Resemblance, and Order\nin Space.\n\n\n\u00a7 2. Resemblance and its opposite, except in the case in which they\nassume the names of Equality and Inequality, are seldom regarded as\nsubjects of science; they are supposed to be perceived by simple\napprehension; by merely applying our senses or directing our attention\nto the two objects at once, or in immediate succession. And this\nsimultaneous, or virtually simultaneous, application of our faculties to\nthe two things which are to be compared, does necessarily constitute the\nultimate appeal, wherever such application is practicable. But, in most\ncases, it is not practicable: the objects cannot be brought so close\ntogether that the feeling of their resemblance (at least a complete\nfeeling of it) directly arises in the mind. We can only compare each of\nthem with some third object, capable of being transported from one to\nthe other. And besides, even when the objects can be brought into\nimmediate juxtaposition, their resemblance or difference is but\nimperfectly known to us, unless we have compared them minutely, part by\npart. Until this has been done, things in reality very dissimilar often\nappear undistinguishably alike. Two lines of very unequal length will\nappear about equal when lying in different directions; but place them\nparallel, with their farther extremities even, and if we look at the\nnearer extremities, their inequality becomes a matter of direct\nperception.\n\nTo ascertain whether, and in what, two phenomena resemble or differ, is\nnot always, therefore, so easy a thing as it might at first appear. When\nthe two cannot be brought into juxtaposition, or not so that the\nobserver is able to compare their several parts in detail, he must\nemploy the indirect means of reasoning and general propositions. When we\ncannot bring two straight lines together, to determine whether they are\nequal, we do it by the physical aid of a foot rule applied first to one\nand then to the other, and the logical aid of the general proposition or\nformula, \"Things which are equal to the same thing are equal to one\nanother.\" The comparison of two things through the intervention of a\nthird thing, when their direct comparison is impossible, is the\nappropriate scientific process for ascertaining resemblances and\ndissimilarities, and is the sum total of what Logic has to teach on the\nsubject.\n\nAn undue extension of this remark induced Locke to consider reasoning\nitself as nothing but the comparison of two ideas through the medium of\na third, and knowledge as the perception of the agreement or\ndisagreement of two ideas: doctrines which the Condillac school blindly\nadopted, without the qualifications and distinctions with which they\nwere studiously guarded by their illustrious author. Where, indeed, the\nagreement or disagreement (otherwise called resemblance or\ndissimilarity) of any two things is the very matter to be determined, as\nis the case particularly in the sciences of quantity and extension;\nthere, the process by which a solution, if not attainable by direct\nperception, must be indirectly sought, consists in comparing these two\nthings through the medium of a third. But this is far from being true of\nall inquiries. The knowledge that bodies fall to the ground is not a\nperception of agreement or disagreement, but of a series of physical\noccurrences, a succession of sensations. Locke's definitions of\nknowledge and of reasoning required to be limited to our knowledge of,\nand reasoning about, resemblances. Nor, even when thus restricted, are\nthe propositions strictly correct; since the comparison is not made, as\nhe represents, between the ideas of the two phenomena, but between the\nphenomena themselves. This mistake has been pointed out in an earlier\npart of our inquiry,[37] and we traced it to an imperfect conception of\nwhat takes place in mathematics, where very often the comparison is\nreally made between the ideas, without any appeal to the outward senses;\nonly, however, because in mathematics a comparison of the ideas is\nstrictly equivalent to a comparison of the phenomena themselves. Where,\nas in the case of numbers, lines, and figures, our idea of an object is\na complete picture of the object, so far as respects the matter in hand;\nwe can, of course, learn from the picture, whatever could be learnt from\nthe object itself by mere contemplation of it as it exists at the\nparticular instant when the picture is taken. No mere contemplation of\ngunpowder would ever teach us that a spark would make it explode, nor,\nconsequently, would the contemplation of the idea of gunpowder do so:\nbut the mere contemplation of a straight line shows that it cannot\ninclose a space: accordingly the contemplation of the idea of it will\nshow the same. What takes place in mathematics is thus no argument that\nthe comparison is between the ideas only. It is always, either\nindirectly or directly, a comparison of the phenomena.\n\nIn cases in which we cannot bring the phenomena to the test of direct\ninspection at all, or not in a manner sufficiently precise, but must\njudge of their resemblance by inference from other resemblances or\ndissimilarities more accessible to observation, we of course require, as\nin all cases of ratiocination, generalizations or formul\u00e6 applicable to\nthe subject. We must reason from laws of nature; from the uniformities\nwhich are observable in the fact of likeness or unlikeness.\n\n\n\u00a7 3. Of these laws or uniformities, the most comprehensive are those\nsupplied by mathematics; the axioms relating to equality, inequality,\nand proportionality, and the various theorems thereon founded. And these\nare the only Laws of Resemblance which require to be, or which can be,\ntreated apart. It is true there are innumerable other theorems which\naffirm resemblances among phenomena; as that the angle of the reflection\nof light is _equal_ to its angle of incidence (equality being merely\nexact resemblance in magnitude). Again, that the heavenly bodies\ndescribe _equal_ areas in equal times; and that their periods of\nrevolution are _proportional_ (another species of resemblance) to the\nsesquiplicate powers of their distances from the centre of force. These\nand similar propositions affirm resemblances, of the same nature with\nthose asserted in the theorems of mathematics; but the distinction is,\nthat the propositions of mathematics are true of all phenomena whatever,\nor at least without distinction of origin; while the truths in question\nare affirmed only of special phenomena, which originate in a certain\nway; and the equalities, proportionalities, or other resemblances, which\nexist between such phenomena, must necessarily be either derived from,\nor identical with, the law of their origin--the law of causation on\nwhich they depend. The equality of the areas described in equal times by\nthe planets, is _derived_ from the laws of the causes; and, until its\nderivation was shown, it was an empirical law. The equality of the\nangles of reflexion and incidence is _identical_ with the law of the\ncause; for the cause is the incidence of a ray of light upon a\nreflecting surface, and the equality in question is the very law\naccording to which that cause produces its effects. This class,\ntherefore, of the uniformities of resemblance between phenomena, are\ninseparable, in fact and in thought, from the laws of the production of\nthose phenomena: and the principles of induction applicable to them are\nno other than those of which we have treated in the preceding chapters\nof this Book.\n\nIt is otherwise with the truths of mathematics. The laws of equality and\ninequality between spaces, or between numbers, have no connexion with\nlaws of causation. That the angle of reflexion is equal to the angle of\nincidence, is a statement of the mode of action of a particular cause;\nbut that when two straight lines intersect each other the opposite\nangles are equal, is true of all such lines and angles, by whatever\ncause produced. That the squares of the periodic times of the planets\nare proportional to the cubes of their distances from the sun, is an\nuniformity derived from the laws of the causes (or forces) which produce\nthe planetary motions; but that the square of any number is four times\nthe square of half the number, is true independently of any cause. The\nonly laws of resemblance, therefore, which we are called upon to\nconsider independently of causation, belong to the province of\nmathematics.\n\n\n\u00a7 4. The same thing is evident with respect to the only one remaining of\nour five categories, Order in Place. The order in place, of the effects\nof a cause, is (like everything else belonging to the effects) a\nconsequence of the laws of that cause. The order in place, or, as we\nhave termed it, the collocation, of the primeval causes, is (as well as\ntheir resemblance) in each instance an ultimate fact, in which no laws\nor uniformities are traceable. The only remaining general propositions\nrespecting order in place, and the only ones which have nothing to do\nwith causation, are some of the truths of geometry; laws through which\nwe are able, from the order in place of certain points, lines, or\nspaces, to infer the order in place of others which are connected with\nthe former in some known mode; quite independently of the particular\nnature of those points, lines, or spaces, in any other respect than\nposition or magnitude, as well as independently of the physical cause\nfrom which in any particular case they happen to derive their origin.\n\nIt thus appears that mathematics is the only department of science into\nthe methods of which it still remains to inquire. And there is the less\nnecessity that this inquiry should occupy us long, as we have already,\nin the Second Book, made considerable progress in it. We there remarked,\nthat the directly inductive truths of mathematics are few in number;\nconsisting of the axioms, together with certain propositions concerning\nexistence, tacitly involved in most of the so-called definitions. And we\ngave what appeared conclusive reasons for affirming that these original\npremises, from which the remaining truths of the science are deduced,\nare, notwithstanding all appearances to the contrary, results of\nobservation and experience; founded, in short, on the evidence of the\nsenses. That things equal to the same thing are equal to one another,\nand that two straight lines which have once intersected one another\ncontinue to diverge, are inductive truths; resting, indeed, like the law\nof universal causation, only on induction _per enumerationem simplicem_;\non the fact that they have been perpetually perceived to be true, and\nnever once found to be false. But, as we have seen in a recent chapter\nthat this evidence, in the case of a law so completely universal as the\nlaw of causation, amounts to the fullest proof, so is this even more\nevidently true of the general propositions to which we are now\nadverting; because, as a perception of their truth in any individual\ncase whatever, requires only the simple act of looking at the objects in\na proper position, there never could have been in their case (what, for\na long period, there were in the case of the law of causation) instances\nwhich were apparently, though not really, exceptions to them. Their\ninfallible truth was recognised from the very dawn of speculation; and\nas their extreme familiarity made it impossible for the mind to conceive\nthe objects under any other law, they were, and still are, generally\nconsidered as truths recognised by their own evidence, or by instinct.\n\n\n\u00a7 5. There is something which seems to require explanation, in the fact\nthat the immense multitude of truths (a multitude still as far from\nbeing exhausted as ever) comprised in the mathematical sciences, can be\nelicited from so small a number of elementary laws. One sees not, at\nfirst, how it is that there can be room for such an infinite variety of\ntrue propositions, on subjects apparently so limited.\n\nTo begin with the science of number. The elementary or ultimate truths\nof this science are the common axioms concerning equality, namely,\n\"Things which are equal to the same thing are equal to one another,\" and\n\"Equals added to equals make equal sums,\" (no other axioms are\nrequired,[38]) together with the definitions of the various numbers.\nLike other so-called definitions, these are composed of two things, the\nexplanation of a name, and the assertion of a fact: of which the latter\nalone can form a first principle or premise of a science. The fact\nasserted in the definition of a number is a physical fact. Each of the\nnumbers two, three, four, &c., denotes physical phenomena, and connotes\na physical property of those phenomena. Two, for instance, denotes all\npairs of things, and twelve all dozens of things, connoting what makes\nthem pairs, or dozens; and that which makes them so is something\nphysical; since it cannot be denied that two apples are physically\ndistinguishable from three apples, two horses from one horse, and so\nforth: that they are a different visible and tangible phenomenon. I am\nnot undertaking to say what the difference is; it is enough that there\nis a difference of which the senses can take cognizance. And although a\nhundred and two horses are not so easily distinguished from a hundred\nand three, as two horses are from three--though in most positions the\nsenses do not perceive any difference--yet they may be so placed that a\ndifference will be perceptible, or else we should never have\ndistinguished them, and given them different names. Weight is\nconfessedly a physical property of things; yet small differences between\ngreat weights are as imperceptible to the senses in most situations, as\nsmall differences between great numbers; and are only put in evidence by\nplacing the two objects in a peculiar position--namely, in the opposite\nscales of a delicate balance.\n\nWhat, then, is that which is connoted by a name of number? Of course\nsome property belonging to the agglomeration of things which we call by\nthe name; and that property is, the characteristic manner in which the\nagglomeration is made up of, and may be separated into, parts. I will\nendeavour to make this more intelligible by a few explanations.\n\nWhen we call a collection of objects _two_, _three_, or _four_, they are\nnot two, three, or four in the abstract; they are two, three, or four\nthings of some particular kind; pebbles, horses, inches, pounds weight.\nWhat the name of number connotes is, the manner in which single objects\nof the given kind must be put together, in order to produce that\nparticular aggregate. If the aggregate be of pebbles, and we call it\n_two_, the name implies that, to compose the aggregate, one pebble must\nbe joined to one pebble. If we call it _three_, one and one and one\npebble must be brought together to produce it, or else one pebble must\nbe joined to an aggregate of the kind called _two_, already existing.\nThe aggregate which we call _four_, has a still greater number of\ncharacteristic modes of formation. One and one and one and one pebble\nmay be brought together; or two aggregates of the kind called _two_ may\nbe united; or one pebble may be added to an aggregate of the kind called\n_three_. Every succeeding number in the ascending series, may be formed\nby the junction of smaller numbers in a progressively greater variety of\nways. Even limiting the parts to two, the number may be formed, and\nconsequently may be divided, in as many different ways as there are\nnumbers smaller than itself; and, if we admit of threes, fours, &c., in\na still greater variety. Other modes of arriving at the same aggregate\npresent themselves, not by the union of smaller, but by the\ndismemberment of larger aggregates. Thus, _three pebbles_ may be formed\nby taking away one pebble from an aggregate of four; _two pebbles_, by\nan equal division of a similar aggregate; and so on.\n\nEvery arithmetical proposition; every statement of the result of an\narithmetical operation; is a statement of one of the modes of formation\nof a given number. It affirms that a certain aggregate might have been\nformed by putting together certain other aggregates, or by withdrawing\ncertain portions of some aggregate; and that, by consequence, we might\nreproduce those aggregates from it, by reversing the process.\n\nThus, when we say that the cube of 12 is 1728, what we affirm is this:\nthat if, having a sufficient number of pebbles or of any other objects,\nwe put them together into the particular sort of parcels or aggregates\ncalled twelves; and put together these twelves again into similar\ncollections; and, finally, make up twelve of these largest parcels; the\naggregate thus formed will be such a one as we call 1728; namely, that\nwhich (to take the most familiar of its modes of formation) may be made\nby joining the parcel called a thousand pebbles, the parcel called seven\nhundred pebbles, the parcel called twenty pebbles, and the parcel called\neight pebbles.\n\nThe converse proposition, that the cube root of 1728 is 12, asserts that\nthis large aggregate may again be decomposed into the twelve twelves of\ntwelves of pebbles which it consists of.\n\nThe modes of formation of any number are innumerable; but when we know\none mode of formation of each, all the rest may be determined\ndeductively. If we know that _a_ is formed from _b_ and _c_, _b_ from\n_a_ and _e_, _c_ from _d_ and _f_, and so forth, until we have included\nall the numbers of any scale we choose to select, (taking care that for\neach number the mode of formation be really a distinct one, not bringing\nus round again to the former numbers, but introducing a new number,) we\nhave a set of propositions from which we may reason to all the other\nmodes of formation of those numbers from one another. Having established\na chain of inductive truths connecting together all the numbers of the\nscale, we can ascertain the formation of any one of those numbers from\nany other by merely travelling from one to the other along the chain.\nSuppose that we know only the following modes of formation: 6 = 4 + 2, 4\n= 7 - 3, 7 = 5 + 2, 5 = 9 - 4. We could determine how 6 may be formed\nfrom 9. For 6 = 4 + 2 = 7 - 3 + 2 = 5 + 2 - 3 + 2 = 9 - 4 + 2 - 3 + 2.\nIt may therefore be formed by taking away 4 and 3, and adding 2 and 2.\nIf we know besides that 2 + 2 = 4, we obtain 6 from 9 in a simpler mode,\nby merely taking away 3.\n\nIt is sufficient, therefore, to select one of the various modes of\nformation of each number, as a means of ascertaining all the rest. And\nsince things which are uniform, and therefore simple, are most easily\nreceived and retained by the understanding, there is an obvious\nadvantage in selecting a mode of formation which shall be alike for all;\nin fixing the connotation of names of number on one uniform principle.\nThe mode in which our existing numerical nomenclature is contrived\npossesses this advantage, with the additional one, that it happily\nconveys to the mind two of the modes of formation of every number. Each\nnumber is considered as formed by the addition of an unit to the number\nnext below it in magnitude, and this mode of formation is conveyed by\nthe place which it occupies in the series. And each is also considered\nas formed by the addition of a number of units less than ten, and a\nnumber of aggregates each equal to one of the successive powers of ten;\nand this mode of its formation is expressed by its spoken name, and by\nits numerical character.\n\nWhat renders arithmetic the type of a deductive science, is the\nfortunate applicability to it of a law so comprehensive as \"The sums of\nequals are equals:\" or (to express the same principle in less familiar\nbut more characteristic language), Whatever is made up of parts, is made\nup of the parts of those parts. This truth, obvious to the senses in all\ncases which can be fairly referred to their decision, and so general as\nto be coextensive with nature itself, being true of all sorts of\nphenomena, (for all admit of being numbered,) must be considered an\ninductive truth, or law of nature, of the highest order. And every\narithmetical operation is an application of this law, or of other laws\ncapable of being deduced from it. This is our warrant for all\ncalculations. We believe that five and two are equal to seven, on the\nevidence of this inductive law, combined with the definitions of those\nnumbers. We arrive at that conclusion (as all know who remember how they\nfirst learned it) by adding a single unit at a time: 5 + 1 = 6,\ntherefore 5 + 1 + 1 = 6 + 1 = 7: and again 2 = 1 + 1, therefore 5 + 2 =\n5 + 1 + 1 = 7.\n\n\n\u00a7 6. Innumerable as are the true propositions which can be formed\nconcerning particular numbers, no adequate conception could be gained,\nfrom these alone, of the extent of the truths composing the science of\nnumber. Such propositions as we have spoken of are the least general of\nall numerical truths. It is true that even these are coextensive with\nall nature: the properties of the number four are true of all objects\nthat are divisible into four equal parts, and all objects are either\nactually or ideally so divisible. But the propositions which compose the\nscience of algebra are true, not of a particular number, but of all\nnumbers; not of all things under the condition of being divided in a\nparticular way, but of all things under the condition of being divided\nin any way--of being designated by a number at all.\n\nSince it is impossible for different numbers to have any of their modes\nof formation completely in common, it is a kind of paradox to say, that\nall propositions which can be made concerning numbers relate to their\nmodes of formation from other numbers, and yet that there are\npropositions which are true of all numbers. But this very paradox leads\nto the real principle of generalization concerning the properties of\nnumbers. Two different numbers cannot be formed in the same manner from\nthe same numbers; but they may be formed in the same manner from\ndifferent numbers; as nine is formed from three by multiplying it into\nitself, and sixteen is formed from four by the same process. Thus there\narises a classification of modes of formation, or in the language\ncommonly used by mathematicians, a classification of Functions. Any\nnumber, considered as formed from any other number, is called a function\nof it; and there are as many kinds of functions as there are modes of\nformation. The simple functions are by no means numerous, most functions\nbeing formed by the combination of several of the operations which form\nsimple functions, or by successive repetitions of some one of those\noperations. The simple functions of any number _x_ are all reducible to\nthe following forms: _x + a_, _x - a_, _a x_, _x/a_, _x^a_, _a [root\nof] x_, log. _x_ (to the base _a_), and the same expressions varied by\nputting _x_ for _a_ and _a_ for _x_, wherever that substitution would\nalter the value: to which perhaps ought to be added sin _x_, and arc\n(sin = _x_). All other functions of _x_ are formed by putting some one\nor more of the simple functions in the place of _x_ or _a_, and\nsubjecting them to the same elementary operations.\n\nIn order to carry on general reasonings on the subject of Functions, we\nrequire a nomenclature enabling us to express any two numbers by names\nwhich, without specifying what particular numbers they are, shall show\nwhat function each is of the other; or, in other words, shall put in\nevidence their mode of formation from one another. The system of general\nlanguage called algebraical notation does this. The expressions _a_ and\n_a^2 + 3a_ denote, the one any number, the other the number formed\nfrom it in a particular manner. The expressions _a_, _b_, _n_, and _(a +\nb)^n_, denote any three numbers, and a fourth which is formed from\nthem in a certain mode.\n\nThe following may be stated as the general problem of the algebraical\ncalculus: F being a certain function of a given number, to find what\nfunction F will be of any function of that number. For example, a\nbinomial _a_ + _b_ is a function of its two parts _a_ and _b_, and the\nparts are, in their turn, functions of _a + b_: now _(a + b)^n_ is a\ncertain function of the binomial; what function will this be of _a_ and\n_b_, the two parts? The answer to this question is the binomial theorem.\nThe formula _(a + b)^n = a^n + (n / 1) a^(n - 1) b + ((n\u00b7(n - 1)) /\n(1\u00b72)) a^(n - 2) b^2 + &c._, shows in what manner the number which is\nformed by multiplying _a + b_ into itself _n_ times, might be formed\nwithout that process, directly from _a_, _b_, and _n_. And of this\nnature are all the theorems of the science of number. They assert the\nidentity of the result of different modes of formation. They affirm that\nsome mode of formation from _x_, and some mode of formation from a\ncertain function of _x_, produce the same number.\n\nBesides these general theorems of formul\u00e6, what remains in the\nalgebraical calculus is the resolution of equations. But the resolution\nof an equation is also a theorem. If the equation be _x^2 + ax = b_,\nthe resolution of this equation, viz. _x = -(1/2) a \u00b1 [root of]((1/4)\na^2 + b)_, is a general proposition, which may be regarded as an\nanswer to the question, If _b_ is a certain function of _x_ and _a_\n(namely _x^2 + ax_), what function is _x_ of _b_ and _a_? The\nresolution of equations is, therefore, a mere variety of the general\nproblem as above stated. The problem is--Given a function, what function\nis it of some other function? And in the resolution of an equation, the\nquestion is, to find what function of one of its own functions the\nnumber itself is.\n\nSuch as above described, is the aim and end of the calculus. As for its\nprocesses, every one knows that they are simply deductive. In\ndemonstrating an algebraical theorem, or in resolving an equation, we\ntravel from the _datum_ to the _qu\u00e6situm_ by pure ratiocination; in\nwhich the only premises introduced, besides the original hypotheses, are\nthe fundamental axioms already mentioned--that things equal to the same\nthing are equal to one another, and that the sums of equal things are\nequal. At each step in the demonstration or in the calculation, we apply\none or other of these truths, or truths deducible from them, as, that\nthe differences, products, &c., of equal numbers are equal.\n\nIt would be inconsistent with the scale of this work, and not necessary\nto its design, to carry the analysis of the truths and processes of\nalgebra any farther; which is also the less needful, as the task has\nbeen, to a very great extent, performed by other writers. Peacock's\nAlgebra, and Dr. Whewell's _Doctrine of Limits_, are full of instruction\non the subject. The profound treatises of a truly philosophical\nmathematician, Professor De Morgan, should be studied by every one who\ndesires to comprehend the evidence of mathematical truths, and the\nmeaning of the obscurer processes of the calculus; and the speculations\nof M. Comte, in his _Cours de Philosophie Positive_, on the philosophy\nof the higher branches of mathematics, are among the many valuable gifts\nfor which philosophy is indebted to that eminent thinker.\n\n\n\u00a7 7. If the extreme generality, and remoteness not so much from sense as\nfrom the visual and tactual imagination, of the laws of number, renders\nit a somewhat difficult effort of abstraction to conceive those laws as\nbeing in reality physical truths obtained by observation; the same\ndifficulty does not exist with regard to the laws of extension. The\nfacts of which those laws are expressions, are of a kind peculiarly\naccessible to the senses, and suggesting eminently distinct images to\nthe fancy. That geometry is a strictly physical science would doubtless\nhave been recognised in all ages, had it not been for the illusions\nproduced by two circumstances. One of these is the characteristic\nproperty, already noticed, of the facts of geometry, that they may be\ncollected from our ideas or mental pictures of objects as effectually as\nfrom the objects themselves. The other is, the demonstrative character\nof geometrical truths; which was at one time supposed to constitute a\nradical distinction between them and physical truths, the latter, as\nresting on merely probable evidence, being deemed essentially uncertain\nand unprecise. The advance of knowledge has, however, made it manifest\nthat physical science, in its better understood branches, is quite as\ndemonstrative as geometry. The task of deducing its details from a few\ncomparatively simple principles is found to be anything but the\nimpossibility it was once supposed to be; and the notion of the superior\ncertainty of geometry is an illusion, arising from the ancient prejudice\nwhich, in that science, mistakes the ideal data from which we reason,\nfor a peculiar class of realities, while the corresponding ideal data of\nany deductive physical science are recognised as what they really are,\nmere hypotheses.\n\nEvery theorem in geometry is a law of external nature, and might have\nbeen ascertained by generalizing from observation and experiment, which\nin this case resolve themselves into comparison and measurement. But it\nwas found practicable, and being practicable, was desirable, to deduce\nthese truths by ratiocination from a small number of general laws of\nnature, the certainty and universality of which are obvious to the most\ncareless observer, and which compose the first principles and ultimate\npremises of the science. Among these general laws must be included the\nsame two which we have noticed as ultimate principles of the Science of\nNumber also, and which are applicable to every description of quantity;\nviz. The sums of equals are equal, and Things which are equal to the\nsame thing are equal to one another; the latter of which may be\nexpressed in a manner more suggestive of the inexhaustible multitude of\nits consequences, by the following terms: Whatever is equal to any one\nof a number of equal magnitudes, is equal to any other of them. To these\ntwo must be added, in geometry, a third law of equality, namely, that\nlines, surfaces, or solid spaces, which can be so applied to one another\nas to coincide, are equal. Some writers have asserted that this law of\nnature is a mere verbal definition; that the expression \"equal\nmagnitudes\" _means_ nothing but magnitudes which can be so applied to\none another as to coincide. But in this opinion I cannot agree. The\nequality of two geometrical magnitudes cannot differ fundamentally in\nits nature from the equality of two weights, two degrees of heat, or two\nportions of duration, to none of which would this pretended definition\nof equality be suitable. None of these things can be so applied to one\nanother as to coincide, yet we perfectly understand what we mean when we\ncall them equal. Things are equal in magnitude, as things are equal in\nweight, when they are felt to be exactly similar in respect of the\nattribute in which we compare them: and the application of the objects\nto each other in the one case, like the balancing them with a pair of\nscales in the other, is but a mode of bringing them into a position in\nwhich our senses can recognise deficiencies of exact resemblance that\nwould otherwise escape our notice.\n\nAlong with these three general principles or axioms, the remainder of\nthe premises of geometry consists of the so-called definitions, that is\nto say, propositions asserting the real existence of the various\nobjects therein designated, together with some one property of each. In\nsome cases more than one property is commonly assumed, but in no case is\nmore than one necessary. It is assumed that there are such things in\nnature as straight lines, and that any two of them setting out from the\nsame point, diverge more and more without limit. This assumption, (which\nincludes and goes beyond Euclid's axiom that two straight lines cannot\ninclose a space,) is as indispensable in geometry, and as evident,\nresting on as simple, familiar, and universal observation, as any of the\nother axioms. It is also assumed that straight lines diverge from one\nanother in different degrees; in other words, that there are such things\nas angles, and that they are capable of being equal or unequal. It is\nassumed that there is such a thing as a circle, and that all its radii\nare equal; such things as ellipses, and that the sums of the focal\ndistances are equal for every point in an ellipse; such things as\nparallel lines, and that those lines are everywhere equally distant.[39]\n\n\n\u00a7 8. It is a matter of more than curiosity to consider, to what\npeculiarity of the physical truths which are the subject of geometry, it\nis owing that they can all be deduced from so small a number of\noriginal premises: why it is that we can set out from only one\ncharacteristic property of each kind of phenomenon, and with that and\ntwo or three general truths relating to equality, can travel from mark\nto mark until we obtain a vast body of derivative truths, to all\nappearance extremely unlike those elementary ones.\n\nThe explanation of this remarkable fact seems to lie in the following\ncircumstances. In the first place, all questions of position and figure\nmay be resolved into questions of magnitude. The position and figure of\nany object are determined, by determining the position of a sufficient\nnumber of points in it; and the position of any point may be determined\nby the magnitude of three rectangular co-ordinates, that is, of the\nperpendiculars drawn from the point to three planes at right angles to\none another, arbitrarily selected. By this transformation of all\nquestions of quality into questions only of quantity, geometry is\nreduced to the single problem of the measurement of magnitudes, that is,\nthe ascertainment of the equalities which exist between them. Now when\nwe consider that by one of the general axioms, any equality, when\nascertained, is proof of as many other equalities as there are other\nthings equal to either of the two equals; and that by another of those\naxioms, any ascertained equality is proof of the equality of as many\npairs of magnitudes as can be formed by the numerous operations which\nresolve themselves into the addition of the equals to themselves or to\nother equals; we cease to wonder that in proportion as a science is\nconversant about equality, it should afford a more copious supply of\nmarks of marks; and that the sciences of number and extension, which are\nconversant with little else than equality, should be the most deductive\nof all the sciences.\n\nThere are also two or three of the principal laws of space or extension\nwhich are unusually fitted for rendering one position or magnitude a\nmark of another, and thereby contributing to render the science largely\ndeductive. First; the magnitudes of inclosed spaces, whether superficial\nor solid, are completely determined by the magnitudes of the lines and\nangles which bound them. Secondly, the length of any line, whether\nstraight or curve, is measured (certain other things being given) by the\nangle which it subtends, and _vice vers\u00e2_. Lastly, the angle which any\ntwo straight lines make with each other at an inaccessible point, is\nmeasured by the angles they severally make with any third line we choose\nto select. By means of these general laws, the measurement of all lines,\nangles, and spaces whatsoever might be accomplished by measuring a\nsingle straight line and a sufficient number of angles; which is the\nplan actually pursued in the trigonometrical survey of a country; and\nfortunate it is that this is practicable, the exact measurement of long\nstraight lines being always difficult, and often impossible, but that of\nangles very easy. Three such generalizations as the foregoing afford\nsuch facilities for the indirect measurement of magnitudes, (by\nsupplying us with known lines or angles which are marks of the magnitude\nof unknown ones, and thereby of the spaces which they inclose,) that it\nis easily intelligible how from a few data we can go on to ascertain the\nmagnitude of an indefinite multitude of lines, angles, and spaces, which\nwe could not easily, or could not at all, measure by any more direct\nprocess.\n\n\n\u00a7 9. Such are the few remarks which it seemed necessary to make in this\nplace, respecting the laws of nature which are the peculiar subject of\nthe sciences of number and extension. The immense part which those laws\ntake in giving a deductive character to the other departments of\nphysical science, is well known; and is not surprising, when we consider\nthat all causes operate according to mathematical laws. The effect is\nalways dependent on, or is a function of, the quantity of the agent; and\ngenerally of its position also. We cannot, therefore, reason respecting\ncausation, without introducing considerations of quantity and extension\nat every step; and if the nature of the phenomena admits of our\nobtaining numerical data of sufficient accuracy, the laws of quantity\nbecome the grand instrument for calculating forward to an effect, or\nbackward to a cause. That in all other sciences, as well as in\ngeometry, questions of quality are scarcely ever independent of\nquestions of quantity, may be seen from the most familiar phenomena.\nEven when several colours are mixed on a painter's palette, the\ncomparative quantity of each entirely determines the colour of the\nmixture.\n\nWith this mere suggestion of the general causes which render\nmathematical principles and processes so predominant in those deductive\nsciences which afford precise numerical data, I must, on the present\noccasion, content myself: referring the reader who desires a more\nthorough acquaintance with the subject, to the first two volumes of M.\nComte's systematic work.\n\nIn the same work, and more particularly in the third volume, are also\nfully discussed the limits of the applicability of mathematical\nprinciples to the improvement of other sciences. Such principles are\nmanifestly inapplicable, where the causes on which any class of\nphenomena depend are so imperfectly accessible to our observation, that\nwe cannot ascertain, by a proper induction, their numerical laws; or\nwhere the causes are so numerous, and intermixed in so complex a manner\nwith one another, that even supposing their laws known, the computation\nof the aggregate effect transcends the powers of the calculus as it is,\nor is likely to be; or lastly, where the causes themselves are in a\nstate of perpetual fluctuation; as in physiology, and still more, if\npossible, in the social science. The mathematical solutions of physical\nquestions become progressively more difficult and imperfect, in\nproportion as the questions divest themselves of their abstract and\nhypothetical character, and approach nearer to the degree of\ncomplication actually existing in nature; insomuch that beyond the\nlimits of astronomical phenomena, and of those most nearly analogous to\nthem, mathematical accuracy is generally obtained \"at the expense of the\nreality of the inquiry:\" while even in astronomical questions,\n\"notwithstanding the admirable simplicity of their mathematical\nelements, our feeble intelligence becomes incapable of following out\neffectually the logical combinations of the laws on which the phenomena\nare dependent, as soon as we attempt to take into simultaneous\nconsideration more than two or three essential influences.\"[40] Of\nthis, the problem of the Three Bodies has already been cited, more than\nonce, as a remarkable instance; the complete solution of so\ncomparatively simple a question having vainly tried the skill of the\nmost profound mathematicians. We may conceive, then, how chimerical\nwould be the hope that mathematical principles could be advantageously\napplied to phenomena dependent on the mutual action of the innumerable\nminute particles of bodies, as those of chemistry, and still more, of\nphysiology; and for similar reasons those principles remain inapplicable\nto the still more complex inquiries, the subjects of which are phenomena\nof society and government.\n\nThe value of mathematical instruction as a preparation for those more\ndifficult investigations, consists in the applicability not of its\ndoctrines, but of its method. Mathematics will ever remain the most\nperfect type of the Deductive Method in general; and the applications of\nmathematics to the deductive branches of physics, furnish the only\nschool in which philosophers can effectually learn the most difficult\nand important portion of their art, the employment of the laws of\nsimpler phenomena for explaining and predicting those of the more\ncomplex. These grounds are quite sufficient for deeming mathematical\ntraining an indispensable basis of real scientific education, and\nregarding (according to the _dictum_ which an old but unauthentic\ntradition ascribes to Plato) one who is [Greek: age\u00f4metr\u00eatos], as\nwanting in one of the most essential qualifications for the successful\ncultivation of the higher branches of philosophy.\n\n\n\n\nCHAPTER XXV.\n\nOF THE GROUNDS OF DISBELIEF.\n\n\n\u00a7 1. The method of arriving at general truths, or general propositions\nfit to be believed, and the nature of the evidence on which they are\ngrounded, have been discussed, as far as space and the writer's\nfaculties permitted, in the twenty-four preceding chapters. But the\nresult of the examination of evidence is not always belief, nor even\nsuspension of judgment; it is sometimes disbelief. The philosophy,\ntherefore, of induction and experimental inquiry is incomplete, unless\nthe grounds not only of belief, but of disbelief, are treated of; and to\nthis topic we shall devote one, and the final, chapter.\n\nBy disbelief is not here to be understood the mere absence of belief.\nThe ground for abstaining from belief is simply the absence or\ninsufficiency of proof; and in considering what is sufficient evidence\nto support any given conclusion, we have already, by implication,\nconsidered what evidence is not sufficient for the same purpose. By\ndisbelief is here meant, not the state of mind in which we form no\nopinion concerning a subject, but that in which we are fully persuaded\nthat some opinion is not true; insomuch that if evidence, even of great\napparent strength, (whether grounded on the testimony of others or on\nour own supposed perceptions,) were produced in favour of the opinion,\nwe should believe that the witnesses spoke falsely, or that they, or we\nourselves if we were the direct percipients, were mistaken.\n\nThat there are such cases, no one is likely to dispute. Assertions for\nwhich there is abundant positive evidence are often disbelieved, on\naccount of what is called their improbability, or impossibility. And the\nquestion for consideration is what, in the present case, these words\nmean, and how far and in what circumstances the properties which they\nexpress are sufficient grounds for disbelief.\n\n\n\u00a7 2. It is to be remarked in the first place, that the positive evidence\nproduced in support of an assertion which is nevertheless rejected on\nthe score of impossibility or improbability, is never such as amounts to\nfull proof. It is always grounded on some approximate generalization.\nThe fact may have been asserted by a hundred witnesses; but there are\nmany exceptions to the universality of the generalization that what a\nhundred witnesses affirm is true. We may seem to ourselves to have\nactually seen the fact: but, that we really see what we think we see, is\nby no means an universal truth; our organs may have been in a morbid\nstate; or we may have inferred something, and imagined that we perceived\nit. The evidence, then, in the affirmative being never more than an\napproximate generalization, all will depend on what the evidence in the\nnegative is. If that also rests on an approximate generalization, it is\na case for comparison of probabilities. If the approximate\ngeneralizations leading to the affirmative are, when added together,\nless strong, or in other words, farther from being universal, than the\napproximate generalizations which support the negative side of the\nquestion, the proposition is said to be improbable, and is to be\ndisbelieved provisionally. If however an alleged fact be in\ncontradiction, not to any number of approximate generalizations, but to\na completed generalization grounded on a rigorous induction, it is said\nto be impossible, and is to be disbelieved totally.\n\nThis last principle, simple and evident as it appears, is the doctrine\nwhich, on the occasion of an attempt to apply it to the question of the\ncredibility of miracles, excited so violent a controversy. Hume's\ncelebrated doctrine, that nothing is credible which is contradictory to\nexperience, or at variance with laws of nature, is merely this very\nplain and harmless proposition, that whatever is contradictory to a\ncomplete induction is incredible. That such a maxim as this should\neither be accounted a dangerous heresy, or mistaken for a great and\nrecondite truth, speaks ill for the state of philosophical speculation\non such subjects.\n\nBut does not (it may be asked) the very statement of the proposition\nimply a contradiction? An alleged fact, according to this theory, is not\nto be believed if it contradict a complete induction. But it is\nessential to the completeness of an induction that it shall not\ncontradict any known fact. Is it not then a _petitio principii_ to say,\nthat the fact ought to be disbelieved because the induction opposed to\nit is complete? How can we have a right to declare the induction\ncomplete, while facts, supported by credible evidence, present\nthemselves in opposition to it?\n\nI answer, we have that right whenever the scientific canons of induction\ngive it to us; that is, whenever the induction _can_ be complete. We\nhave it, for example, in a case of causation in which there has been an\n_experimentum crucis_. If an antecedent A, superadded to a set of\nantecedents in all other respects unaltered, is followed by an effect B\nwhich did not exist before, A is, in that instance at least, the cause\nof B, or an indispensable part of its cause; and if A be tried again\nwith many totally different sets of antecedents and B still follows,\nthen it is the whole cause. If these observations or experiments have\nbeen repeated so often, and by so many persons, as to exclude all\nsupposition of error in the observer, a law of nature is established;\nand so long as this law is received as such, the assertion that on any\nparticular occasion A took place, and yet B did not follow, _without any\ncounteracting cause_, must be disbelieved. Such an assertion is not to\nbe credited on any less evidence than what would suffice to overturn the\nlaw. The general truths, that whatever has a beginning has a cause, and\nthat when none but the same causes exist, the same effects follow, rest\non the strongest inductive evidence possible; the proposition that\nthings affirmed by even a crowd of respectable witnesses are true, is\nbut an approximate generalization; and--even if we fancy we actually saw\nor felt the fact which is in contradiction to the law--what a human\nbeing can see is no more than a set of appearances; from which the real\nnature of the phenomenon is merely an inference, and in this inference\napproximate generalizations usually have a large share. If, therefore,\nwe make our election to hold by the law, no quantity of evidence\nwhatever ought to persuade us that there has occurred anything in\ncontradiction to it. If, indeed, the evidence produced is such that it\nis more likely that the set of observations and experiments on which the\nlaw rests should have been inaccurately performed or incorrectly\ninterpreted, than that the evidence in question should be false, we may\nbelieve the evidence; but then we must abandon the law. And since the\nlaw was received on what seemed a complete induction, it can only be\nrejected on evidence equivalent; namely, as being inconsistent not with\nany number of approximate generalizations, but with some other and\nbetter established law of nature. This extreme case, of a conflict\nbetween two supposed laws of nature, has probably never actually\noccurred where, in the process of investigating both the laws, the true\ncanons of scientific induction had been kept in view; but if it did\noccur, it must terminate in the total rejection of one of the supposed\nlaws. It would prove that there must be a flaw in the logical process by\nwhich either one or the other was established: and if there be so, that\nsupposed general truth is no truth at all. We cannot admit a proposition\nas a law of nature, and yet believe a fact in real contradiction to it.\nWe must disbelieve the alleged fact, or believe that we were mistaken in\nadmitting the supposed law.\n\nBut in order that any alleged fact should be contradictory to a law of\ncausation, the allegation must be, not simply that the cause existed\nwithout being followed by the effect, for that would be no uncommon\noccurrence; but that this happened in the absence of any adequate\ncounteracting cause. Now in the case of an alleged miracle, the\nassertion is the exact opposite of this. It is, that the effect was\ndefeated, not in the absence, but in consequence of a counteracting\ncause, namely, a direct interposition of an act of the will of some\nbeing who has power over nature; and in particular of a Being, whose\nwill being assumed to have endowed all the causes with the powers by\nwhich they produce their effects, may well be supposed able to\ncounteract them. A miracle (as was justly remarked by Brown[41]) is no\ncontradiction to the law of cause and effect; it is a new effect,\nsupposed to be produced by the introduction of a new cause. Of the\nadequacy of that cause, if present, there can be no doubt; and the only\nantecedent improbability which can be ascribed to the miracle, is the\nimprobability that any such cause existed.\n\nAll, therefore, which Hume has made out, and this he must be considered\nto have made out, is, that (at least in the imperfect state of our\nknowledge of natural agencies, which leaves it always possible that some\nof the physical antecedents may have been hidden from us,) no evidence\ncan prove a miracle to any one who did not previously believe the\nexistence of a being or beings with supernatural power; or who believes\nhimself to have full proof that the character of the Being whom he\nrecognises, is inconsistent with his having seen fit to interfere on the\noccasion in question.\n\nIf we do not already believe in supernatural agencies, no miracle can\nprove to us their existence. The miracle itself, considered merely as an\nextraordinary fact, may be satisfactorily certified by our senses or by\ntestimony; but nothing can ever prove that it is a miracle: there is\nstill another possible hypothesis, that of its being the result of some\nunknown natural cause: and this possibility cannot be so completely shut\nout, as to leave no alternative but that of admitting the existence and\nintervention of a being superior to nature. Those, however, who already\nbelieve in such a being, have two hypotheses to choose from, a\nsupernatural and an unknown natural agency; and they have to judge which\nof the two is the most probable in the particular case. In forming this\njudgment, an important element of the question will be the conformity of\nthe result to the laws of the supposed agent, that is, to the character\nof the Deity as they conceive it. But, with the knowledge which we now\npossess of the general uniformity of the course of nature, religion,\nfollowing in the wake of science, has been compelled to acknowledge the\ngovernment of the universe as being on the whole carried on by general\nlaws, and not by special interpositions. To whoever holds this belief,\nthere is a general presumption against any supposition of divine agency\nnot operating through general laws, or in other words, there is an\nantecedent improbability in every miracle, which, in order to outweigh\nit, requires an extraordinary strength of antecedent probability derived\nfrom the special circumstances of the case.\n\n\n\u00a7 3. It appears from what has been said, that the assertion that a cause\nhas been defeated of an effect which is connected with it by a\ncompletely ascertained law of causation, is to be disbelieved or not,\naccording to the probability or improbability that there existed in the\nparticular instance an adequate counteracting cause. To form an estimate\nof this, is not more difficult than of other probabilities. With regard\nto all _known_ causes capable of counteracting the given causes, we have\ngenerally some previous knowledge of the frequency or rarity of their\noccurrence, from which we may draw an inference as to the antecedent\nimprobability of their having been present in any particular case. And\nneither in respect to known or unknown causes are we required to\npronounce on the probability of their existing in nature, but only of\ntheir having existed at the time and place at which the transaction is\nalleged to have happened. We are seldom, therefore, without the means\n(when the circumstances of the case are at all known to us) of judging\nhow far it is likely that such a cause should have existed at that time\nand place without manifesting its presence by some other marks, and (in\nthe case of an unknown cause) without having hitherto manifested its\nexistence in any other instance. According as this circumstance, or the\nfalsity of the testimony, appears more improbable, that is, conflicts\nwith an approximate generalization of a higher order, we believe the\ntestimony, or disbelieve it; with a stronger or a weaker degree of\nconviction, according to the preponderance: at least until we have\nsifted the matter further.\n\nSo much, then, for the case in which the alleged fact conflicts, or\nappears to conflict, with a real law of causation. But a more common\ncase, perhaps, is that of its conflicting with uniformities of mere\ncoexistence, not proved to be dependent on causation: in other words,\nwith the properties of Kinds. It is with these uniformities principally,\nthat the marvellous stories related by travellers are apt to be at\nvariance: as of men with tails, or with wings, and (until confirmed by\nexperience) of flying fish; or of ice, in the celebrated anecdote of the\nDutch travellers and the King of Siam. Facts of this description, facts\npreviously unheard of but which could not from any known law of\ncausation be pronounced impossible, are what Hume characterizes as not\ncontrary to experience, but merely unconformable to it; and Bentham, in\nhis treatise on Evidence, denominates them facts disconformable _in\nspecie_, as distinguished from such as are disconformable _in toto_ or\nin _degree_.\n\nIn a case of this description, the fact asserted is the existence of a\nnew Kind; which in itself is not in the slightest degree incredible, and\nonly to be rejected if the improbability that any variety of object\nexisting at the particular place and time should not have been\ndiscovered sooner, be greater than that of error or mendacity in the\nwitnesses. Accordingly, such assertions, when made by credible persons,\nand of unexplored places, are not disbelieved, but at most regarded as\nrequiring confirmation from subsequent observers; unless the alleged\nproperties of the supposed new Kind are at variance with known\nproperties of some larger kind which includes it; or in other words,\nunless, in the new Kind which is asserted to exist, some properties are\nsaid to have been found disjoined from others which have always been\nknown to accompany them; as in the case of Pliny's men, or any other\nkind of animal of a structure different from that which has always been\nfound to coexist with animal life. On the mode of dealing with any such\ncase, little needs be added to what has been said on the same topic in\nthe twenty-second chapter.[42] When the uniformities of coexistence\nwhich the alleged fact would violate, are such as to raise a strong\npresumption of their being the result of causation, the fact which\nconflicts with them is to be disbelieved; at least provisionally, and\nsubject to further investigation. When the presumption amounts to a\nvirtual certainty, as in the case of the general structure of organized\nbeings, the only question requiring consideration is whether, in\nphenomena so little understood, there may not be liabilities to\ncounteraction from causes hitherto unknown; or whether the phenomena may\nnot be capable of originating in some other way, which would produce a\ndifferent set of derivative uniformities. Where (as in the case of the\nflying fish, or the ornithorhynchus) the generalization to which the\nalleged fact would be an exception is very special and of limited range,\nneither of the above suppositions can be deemed very improbable; and it\nis generally, in the case of such alleged anomalies, wise to suspend our\njudgment, pending the subsequent inquiries which will not fail to\nconfirm the assertion if it be true. But when the generalization is very\ncomprehensive, embracing a vast number and variety of observations, and\ncovering a considerable province of the domain of nature; then, for\nreasons which have been fully explained, such an empirical law comes\nnear to the certainty of an ascertained law of causation: and any\nalleged exception to it cannot be admitted, unless on the evidence of\nsome law of causation proved by a still more complete induction.\n\nSuch uniformities in the course of nature as do not bear marks of being\nthe results of causation, are, as we have already seen, admissible as\nuniversal truths with a degree of credence proportioned to their\ngenerality. Those which are true of all things whatever, or at least\nwhich are totally independent of the varieties of Kinds, namely, the\nlaws of number and extension, to which we may add the law of causation\nitself, are probably the only ones, an exception to which is absolutely\nand permanently incredible. Accordingly, it is to assertions supposed to\nbe contradictory to these laws, or to some others coming near to them in\ngenerality, that the word impossibility (at least _total_ impossibility)\nseems to be generally confined. Violations of other laws, of special\nlaws of causation for instance, are said, by persons studious of\naccuracy in expression, to be impossible _in the circumstances of the\ncase_; or impossible unless some cause had existed which did not exist\nin the particular case.[43] Of no assertion, not in contradiction to\nsome of these very general laws, will more than improbability be\nasserted by any cautious person; and improbability not of the highest\ndegree, unless the time and place in which the fact is said to have\noccurred, render it almost certain that the anomaly, if real, could not\nhave been overlooked by other observers. Suspension of judgment is in\nall other cases the resource of the judicious inquirer; provided the\ntestimony in favour of the anomaly presents, when well sifted, no\nsuspicious circumstances.\n\nBut the testimony is scarcely ever found to stand that test, in cases in\nwhich the anomaly is not real. In the instances on record in which a\ngreat number of witnesses, of good reputation and scientific\nacquirements, have testified to the truth of something which has turned\nout untrue, there have almost always been circumstances which, to a keen\nobserver who had taken due pains to sift the matter, would have rendered\nthe testimony untrustworthy. There have generally been means of\naccounting for the impression on the senses or minds of the alleged\npercipients, by fallacious appearances; or some epidemic delusion,\npropagated by the contagious influence of popular feeling, has been\nconcerned in the case; or some strong interest has been\nimplicated--religious zeal, party feeling, vanity, or at least the\npassion for the marvellous, in persons strongly susceptible of it. When\nnone of these or similar circumstances exist to account for the apparent\nstrength of the testimony; and where the assertion is not in\ncontradiction either to those universal laws which know no counteraction\nor anomaly, or to the generalizations next in comprehensiveness to them,\nbut would only amount, if admitted, to the existence of an unknown cause\nor an anomalous Kind, in circumstances not so thoroughly explored but\nthat it is credible that things hitherto unknown may still come to\nlight; a cautious person will neither admit nor reject the testimony,\nbut will wait for confirmation at other times and from other unconnected\nsources. Such ought to have been the conduct of the King of Siam when\nthe Dutch travellers affirmed to him the existence of ice. But an\nignorant person is as obstinate in his contemptuous incredulity as he is\nunreasonably credulous. Anything unlike his own narrow experience he\ndisbelieves, if it flatters no propensity; any nursery tale is swallowed\nimplicitly by him if it does.\n\n\n\u00a7 4. I shall now advert to a very serious misapprehension of the\nprinciples of the subject, which has been committed by some of the\nwriters against Hume's Essay on Miracles, and by Bishop Butler before\nthem, in their anxiety to destroy what appeared to them a formidable\nweapon of assault against the Christian religion; and the effect of\nwhich is entirely to confound the doctrine of the Grounds of Disbelief.\nThe mistake consists in overlooking the distinction between (what may be\ncalled) improbability before the fact, and improbability after it; or\n(since, as Mr. Venn remarks, the distinction of past and future is not\nthe material circumstance) between the improbability of a mere guess\nbeing right, and the improbability of an alleged fact being true.\n\nMany events are altogether improbable to us, before they have happened,\nor before we are informed of their happening, which are not in the least\nincredible when we are informed of them, because not contrary to any,\neven approximate, induction. In the cast of a perfectly fair die, the\nchances are five to one against throwing ace, that is, ace will be\nthrown on an average only once in six throws. But this is no reason\nagainst believing that ace was thrown on a given occasion, if any\ncredible witness asserts it; since though ace is only thrown once in six\ntimes, _some_ number which is only thrown once in six times must have\nbeen thrown if the die was thrown at all. The improbability, then, or in\nother words, the unusualness, of any fact, is no reason for disbelieving\nit, if the nature of the case renders it certain that either that or\nsomething equally improbable, that is, equally unusual, did happen. Nor\nis this all: for even if the other five sides of the die were all twos,\nor all threes, yet as ace would still on the average come up once in\nevery six throws, its coming up in a given throw would be not in any way\ncontradictory to experience. If we disbelieved all facts which had the\nchances against them beforehand, we should believe hardly anything. We\nare told that A. B. died yesterday: the moment before we were so told,\nthe chances against his having died on that day may have been ten\nthousand to one; but since he was certain to die at some time or other,\nand when he died must necessarily die on some particular day, while the\npreponderance of chances is very great against every day in particular,\nexperience affords no ground for discrediting any testimony which may be\nproduced to the event's having taken place on a given day.\n\nYet it has been considered, by Dr. Campbell and others, as a complete\nanswer to Hume's doctrine (that things are incredible which are\n_contrary_ to the uniform course of experience), that we do not\ndisbelieve, merely because the chances were against them, things in\nstrict _conformity_ to the uniform course of experience; that we do not\ndisbelieve an alleged fact merely because the combination of causes on\nwhich it depends occurs only once in a certain number of times. It is\nevident that whatever is shown by observation, or can be proved from\nlaws of nature, to occur in a certain proportion (however small) of the\nwhole number of possible cases, is not contrary to experience; though we\nare right in disbelieving it, if some other supposition respecting the\nmatter in question involves on the whole a less departure from the\nordinary course of events. Yet, on such grounds as this have able\nwriters been led to the extraordinary conclusion, that nothing supported\nby credible testimony ought ever to be disbelieved.\n\n\n\u00a7 5. We have considered two species of events, commonly said to be\nimprobable; one kind which are in no way extraordinary, but which,\nhaving an immense preponderance of chances against them, are improbable\nuntil they are affirmed, but no longer; another kind which, being\ncontrary to some recognised law of nature, are incredible on any amount\nof testimony except such as would be sufficient to shake our belief in\nthe law itself. But between these two classes of events, there is an\nintermediate class, consisting of what are commonly termed Coincidences:\nin other words, those combinations of chances which present some\npeculiar and unexpected regularity, assimilating them, in so far, to the\nresults of law. As if, for example, in a lottery of a thousand tickets,\nthe numbers should be drawn in the exact order of what are called the\nnatural numbers, 1, 2, 3, &c. We have still to consider the principles\nof evidence applicable to this case: whether there is any difference\nbetween coincidences and ordinary events, in the amount of testimony or\nother evidence necessary to render them credible.\n\nIt is certain, that on every rational principle of expectation, a\ncombination of this peculiar sort may be expected quite as often as any\nother given series of a thousand numbers; that with perfectly fair dice,\nsixes will be thrown twice, thrice, or any number of times in\nsuccession, quite as often in a thousand or a million throws, as any\nother succession of numbers fixed upon beforehand; and that no judicious\nplayer would give greater odds against the one series than against the\nother. Notwithstanding this, there is a general disposition to regard\nthe one as much more improbable than the other, and as requiring much\nstronger evidence to make it credible. Such is the force of this\nimpression, that it has led some thinkers to the conclusion, that nature\nhas greater difficulty in producing regular combinations than irregular\nones; or in other words, that there is some general tendency of things,\nsome law, which prevents regular combinations from occurring, or at\nleast from occurring so often as others. Among these thinkers may be\nnumbered D'Alembert; who, in an Essay on Probabilities to be found in\nthe fifth volume of his _M\u00e9langes_, contends that regular combinations,\nthough equally probable according to the mathematical theory with any\nothers, are physically less probable. He appeals to common sense, or in\nother words, to common impressions; saying, if dice thrown repeatedly in\nour presence gave sixes every time, should we not, before the number of\nthrows had reached ten, (not to speak of thousands of millions,) be\nready to affirm, with the most positive conviction, that the dice were\nfalse?\n\nThe common and natural impression is in favour of D'Alembert: the\nregular series would be thought much more unlikely than an irregular.\nBut this common impression is, I apprehend, merely grounded on the fact,\nthat scarcely anybody remembers to have ever seen one of these peculiar\ncoincidences: the reason of which is simply that no one's experience\nextends to anything like the number of trials, within which that or any\nother given combination of events can be expected to happen. The chance\nof sixes on a single throw of two dice being 1/36, the chance of sixes\nten times in succession is 1 divided by the tenth power of 36; in other\nwords, such a concurrence is only likely to happen once in\n3,656,158,440,062,976 trials, a number which no dice-player's experience\ncomes up to a millionth part of. But if, instead of sixes ten times, any\nother given succession of ten throws had been fixed upon, it would have\nbeen exactly as unlikely that in any individual's experience that\nparticular succession had ever occurred; although this does not _seem_\nequally improbable, because no one could possibly have remembered\nwhether it had occurred or not, and because the comparison is tacitly\nmade, not between sixes ten times and any one particular series of\nthrows, but between all regular and all irregular successions taken\ntogether.\n\nThat (as D'Alembert says) if the succession of sixes was actually thrown\nbefore our eyes, we should ascribe it not to chance, but to unfairness\nin the dice, is unquestionably true. But this arises from a totally\ndifferent principle. We should then be considering, not the probability\nof the fact in itself, but the comparative probability with which, when\nit is known to have happened, it may be referred to one or to another\ncause. The regular series is not at all less likely than the irregular\none to be brought about by chance, but it is much more likely than the\nirregular one to be produced by design; or by some general cause\noperating through the structure of the dice. It is the nature of casual\ncombinations to produce a repetition of the same event, as often and no\noftener than any other series of events. But it is the nature of general\ncauses to reproduce, in the same circumstances, always the same event.\nCommon sense and science alike dictate that, all other things being the\nsame, we should rather attribute the effect to a cause which if real\nwould be very likely to produce it, than to a cause which would be very\nunlikely to produce it. According to Laplace's sixth theorem, which we\ndemonstrated in a former chapter, the difference of probability arising\nfrom the superior _efficacy_ of the constant cause, unfairness in the\ndice, would after a very few throws far outweigh any antecedent\nprobability which there could be against its existence.\n\nD'Alembert should have put the question in another manner. He should\nhave supposed that we had ourselves previously tried the dice, and knew\nby ample experience that they were fair. Another person then tries them\nin our absence, and assures us that he threw sixes ten times in\nsuccession. Is the assertion credible or not? Here the effect to be\naccounted for is not the occurrence itself, but the fact of the\nwitness's asserting it. This may arise either from its having really\nhappened, or from some other cause. What we have to estimate is the\ncomparative probability of these two suppositions.\n\nIf the witness affirmed that he had thrown any other series of numbers,\nsupposing him to be a person of veracity, and tolerable accuracy, and to\nprofess that he took particular notice, we should believe him. But the\nten sixes are exactly as likely to have been really thrown as the other\nseries. If, therefore, this assertion is less credible than the other,\nthe reason must be, not that it is less likely than the other to be made\ntruly, but that it is more likely than the other to be made falsely.\n\nOne reason obviously presents itself why what is called a coincidence,\nshould be oftener asserted falsely than an ordinary combination. It\nexcites wonder. It gratifies the love of the marvellous. The motives,\ntherefore, to falsehood, one of the most frequent of which is the desire\nto astonish, operate more strongly in favour of this kind of assertion\nthan of the other kind. Thus far there is evidently more reason for\ndiscrediting an alleged coincidence, than a statement in itself not more\nprobable, but which if made would not be thought remarkable. There are\ncases, however, in which the presumption on this ground would be the\nother way. There are some witnesses who, the more extraordinary an\noccurrence might appear, would be the more anxious to verify it by the\nutmost carefulness of observation before they would venture to believe\nit, and still more before they would assert it to others.\n\n\n\u00a7 6. Independently, however, of any peculiar chances of mendacity\narising from the nature of the assertion, Laplace contends, that merely\non the general ground of the fallibility of testimony, a coincidence is\nnot credible on the same amount of testimony on which we should be\nwarranted in believing an ordinary combination of events. In order to do\njustice to his argument, it is necessary to illustrate it by the example\nchosen by himself.\n\nIf, says Laplace, there were one thousand tickets in a box, and one only\nhas been drawn out, then if an eye-witness affirms that the number drawn\nwas 79, this, though the chances were 999 in 1000 against it, is not on\nthat account the less credible; its credibility is equal to the\nantecedent probability of the witness's veracity. But if there were in\nthe box 999 black balls and only one white, and the witness affirms that\nthe white ball was drawn, the case according to Laplace is very\ndifferent: the credibility of his assertion is but a small fraction of\nwhat it was in the former case; the reason of the difference being as\nfollows.\n\nThe witnesses of whom we are speaking must, from the nature of the case,\nbe of a kind whose credibility falls materially short of certainty: let\nus suppose, then, the credibility of the witness in the case in question\nto be 9/10; that is, let us suppose that in every ten statements which\nthe witness makes, nine on an average are correct, and one incorrect.\nLet us now suppose that there have taken place a sufficient number of\ndrawings to exhaust all the possible combinations, the witness deposing\nin every one. In one case out of every ten in all these drawings he will\nactually have made a false announcement. But in the case of the thousand\ntickets these false announcements will have been distributed impartially\nover all the numbers, and of the 999 cases in which No. 79 was not\ndrawn, there will have been only one case in which it was announced. On\nthe contrary, in the case of the thousand balls, (the announcement being\nalways either \"black\" or \"white,\") if white was not drawn, and there was\na false announcement, that false announcement _must_ have been white;\nand since by the supposition there was a false announcement once in\nevery ten times, white will have been announced falsely in one tenth\npart of all the cases in which it was not drawn, that is, in one tenth\npart of 999 cases out of every thousand. White, then, is drawn, on an\naverage, exactly as often as No. 79, but it is announced, without having\nbeen really drawn, 999 times as often as No. 79; the announcement\ntherefore requires a much greater amount of testimony to render it\ncredible.[44]\n\nTo make this argument valid it must of course be supposed, that the\nannouncements made by the witness are average specimens of his general\nveracity and accuracy; or, at least, that they are neither more nor less\nso in the case of the black and white balls, than in the case of the\nthousand tickets. This assumption, however, is not warranted. A person\nis far less likely to mistake, who has only one form of error to guard\nagainst, than if he had 999 different errors to avoid. For instance, in\nthe example chosen, a messenger who might make a mistake once in ten\ntimes in reporting the number drawn in a lottery, might not err once in\na thousand times if sent simply to observe whether a ball was black or\nwhite. Laplace's argument therefore is faulty even as applied to his own\ncase. Still less can that case be received as completely representing\nall cases of coincidence. Laplace has so contrived his example, that\nthough black answers to 999 distinct possibilities, and white only to\none, the witness has nevertheless no bias which can make him prefer\nblack to white. The witness did not know that there were 999 black balls\nin the box and only one white; or if he did, Laplace has taken care to\nmake all the 999 cases so undistinguishably alike, that there is hardly\na possibility of any cause of falsehood or error operating in favour of\nany of them, which would not operate in the same manner if there were\nonly one. Alter this supposition, and the whole argument falls to the\nground. Let the balls, for instance, be numbered, and let the white ball\nbe No. 79. Considered in respect of their colour, there are but two\nthings which the witness can be interested in asserting, or can have\ndreamt or hallucinated, or has to choose from if he answers at random,\nviz. black and white: but considered in respect of the numbers attached\nto them, there are a thousand: and if his interest or error happens to\nbe connected with the numbers, though the only assertion he makes is\nabout the colour, the case becomes precisely assimilated to that of the\nthousand tickets. Or instead of the balls suppose a lottery, with 1000\ntickets and but one prize, and that I hold No. 79, and being interested\nonly in that, ask the witness not what was the number drawn, but whether\nit was 79 or some other. There are now only two cases, as in Laplace's\nexample; yet he surely would not say that if the witness answered 79,\nthe assertion would be in an enormous proportion less credible, than if\nhe made the same answer to the same question asked in the other way. If,\nfor instance, (to put a case supposed by Laplace himself,) he has staked\na large sum on one of the chances, and thinks that by announcing its\noccurrence he shall increase his credit; he is equally likely to have\nbetted on any one of the 999 numbers which are attached to black balls,\nand so far as the chances of mendacity from this cause are concerned,\nthere will be 999 times as many chances of his announcing black falsely,\nas white.\n\nOr suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and\nthat of these one man has been killed, and it is not known which. I ask\nthe question, and the witness answers, the Frenchman. This was not only\nas improbable _\u00e0 priori_, but is in itself as singular a circumstance,\nas remarkable a coincidence, as the drawing of the white ball: yet we\nshould believe the statement as readily, as if the answer had been John\nThompson. Because though the 999 Englishmen were all alike in the point\nin which they differed from the Frenchman, they were not, like the 999\nblack balls, undistinguishable in every other respect; but being all\ndifferent, they admitted as many chances of interest or error, as if\neach man had been of a different nation; and if a lie was told or a\nmistake made, the misstatement was as likely to fall on any Jones or\nThompson of the set, as on the Frenchman.\n\nThe example of a coincidence selected by D'Alembert, that of sixes\nthrown on a pair of dice ten times in succession, belongs to this sort\nof cases rather than to such as Laplace's. The coincidence is here far\nmore remarkable, because of far rarer occurrence, than the drawing of\nthe white ball. But though the improbability of its really occurring is\ngreater, the superior probability of its being announced falsely cannot\nbe established with the same evidence. The announcement \"black\"\nrepresented 999 cases, but the witness may not have known this, and if\nhe did, the 999 cases are so exactly alike, that there is really only\none set of possible causes of mendacity corresponding to the whole. The\nannouncement \"sixes _not_ drawn ten times,\" represents, and is known by\nthe witness to represent, a great multitude of contingencies, every one\nof which being unlike every other, there may be a different and a fresh\nset of causes of mendacity corresponding to each.\n\nIt appears to me, therefore, that Laplace's doctrine is not strictly\ntrue of any coincidences, and is wholly inapplicable to most: and that\nto know whether a coincidence does or does not require more evidence to\nrender it credible than an ordinary event, we must refer, in every\ninstance, to first principles, and estimate afresh what is the\nprobability that the given testimony would have been delivered in that\ninstance, supposing the fact which it asserts not to be true.\n\nWith these remarks we close the discussion of the Grounds of Disbelief;\nand along with it, such exposition as space admits, and as the writer\nhas it in his power to furnish, of the Logic of Induction.\n\nFOOTNOTES:\n\n[1] _Cours de Philosophie Positive_, ii. 656.\n\n[2] Vide supra, book iii. ch. xi.\n\n[3] _Philosophy of Discovery_, pp. 185 et seqq.\n\n[4] _Philosophie Positive_, ii. 434-437.\n\n[5] As an example of legitimate hypothesis according to the test here\nlaid down, has been justly cited that of Broussais, who, proceeding on\nthe very rational principle that every disease must originate in some\ndefinite part or other of the organism, boldly assumed that certain\nfevers, which not being known to be local were called constitutional,\nhad their origin in the mucous membrane of the alimentary canal. The\nsupposition was indeed, as is now generally admitted, erroneous; but he\nwas justified in making it, since by deducing the consequences of the\nsupposition, and comparing them with the facts of those maladies, he\nmight be certain of disproving his hypothesis if it was ill founded, and\nmight expect that the comparison would materially aid him in framing\nanother more conformable to the phenomena.\n\nThe doctrine now universally received, that the earth is a natural\nmagnet, was originally an hypothesis of the celebrated Gilbert.\n\nAnother hypothesis, to the legitimacy of which no objection can lie, and\nwhich is well calculated to light the path of scientific inquiry, is\nthat suggested by several recent writers, that the brain is a voltaic\npile, and that each of its pulsations is a discharge of electricity\nthrough the system. It has been remarked that the sensation felt by the\nhand from the beating of a brain, bears a strong resemblance to a\nvoltaic shock. And the hypothesis, if followed to its consequences,\nmight afford a plausible explanation of many physiological facts, while\nthere is nothing to discourage the hope that we may in time sufficiently\nunderstand the conditions of voltaic phenomena to render the truth of\nthe hypothesis amenable to observation and experiment.\n\nThe attempt to localize, in different regions of the brain, the physical\norgans of our different mental faculties and propensities, was, on the\npart of its original author, a legitimate example of a scientific\nhypothesis; and we ought not, therefore, to blame him for the extremely\nslight grounds on which he often proceeded, in an operation which could\nonly be tentative, though we may regret that materials barely sufficient\nfor a first rude hypothesis should have been hastily worked up into the\nvain semblance of a science. If there be really a connexion between the\nscale of mental endowments and the various degrees of complication in\nthe cerebral system, the nature of that connexion was in no other way so\nlikely to be brought to light as by framing, in the first instance, an\nhypothesis similar to that of Gall. But the verification of any such\nhypothesis is attended, from the peculiar nature of the phenomena, with\ndifficulties which phrenologists have not shown themselves even\ncompetent to appreciate, much less to overcome.\n\nMr. Darwin's remarkable speculation on the Origin of Species is another\nunimpeachable example of a legitimate hypothesis. What he terms \"natural\nselection\" is not only a _vera causa_, but one proved to be capable of\nproducing effects of the same kind with those which the hypothesis\nascribes to it: the question of possibility is entirely one of degree.\nIt is unreasonable to accuse Mr. Darwin (as has been done) of violating\nthe rules of Induction. The rules of Induction are concerned with the\nconditions of Proof. Mr. Darwin has never pretended that his doctrine\nwas proved. He was not bound by the rules of Induction, but by those of\nHypothesis. And these last have seldom been more completely fulfilled.\nHe has opened a path of inquiry full of promise, the results of which\nnone can foresee. And is it not a wonderful feat of scientific knowledge\nand ingenuity to have rendered so bold a suggestion, which the first\nimpulse of every one was to reject at once, admissible and discussable,\neven as a conjecture?\n\n[6] Whewell's _Phil. of Discovery_, pp. 275, 276.\n\n[7] What has most contributed to accredit the hypothesis of a physical\nmedium for the conveyance of light, is the certain fact that light\n_travels_, (which cannot be proved of gravitation,) that its\ncommunication is not instantaneous, but requires time, and that it is\nintercepted (which gravitation is not) by intervening objects. These are\nanalogies between its phenomena and those of the mechanical motion of a\nsolid or fluid substance. But we are not entitled to assume that\nmechanical motion is the only power in nature capable of exhibiting\nthose attributes.\n\n[8] _Phil. of Disc._ p. 274.\n\n[9] P. 271.\n\n[10] P. 251 and the whole of Appendix G.\n\n[11] In Dr. Whewell's latest version of his theory (_Philosophy of\nDiscovery_, p. 331) he makes a concession respecting the medium of the\ntransmission of light, which, taken in conjunction with the rest of his\ndoctrine on the subject, is not, I confess, very intelligible to me, but\nwhich goes far towards removing, if it does not actually remove, the\nwhole of the difference between us. He is contending, against Sir\nWilliam Hamilton, that all matter has weight. Sir William, in proof of\nthe contrary, cited the luminiferous ether, and the calorific and\nelectric fluids, \"which,\" he said, \"we can neither denude of their\ncharacter of substance, nor clothe with the attribute of weight.\" \"To\nwhich,\" continues Dr. Whewell, \"my reply is, that precisely because I\ncannot clothe these agents with the attribute of Weight, I _do_ denude\nthem of the character of Substance. They are not substances, but\nagencies. These Imponderable Agents, are not properly called\nImponderable Fluids. This I conceive that I have proved.\" Nothing can be\nmore philosophical. But if the luminiferous ether is not matter, and\nfluid matter too, what is the meaning of its undulations? Can an agency\nundulate? Can there be alternate motion forward and backward of the\nparticles of an agency? And does not the whole mathematical theory of\nthe undulations imply them to be material? Is it not a series of\ndeductions from the known properties of elastic fluids? _This_ opinion\nof Dr. Whewell reduces the undulations to a figure of speech, and the\nundulatory theory to the proposition which all must admit, that the\ntransmission of light takes place according to laws which present a very\nstriking and remarkable agreement with those of undulations. If Dr.\nWhewell is prepared to stand by this doctrine, I have no difference with\nhim on the subject.\n\nSince this chapter was written, the hypothesis of the luminiferous ether\nhas acquired a great accession of apparent strength, by being adopted\ninto the new doctrine of the Conservation of Force, as affording a\nmechanism by which to explain the mode of production not of light only,\nbut of heat, and probably of all the other so-called imponderable\nagencies. In the present immature stage of the great speculation in\nquestion, I would not undertake to define the ultimate relation of the\nhypothetical fluid to it; but I must remark that the essential part of\nthe new theory, the reciprocal convertibility and interchangeability of\nthese great cosmic agencies, is quite independent of the molecular\nmotions which have been imagined as the immediate causes of those\ndifferent manifestations and of their substitutions for one another; and\nthe former doctrine by no means necessarily carries the latter with it.\nI confess that the entire theory of the vibrations of the ether, and the\nmovements which these vibrations are supposed to communicate to the\nparticles of solid bodies, seems to me at present the weakest part of\nthe new system, tending rather to weigh down than to prop up those of\nits doctrines which rest on real scientific induction.\n\n[12] Thus, water, of which eight-ninths in weight are oxygen, dissolves\nmost bodies which contain a high proportion of oxygen, such as all the\nnitrates, (which have more oxygen than any others of the common salts,)\nmost of the sulphates, many of the carbonates, &c. Again, bodies largely\ncomposed of combustible elements, like hydrogen and carbon, are soluble\nin bodies of similar composition; rosin, for instance, will dissolve in\nalcohol, tar in oil of turpentine. This empirical generalization is far\nfrom being universally true; no doubt because it is a remote, and\ntherefore easily defeated, result of general laws too deep for us at\npresent to penetrate; but it will probably in time suggest processes of\ninquiry, leading to the discovery of those laws.\n\n[13] Or (according to Laplace's theory) the sun and the sun's rotation.\n\n[14] Supra, book iii. ch. v. \u00a7 7.\n\n[15] Supra, book iii. ch. x. \u00a7 2.\n\n[16] In the preceding discussion, the _mean_ is spoken of as if it were\nexactly the same thing with the _average_. But the mean for purposes of\ninductive inquiry, is not the average, or arithmetical mean, though in a\nfamiliar illustration of the theory the difference may be disregarded.\nIf the deviations on one side of the average are much more numerous than\nthose on the other (these last being fewer but greater), the effect due\nto the invariable cause, as distinct from the variable ones, will not\ncoincide with the average, but will be either below or above the\naverage, whichever be the side on which the greatest number of the\ninstances are found. This follows from a truth, ascertained both\ninductively and deductively, that small deviations from the true central\npoint are greatly more frequent than large ones. The mathematical law\nis, \"that the most probable determination of one or more invariable\nelements from observation is that in which _the sum of the squares_ of\nthe individual aberrations,\" or deviations, \"_shall be the least\npossible_.\" See this principle stated, and its grounds popularly\nexplained, by Sir John Herschel, in his review of Quetelet on\nProbabilities, _Essays_, pp. 395 _et seq._\n\n[17] _Essai Philosophique sur les Probabilit\u00e9s_, fifth Paris Edition, p.\n7.\n\n[18] It even appears to me that the calculation of chances, where there\nare no data grounded either on special experience or on special\ninference, must, in an immense majority of cases, break down, from sheer\nimpossibility of assigning any principle by which to be guided in\nsetting out the list of possibilities. In the case of the coloured balls\nwe have no difficulty in making the enumeration, because we ourselves\ndetermine what the possibilities shall be. But suppose a case more\nanalogous to those which occur in nature: instead of three colours, let\nthere be in the box all possible colours: we being supposed ignorant of\nthe comparative frequency with which different colours occur in nature,\nor in the productions of art. How is the list of cases to be made out?\nIs every distinct shade to count as a colour? If so, is the test to be a\ncommon eye, or an educated eye, a painter's for instance? On the answer\nto these questions would depend whether the chances against some\nparticular colour would be estimated at ten, twenty, or perhaps five\nhundred to one. While if we knew from experience that the particular\ncolour occurs on an average a certain number of times in every hundred\nor thousand, we should not require to know anything either of the\nfrequency or of the number of the other possibilities.\n\n[19] _Prospective Review_ for February 1850.\n\n[20] \"If this be not so, why do we feel so much more probability added\nby the first instance, than by any single subsequent instance? Why,\nexcept that the first instance gives us its possibility (a cause\n_adequate_ to it), while every other only gives us the frequency of its\nconditions? If no reference to a cause be supposed, possibility would\nhave no meaning; yet it is clear, that, antecedent to its happening, we\nmight have supposed the event impossible, _i.e._, have believed that\nthere was no physical energy really existing in the world equal to\nproducing it.... After the first time of happening, which is, then, more\nimportant to the whole probability than any other single instance\n(because proving the possibility), the _number_ of times becomes\nimportant as an index to the intensity or extent of the cause, and its\nindependence of any particular time. If we took the case of a tremendous\nleap, for instance, and wished to form an estimate of the probability of\nits succeeding a certain number of times; the first instance, by showing\nits possibility (before doubtful) is of the most importance; but every\nsucceeding leap shows the power to be more perfectly under control,\ngreater and more invariable, and so increases the probability; and no\none would think of reasoning in this case straight from one instance to\nthe next, without referring to the physical energy which each leap\nindicated. Is it not then clear that we do not ever\" (let us rather say,\nthat we do not in an advanced state of our knowledge) \"conclude directly\nfrom the happening of an event to the probability of its happening\nagain; but that we refer to the cause, regarding the past cases as an\nindex to the cause, and the cause as our guide to the future?\"--_Ibid._\n\n[21] The writer last quoted says that the valuation of chances by\ncomparing the number of cases in which the event occurs with the number\nin which it does not occur, \"would generally be wholly erroneous,\" and\n\"is not the true theory of probability.\" It is at least that which forms\nthe foundation of insurance, and of all those calculations of chances in\nthe business of life which experience so abundantly verifies. The reason\nwhich the reviewer gives for rejecting the theory, is that it \"would\nregard an event as certain which had hitherto never failed; which is\nexceedingly far from the truth, even for a very large number of constant\nsuccesses.\" This is not a defect in a particular theory, but in any\ntheory of chances. No principle of evaluation can provide for such a\ncase as that which the reviewer supposes. If an event has never once\nfailed, in a number of trials sufficient to eliminate chance, it really\nhas all the certainty which can be given by an empirical law: it _is_\ncertain during the continuance of the same collocation of causes which\nexisted during the observations. If it ever fails, it is in consequence\nof some change in that collocation. Now, no theory of chances will\nenable us to infer the future probability of an event from the past, if\nthe causes in operation, capable of influencing the event, have\nintermediately undergone a change.\n\n[22] Pp. 18, 19. The theorem is not stated by Laplace in the exact terms\nin which I have stated it; but the identity of import of the two modes\nof expression is easily demonstrable.\n\n[23] For a fuller treatment of the many interesting questions raised by\nthe theory of probabilities, I may now refer to a recent work by Mr.\nVenn, Fellow of Caius College, Cambridge, \"The Logic of Chance;\" one of\nthe most thoughtful and philosophical treatises on any subject connected\nwith Logic and Evidence, which have been produced in this or any other\ncountry for many years. Some criticisms contained in it have been very\nuseful to me in revising the corresponding chapters of the present work.\nIn several of Mr. Venn's opinions, however, I do not agree. What these\nare will be obvious to any reader of Mr. Venn's work who is also a\nreader of this.\n\n[24] There was no greater foundation for this than for Newton's\ncelebrated conjecture that the diamond was combustible. He grounded his\nguess on the very high refracting power of the diamond, comparatively to\nits density; a peculiarity which had been observed to exist in\ncombustible substances; and on similar grounds he conjectured that\nwater, though not combustible, contained a combustible ingredient.\nExperiment having subsequently shown that in both instances he guessed\nright, the prophecy is considered to have done great honour to his\nscientific sagacity; but it is to this day uncertain whether the guess\nwas, in truth, what there are so many examples of in the history of\nscience, a farsighted anticipation of a law afterwards to be discovered.\nThe progress of science has not hitherto shown ground for believing that\nthere is any real connexion between combustibility and a high refracting\npower.\n\n[25] Hartley's _Observations on Man_, vol. i. p. 16. The passage is not\nin Priestley's curtailed edition.\n\n[26] I am happy to be able to quote the following excellent passage from\nMr. Baden Powell's _Essay on the Inductive Philosophy_, in confirmation,\nboth in regard to history and to doctrine, of the statement made in the\ntext. Speaking of the \"conviction of the universal and permanent\nuniformity of nature,\" Mr. Powell says (pp. 98-100),\n\n\"We may remark that this idea, in its proper extent, is by no means one\nof popular acceptance or natural growth. Just so far as the daily\nexperience of every one goes, so far indeed he comes to embrace a\ncertain persuasion of this kind, but merely to this limited extent, that\nwhat is going on around him at present, in his own narrow sphere of\nobservation, will go on in like manner in future. The peasant believes\nthat the sun which rose to-day will rise again to-morrow; that the seed\nput into the ground will be followed in due time by the harvest this\nyear as it was last year, and the like; but has no notion of such\ninferences in subjects beyond his immediate observation. And it should\nbe observed that each class of persons, in admitting this belief within\nthe limited range of his own experience, though he doubt or deny it in\neverything beyond, is, in fact, bearing unconscious testimony to its\nuniversal truth. Nor, again, is it only among the _most_ ignorant that\nthis limitation is put upon the truth. There is a very general\npropensity to believe that everything beyond common experience, or\nespecially ascertained laws of nature, is left to the dominion of chance\nor fate or arbitrary intervention; and even to object to any attempted\nexplanation by physical causes, if conjecturally thrown out for an\napparently unaccountable phenomenon.\n\n\"The precise doctrine of the _generalization_ of this idea of the\nuniformity of nature, so far from being obvious, natural, or intuitive,\nis utterly beyond the attainment of the many. In all the extent of its\nuniversality it is characteristic of the philosopher. It is clearly the\nresult of philosophic cultivation and training, and by no means the\nspontaneous offspring of any primary principle naturally inherent in the\nmind, as some seem to believe. It is no mere vague persuasion taken up\nwithout examination, as a common prepossession to which we are always\naccustomed; on the contrary, all common prejudices and associations are\nagainst it. It is pre-eminently _an acquired idea_. It is not attained\nwithout deep study and reflection. The best informed philosopher is the\nman who most firmly believes it, even in opposition to received notions;\nits acceptance depends on the extent and profoundness of his inductive\nstudies.\"\n\n[27] Supra, book iii. ch. iii. \u00a7 1.\n\n[28] It deserves remark, that these early generalizations did not, like\nscientific inductions, presuppose causation. What they did presuppose,\nwas _uniformity_ in physical facts. But the observers were as ready to\npresume uniformity in the coexistences of facts as in the sequences. On\nthe other hand, they never thought of assuming that this uniformity was\na principle pervading all nature: their generalizations did not imply\nthat there was uniformity in everything, but only that as much\nuniformity as existed within their observation, existed also beyond it.\nThe induction, Fire burns, does not require for its validity that all\nnature should observe uniform laws, but only that there should be\nuniformity in one particular class of natural phenomena: the effects of\nfire on the senses and on combustible substances. And uniformity to this\nextent was not assumed, anterior to the experience, but proved by the\nexperience. The same observed instances which proved the narrower truth,\nproved as much of the wider one as corresponded to it. It is from losing\nsight of this fact, and considering the law of causation in its full\nextent as necessarily presupposed in the very earliest generalizations,\nthat persons have been led into the belief that the law of causation is\nknown _\u00e0 priori_, and is not itself a conclusion from experience.\n\n[29] Book ii. chap. iii.\n\n[30] One of the most rising thinkers of the new generation in France, M.\nTaine (who has given, in the Revue des Deux Mondes, the most masterly\nanalysis, at least in one point of view, ever made of the present work),\nthough he rejects, on this and similar points of psychology, the\nintuition theory in its ordinary form, nevertheless assigns to the law\nof causation, and to some other of the most universal laws, that\ncertainty beyond the bounds of human experience, which I have not been\nable to accord to them. He does this on the faith of our faculty of\nabstraction, in which he seems to recognise an independent source of\nevidence, not indeed disclosing truths not contained in our experience,\nbut affording an assurance which experience cannot give, of the\nuniversality of those which it does contain. By abstraction M. Taine\nseems to think that we are able, not merely to analyse that part of\nnature which we see, and exhibit apart the elements which pervade it,\nbut to distinguish such of them as are elements of the system of nature\nconsidered as a whole, not incidents belonging to our limited\nterrestrial experience. I am not sure that I fully enter into M. Taine's\nmeaning; but I confess I do not see how any mere abstract conception,\nelicited by our minds from our experience, can be evidence of an\nobjective fact in universal Nature, beyond what the experience itself\nbears witness of; or how, in the process of interpreting in general\nlanguage the testimony of experience, the limitations of the testimony\nitself can be cast off.\n\n[31] Book i. chap. vii.\n\n[32] In some cases, a Kind is sufficiently identified by some one\nremarkable property: but most commonly several are required; each\nproperty considered singly, being a joint property of that and of other\nKinds. The colour and brightness of the diamond are common to it with\nthe paste from which false diamonds are made; its octohedral form is\ncommon to it with alum, and magnetic iron ore; but the colour and\nbrightness and the form together, identify its Kind; that is, are a mark\nto us that it is combustible; that when burnt it produces carbonic acid;\nthat it cannot be cut with any known substance; together with many other\nascertained properties, and the fact that there exist an indefinite\nnumber still unascertained.\n\n[33] This doctrine of course assumes that the allotropic forms of what\nis chemically the same substance are so many different Kinds; and such,\nin the sense in which the word Kind is used in this treatise, they\nreally are.\n\n[34] Mr. De Morgan, in his _Formal Logic_, makes the just remark, that\nfrom two such premises as Most A are B, and Most A are C, we may infer\nwith certainty that some B are C. But this is the utmost limit of the\nconclusions which can be drawn from two approximate generalizations,\nwhen the precise degree of their approximation to universality is\nunknown or undefined.\n\n[35] _Rationale of Judicial Evidence_, vol. iii. p. 224.\n\n[36] Supra, vol. i. p. 115.\n\n[37] Supra, book i. ch. v. \u00a7 1, and book ii. ch. v. \u00a7 5.\n\n[38] The axiom, \"Equals subtracted from equals leave equal differences,\"\nmay be demonstrated from the two axioms in the text. If A = _a_ and B =\n_b_, A - B = _a - b_. For if not, let A - B = _a - b + c_. Then since B\n= _b_, adding equals to equals, A = _a + c_. But A = _a_. Therefore _a =\na + c_, which is impossible.\n\nThis proposition having been demonstrated, we may, by means of it,\ndemonstrate the following: \"If equals be added to unequals, the sums are\nunequal.\" If A = _a_ and B not = _b_, A + B is not = _a + b_. For\nsuppose it be so. Then, since A = _a_ and A + B = _a + b_, subtracting\nequals from equals, B = _b_; which is contrary to the hypothesis.\n\nSo again, it may be proved that two things, one of which is equal and\nthe other unequal to a third thing, are unequal to one another. If A =\n_a_ and A not = B, neither is _a_ = B. For suppose it to be equal. Then\nsince A = _a_ and _a_ = B, and since things equal to the same thing are\nequal to one another, A = B: which is contrary to the hypothesis.\n\n[39] Geometers have usually preferred to define parallel lines by the\nproperty of being in the same plane and never meeting. This, however,\nhas rendered it necessary for them to assume, as an additional axiom,\nsome other property of parallel lines; and the unsatisfactory manner in\nwhich properties for that purpose have been selected by Euclid and\nothers has always been deemed the opprobrium of elementary geometry.\nEven as a verbal definition, equidistance is a fitter property to\ncharacterize parallels by, since it is the attribute really involved in\nthe signification of the name. If to be in the same plane and never to\nmeet were all that is meant by being parallel, we should feel no\nincongruity in speaking of a curve as parallel to its asymptote. The\nmeaning of parallel lines is, lines which pursue exactly the same\ndirection, and which, therefore, neither draw nearer nor go farther from\none another; a conception suggested at once by the contemplation of\nnature. That the lines will never meet is of course included in the more\ncomprehensive proposition that they are everywhere equally distant. And\nthat any straight lines which are in the same plane and not equidistant\nwill certainly meet, may be demonstrated in the most rigorous manner\nfrom the fundamental property of straight lines assumed in the text,\nviz. that if they set out from the same point, they diverge more and\nmore without limit.\n\n[40] _Philosophie Positive_, iii. 414-416.\n\n[41] See the two remarkable notes (A) and (F), appended to his _Inquiry\ninto the Relation of Cause and Effect_.\n\n[42] Supra, pp. 119, 120.\n\n[43] A writer to whom I have several times referred, gives as the\ndefinition of an impossibility, that which there exists in the world no\ncause adequate to produce. This definition does not take in such\nimpossibilities as these--that two and two should make five; that two\nstraight lines should inclose a space; or that anything should begin to\nexist without a cause. I can think of no definition of impossibility\ncomprehensive enough to include all its varieties, except the one which\nI have given: viz. An impossibility is that, the truth of which would\nconflict with a complete induction, that is, with the most conclusive\nevidence which we possess of universal truth.\n\nAs to the reputed impossibilities which rest on no other grounds than\nour ignorance of any cause capable of producing the supposed effects;\nvery few of them are certainly impossible, or permanently incredible.\nThe facts of travelling seventy miles an hour, painless surgical\noperations, and conversing by instantaneous signals between London and\nNew York, held a high place, not many years ago, among such\nimpossibilities.\n\n[44] Not, however, as might at first sight appear, 999 times as much. A\ncomplete analysis of the cases shows that (always assuming the veracity\nof the witness to be 9/10) in 10,000 drawings, the drawing of No. 79\nwill occur nine times, and be announced incorrectly once; the\ncredibility therefore of the announcement of No. 79 is 9/10; while the\ndrawing of a white ball will occur nine times, and be announced\nincorrectly 999 times. The credibility therefore of the announcement of\nwhite is 9/1008, and the ratio of the two 1008:10; the one announcement\nbeing thus only about a hundred times more credible than the other,\ninstead of 999 times.\n\n\n\n\nBOOK IV.\n\nOF OPERATIONS SUBSIDIARY TO INDUCTION.\n\n\n\"Clear and distinct ideas are terms which, though familiar and frequent\nin men's mouths, I have reason to think every one who uses does not\nperfectly understand. And possibly it is but here and there one who\ngives himself the trouble to consider them so far as to know what he\nhimself or others precisely mean by them; I have, therefore, in most\nplaces, chose to put determinate or determined, instead of clear and\ndistinct, as more likely to direct men's thoughts to my meaning in this\nmatter.\"--LOCKE'S _Essay on the Human Understanding_; Epistle to the\nReader.\n\n\"Il ne peut y avoir qu'une m\u00e9thode parfaite, qui est la _m\u00e9thode\nnaturelle_; on nomme ainsi un arrangement dans lequel les \u00eatres du m\u00eame\ngenre seraient plus voisins entre eux que ceux de tous les autres\ngenres; les genres du m\u00eame ordre, plus que ceux de tous les autres\nordres; et ainsi de suite. Cette m\u00e9thode est l'id\u00e9al auquel l'histoire\nnaturelle doit tendre; car il est \u00e9vident que si l'on y parvenait, l'on\naurait l'expression exacte et compl\u00e8te de la nature enti\u00e8re.\"--CUVIER,\n_R\u00e8gne Animal_, Introduction.\n\n\"Deux grandes notions philosophiques dominent la th\u00e9orie fondamentale de\nla m\u00e9thode naturelle proprement dite, savoir la formation des groupes\nnaturels, et ensuite leur succession hi\u00e9rarchique.\"--COMTE, _Cours de\nPhilosophie Positive_, 42me le\u00e7on.\n\n\n\n\nCHAPTER I.\n\nOF OBSERVATION AND DESCRIPTION.\n\n\n\u00a7 1. The inquiry which occupied us in the two preceding books, has\nconducted us to what appears a satisfactory solution of the principal\nproblem of Logic, according to the conception I have formed of the\nscience. We have found, that the mental process with which Logic is\nconversant, the operation of ascertaining truths by means of evidence,\nis always, even when appearances point to a different theory of it, a\nprocess of induction. And we have particularized the various modes of\ninduction, and obtained a clear view of the principles to which it must\nconform, in order to lead to results which can be relied on.\n\nThe consideration of Induction, however, does not end with the direct\nrules for its performance. Something must be said of those other\noperations of the mind, which are either necessarily presupposed in all\ninduction, or are instrumental to the more difficult and complicated\ninductive processes. The present book will be devoted to the\nconsideration of these subsidiary operations: among which our attention\nmust first be given to those, which are indispensable preliminaries to\nall induction whatsoever.\n\nInduction being merely the extension to a class of cases, of something\nwhich has been observed to be true in certain individual instances of\nthe class; the first place among the operations subsidiary to induction,\nis claimed by Observation. This is not, however, the place to lay down\nrules for making good observers; nor is it within the competence of\nLogic to do so, but of the art of intellectual Education. Our business\nwith observation is only in its connexion with the appropriate problem\nof logic, the estimation of evidence. We have to consider, not how or\nwhat to observe, but under what conditions observation is to be relied\non; what is needful, in order that the fact, supposed to be observed,\nmay safely be received as true.\n\n\n\u00a7 2. The answer to this question is very simple, at least in its first\naspect. The sole condition is, that what is supposed to have been\nobserved shall really have been observed; that it be an observation, not\nan inference. For in almost every act of our perceiving faculties,\nobservation and inference are intimately blended. What we are said to\nobserve is usually a compound result, of which one-tenth may be\nobservation, and the remaining nine-tenths inference.\n\nI affirm, for example, that I hear a man's voice. This would pass, in\ncommon language, for a direct perception. All, however, which is really\nperception, is that I hear a sound. That the sound is a voice, and that\nvoice the voice of a man, are not perceptions but inferences. I affirm,\nagain, that I saw my brother at a certain hour this morning. If any\nproposition concerning a matter of fact would commonly be said to be\nknown by the direct testimony of the senses, this surely would be so.\nThe truth, however, is far otherwise. I only saw a certain coloured\nsurface; or rather I had the kind of visual sensations which are usually\nproduced by a coloured surface; and from these as marks, known to be\nsuch by previous experience, I concluded that I saw my brother. I might\nhave had sensations precisely similar, when my brother was not there. I\nmight have seen some other person so nearly resembling him in\nappearance, as, at the distance, and with the degree of attention which\nI bestowed, to be mistaken for him. I might have been asleep, and have\ndreamed that I saw him; or in a state of nervous disorder, which brought\nhis image before me in a waking hallucination. In all these modes, many\nhave been led to believe that they saw persons well known to them, who\nwere dead or far distant. If any of these suppositions had been true,\nthe affirmation that I saw my brother would have been erroneous; but\nwhatever was matter of direct perception, namely the visual sensations,\nwould have been real. The inference only would have been ill grounded;\nI should have ascribed those sensations to a wrong cause.\n\nInnumerable instances might be given, and analysed in the same manner,\nof what are vulgarly called errors of sense. There are none of them\nproperly errors of sense; they are erroneous inferences from sense. When\nI look at a candle through a multiplying glass, I see what seems a dozen\ncandles instead of one: and if the real circumstances of the case were\nskilfully disguised, I might suppose that there were really that number;\nthere would be what is called an optical deception. In the kaleidoscope\nthere really is that deception: when I look through the instrument,\ninstead of what is actually there, namely a casual arrangement of\ncoloured fragments, the appearance presented is that of the same\ncombination several times repeated in symmetrical arrangement round a\npoint. The delusion is of course effected by giving me the same\nsensations which I should have had if such a symmetrical combination had\nreally been presented to me. If I cross two of my fingers, and bring any\nsmall object, a marble for instance, into contact with both, at points\nnot usually touched simultaneously by one object, I can hardly, if my\neyes are shut, help believing that there are two marbles instead of one.\nBut it is not my touch in this case, nor my sight in the other, which is\ndeceived; the deception, whether durable or only momentary, is in my\njudgment. From my senses I have only the sensations, and those are\ngenuine. Being accustomed to have those or similar sensations when, and\nonly when, a certain arrangement of outward objects is present to my\norgans, I have the habit of instantly, when I experience the sensations,\ninferring the existence of that state of outward things. This habit has\nbecome so powerful, that the inference, performed with the speed and\ncertainty of an instinct, is confounded with intuitive perceptions. When\nit is correct, I am unconscious that it ever needed proof; even when I\nknow it to be incorrect, I cannot without considerable effort abstain\nfrom making it. In order to be aware that it is not made by instinct but\nby an acquired habit, I am obliged to reflect on the slow process\nthrough which I learnt to judge by the eye of many things which I now\nappear to perceive directly by sight; and on the reverse operation\nperformed by persons learning to draw, who with difficulty and labour\ndivest themselves of their acquired perceptions, and learn afresh to see\nthings as they appear to the eye.\n\nIt would be easy to prolong these illustrations, were there any need to\nexpatiate on a topic so copiously exemplified in various popular works.\nFrom the examples already given, it is seen sufficiently, that the\nindividual facts from which we collect our inductive generalizations are\nscarcely ever obtained by observation alone. Observation extends only to\nthe sensations by which we recognise objects; but the propositions which\nwe make use of, either in science or in common life, relate mostly to\nthe objects themselves. In every act of what is called observation,\nthere is at least one inference--from the sensations to the presence of\nthe object; from the marks or diagnostics, to the entire phenomenon. And\nhence, among other consequences, follows the seeming paradox, that a\ngeneral proposition collected from particulars is often more certainly\ntrue than any one of the particular propositions from which, by an act\nof induction, it was inferred. For, each of those particular (or rather\nsingular) propositions involved an inference, from the impression on the\nsenses to the fact which caused that impression: and this inference may\nhave been erroneous in any one of the instances, but cannot well have\nbeen erroneous in all of them, provided their number was sufficient to\neliminate chance. The conclusion, therefore, that is, the general\nproposition, may deserve more complete reliance than it would be safe to\nrepose in any one of the inductive premises.\n\nThe logic of observation, then, consists solely in a correct\ndiscrimination between that, in a result of observation, which has\nreally been perceived, and that which is an inference from the\nperception. Whatever portion is inference, is amenable to the rules of\ninduction already treated of, and requires no further notice here: the\nquestion for us in this place is, when all which is inference is taken\naway, what remains. There remains, in the first place, the mind's own\nfeelings or states of consciousness, namely, its outward feelings or\nsensations, and its inward feelings--its thoughts, emotions, and\nvolitions. Whether anything else remains, or all else is inference from\nthis; whether the mind is capable of directly perceiving or apprehending\nanything except states of its own consciousness--is a problem of\nmetaphysics not to be discussed in this place. But after excluding all\nquestions on which metaphysicians differ, it remains true, that for most\npurposes the discrimination we are called upon practically to exercise\nis that between sensations or other feelings, of our own or of other\npeople, and inferences drawn from them. And on the theory of Observation\nthis is all which seems necessary to be said for the purposes of the\npresent work.\n\n\n\u00a7 3. If, in the simplest observation, or in what passes for such, there\nis a large part which is not observation but something else; so in the\nsimplest description of an observation, there is, and must always be,\nmuch more asserted than is contained in the perception itself. We cannot\ndescribe a fact, without implying more than the fact. The perception is\nonly of one individual thing; but to describe it is to affirm a\nconnexion between it and every other thing which is either denoted or\nconnoted by any of the terms used. To begin with an example, than which\nnone can be conceived more elementary: I have a sensation of sight, and\nI endeavour to describe it by saying that I see something white. In\nsaying this, I do not solely affirm my sensation; I also class it. I\nassert a resemblance between the thing I see, and all things which I and\nothers are accustomed to call white. I assert that it resembles them in\nthe circumstance in which they all resemble one another, in that which\nis the ground of their being called by the name. This is not merely one\nway of describing an observation, but the only way. If I would either\nregister my observation for my own future use, or make it known for the\nbenefit of others, I must assert a resemblance between the fact which I\nhave observed and something else. It is inherent in a description, to be\nthe statement of a resemblance, or resemblances.\n\nWe thus see that it is impossible to express in words any result of\nobservation, without performing an act possessing what Dr. Whewell\nconsiders to be characteristic of Induction. There is always something\nintroduced which was not included in the observation itself; some\nconception common to the phenomenon with other phenomena to which it is\ncompared. An observation cannot be spoken of in language at all without\ndeclaring more than that one observation; without assimilating it to\nother phenomena already observed and classified. But this identification\nof an object--this recognition of it as possessing certain known\ncharacteristics--has never been confounded with Induction. It is an\noperation which precedes all induction, and supplies it with its\nmaterials. It is a perception of resemblances, obtained by comparison.\n\nThese resemblances are not always apprehended directly, by merely\ncomparing the object observed with some other present object, or with\nour recollection of an object which is absent. They are often\nascertained through intermediate marks, that is, deductively. In\ndescribing some new kind of animal, suppose me to say that it measures\nten feet in length, from the forehead to the extremity of the tail. I\ndid not ascertain this by the unassisted eye. I had a two-foot rule\nwhich I applied to the object, and, as we commonly say, measured it; an\noperation which was not wholly manual, but partly also mathematical,\ninvolving the two propositions, Five times two is ten, and Things which\nare equal to the same thing are equal to one another. Hence, the fact\nthat the animal is ten feet long is not an immediate perception, but a\nconclusion from reasoning; the minor premises alone being furnished by\nobservation of the object. Nevertheless, this is called an observation\nor a description of the animal, not an induction respecting it.\n\nTo pass at once from a very simple to a very complex example: I affirm\nthat the earth is globular. The assertion is not grounded on direct\nperception; for the figure of the earth cannot, by us, be directly\nperceived, though the assertion would not be true unless circumstances\ncould be supposed under which its truth could be so perceived. That the\nform of the earth is globular is inferred from certain marks, as for\ninstance from this, that its shadow thrown upon the moon is circular; or\nthis, that on the sea, or any extensive plain, our horizon is always a\ncircle; either of which marks is incompatible with any other than a\nglobular form. I assert further, that the earth is that particular kind\nof globe which is termed an oblate spheroid; because it is found by\nmeasurement in the direction of the meridian, that the length on the\nsurface of the earth which subtends a given angle at its centre,\ndiminishes as we recede from the equator and approach the poles. But\nthese propositions, that the earth is globular, and that it is an oblate\nspheroid, assert, each of them, an individual fact; in its own nature\ncapable of being perceived by the senses when the requisite organs and\nthe necessary position are supposed, and only not actually perceived\nbecause those organs and that position are wanting. This identification\nof the earth, first as a globe, and next as an oblate spheroid, which,\nif the fact could have been seen, would have been called a description\nof the figure of the earth, may without impropriety be so called when,\ninstead of being seen, it is inferred. But we could not without\nimpropriety call either of these assertions an induction from facts\nrespecting the earth. They are not general propositions collected from\nparticular facts, but particular facts deduced from general\npropositions. They are conclusions obtained deductively, from premises\noriginating in induction: but of these premises some were not obtained\nby observation of the earth, nor had any peculiar reference to it.\n\nIf, then, the truth respecting the figure of the earth is not an\ninduction, why should the truth respecting the figure of the earth's\norbit be so? The two cases only differ in this, that the form of the\norbit was not, like the form of the earth itself, deduced by\nratiocination from facts which were marks of ellipticity, but was got at\nby boldly guessing that the path was an ellipse, and finding afterwards,\non examination, that the observations were in harmony with the\nhypothesis. According to Dr. Whewell, however, this process of guessing\nand verifying our guesses is not only induction, but the whole of\ninduction: no other exposition can be given of that logical operation.\nThat he is wrong in the latter assertion, the whole of the preceding\nbook has, I hope, sufficiently proved; and that the process by which the\nellipticity of the planetary orbits was ascertained, is not induction at\nall, was attempted to be shown in the second chapter of the same\nbook.[1] We are now, however, prepared to go more into the heart of the\nmatter than at that earlier period of our inquiry, and to show, not\nmerely what the operation in question is not, but what it is.\n\n\n\u00a7 4. We observed, in the second chapter, that the proposition \"the earth\nmoves in an ellipse,\" so far as it only serves for the colligation or\nconnecting together of actual observations, (that is, as it only affirms\nthat the observed positions of the earth may be correctly represented by\nas many points in the circumference of an imaginary ellipse,) is not an\ninduction, but a description: it is an induction, only when it affirms\nthat the intermediate positions, of which there has been no direct\nobservation, would be found to correspond to the remaining points of the\nsame elliptic circumference. Now, though this real induction is one\nthing, and the description another, we are in a very different condition\nfor making the induction before we have obtained the description, and\nafter it. For inasmuch as the description, like all other descriptions,\ncontains the assertion of a resemblance between the phenomenon described\nand something else; in pointing out something which the series of\nobserved places of a planet resembles, it points out something in which\nthe several places themselves agree. If the series of places correspond\nto as many points of an ellipse, the places themselves agree in being\nsituated in that ellipse. We have, therefore, by the same process which\ngave us the description, obtained the requisites for an induction by the\nMethod of Agreement. The successive observed places of the earth being\nconsidered as effects, and its motion as the cause which produces them,\nwe find that those effects, that is, those places, agree in the\ncircumstance of being in an ellipse. We conclude that the remaining\neffects, the places which have not been observed, agree in the same\ncircumstance, and that the _law_ of the motion of the earth is motion in\nan ellipse.\n\nThe Colligation of Facts, therefore, by means of hypotheses, or, as Dr.\nWhewell prefers to say, by means of Conceptions, instead of being, as he\nsupposes, Induction itself, takes its proper place among operations\nsubsidiary to Induction. All Induction supposes that we have previously\ncompared the requisite number of individual instances, and ascertained\nin what circumstances they agree. The Colligation of Facts is no other\nthan this preliminary operation. When Kepler, after vainly endeavouring\nto connect the observed places of a planet by various hypotheses of\ncircular motion, at last tried the hypothesis of an ellipse and found it\nanswer to the phenomena; what he really attempted, first unsuccessfully\nand at last successfully, was to discover the circumstance in which all\nthe observed positions of the planet agreed. And when he in like manner\nconnected another set of observed facts, the periodic times of the\ndifferent planets, by the proposition that the squares of the times are\nproportional to the cubes of the distances, what he did was simply to\nascertain the property in which the periodic times of all the different\nplanets agreed.\n\nSince, therefore, all that is true and to the purpose in Dr. Whewell's\ndoctrine of Conceptions might be fully expressed by the more familiar\nterm Hypothesis; and since his Colligation of Facts by means of\nappropriate Conceptions, is but the ordinary process of finding by a\ncomparison of phenomena, in what consists their agreement or\nresemblance; I would willingly have confined myself to those better\nunderstood expressions, and persevered to the end in the same abstinence\nwhich I have hitherto observed from ideological discussions; considering\nthe mechanism of our thoughts to be a topic distinct from and irrelevant\nto the principles and rules by which the trustworthiness of the results\nof thinking is to be estimated. Since, however, a work of such high\npretensions, and, it must also be said, of so much real merit, has\nrested the whole theory of Induction upon such ideological\nconsiderations, it seems necessary for others who follow, to claim for\nthemselves and their doctrines whatever position may properly belong to\nthem on the same metaphysical ground. And this is the object of the\nsucceeding chapter.\n\n\n\n\nCHAPTER II.\n\nOF ABSTRACTION, OR THE FORMATION OF CONCEPTIONS.\n\n\n\u00a7 1. The metaphysical inquiry into the nature and composition of what\nhave been called Abstract Ideas, or in other words, of the notions which\nanswer in the mind to classes and to general names, belongs not to\nLogic, but to a different science, and our purpose does not require that\nwe should enter upon it here. We are only concerned with the universally\nacknowledged fact, that such notions or conceptions do exist. The mind\ncan conceive a multitude of individual things as one assemblage or\nclass; and general names do really suggest to us certain ideas or mental\nrepresentations, otherwise we could not use the names with consciousness\nof a meaning. Whether the idea called up by a general name is composed\nof the various circumstances in which all the individuals denoted by the\nname agree, and of no others, (which is the doctrine of Locke, Brown,\nand the Conceptualists;) or whether it be the idea of some one of those\nindividuals, clothed in its individualizing peculiarities, but with the\naccompanying knowledge that those peculiarities are not properties of\nthe class, (which is the doctrine of Berkeley, Mr. Bailey,[2] and the\nmodern Nominalists;) or whether (as held by Mr. James Mill) the idea of\nthe class is that of a miscellaneous assemblage of individuals belonging\nto the class; or whether, finally, (what appears to be the truest\nopinion,) it be any one or any other of all these, according to the\naccidental circumstances of the case; certain it is, that _some_ idea or\nmental conception is suggested by a general name, whenever we either\nhear it or employ it with consciousness of a meaning. And this, which we\nmay call if we please a general idea, _represents_ in our minds the\nwhole class of things to which the name is applied. Whenever we think or\nreason concerning the class, we do so by means of this idea. And the\nvoluntary power which the mind has, of attending to one part of what is\npresent to it at any moment, and neglecting another part, enables us to\nkeep our reasonings and conclusions respecting the class unaffected by\nanything in the idea or mental image which is not really, or at least\nwhich we do not really believe to be, common to the whole class.[3]\n\nThere are, then, such things as general conceptions, or conceptions by\nmeans of which we can think generally: and when we form a set of\nphenomena into a class, that is, when we compare them with one another\nto ascertain in what they agree, some general conception is implied in\nthis mental operation. And inasmuch as such a comparison is a necessary\npreliminary to Induction, it is most true that Induction could not go on\nwithout general conceptions.\n\n\n\u00a7 2. But it does not therefore follow that these general conceptions\nmust have existed in the mind previously to the comparison. It is not a\nlaw of our intellect, that in comparing things with each other and\ntaking note of their agreement we merely recognise as realized in the\noutward world something that we already had in our minds. The conception\noriginally found its way to us as the _result_ of such a comparison. It\nwas obtained (in metaphysical phrase) by _abstraction_ from individual\nthings. These things may be things which we perceived or thought of on\nformer occasions, but they may also be the things which we are\nperceiving or thinking of on the very occasion. When Kepler compared the\nobserved places of the planet Mars, and found that they agreed in being\npoints of an elliptic circumference, he applied a general conception\nwhich was already in his mind, having been derived from his former\nexperience. But this is by no means universally the case. When we\ncompare several objects and find them to agree in being white, or when\nwe compare the various species of ruminating animals and find them to\nagree in being cloven-footed, we have just as much a general conception\nin our minds as Kepler had in his: we have the conception of \"a white\nthing,\" or the conception of \"a cloven-footed animal.\" But no one\nsupposes that we necessarily bring these conceptions with us, and\n_superinduce_ them (to adopt Dr. Whewell's expression) upon the facts:\nbecause in these simple cases everybody sees that the very act of\ncomparison which ends in our connecting the facts by means of the\nconception, may be the source from which we derive the conception\nitself. If we had never seen any white object or had never seen any\ncloven-footed animal before, we should at the same time and by the same\nmental act acquire the idea, and employ it for the colligation of the\nobserved phenomena. Kepler, on the contrary, really had to bring the\nidea with him, and superinduce it upon the facts; he could not evolve it\nout of them: if he had not already had the idea, he would not have been\nable to acquire it by a comparison of the planet's positions. But this\ninability was a mere accident: the idea of an ellipse could have been\nacquired from the paths of the planets as effectually as from anything\nelse, if the paths had not happened to be invisible. If the planet had\nleft a visible track, and we had been so placed that we could see it at\nthe proper angle, we might have abstracted our original idea of an\nellipse from the planetary orbit. Indeed, every conception which can be\nmade the instrument for connecting a set of facts, might have been\noriginally evolved from those very facts. The conception is a conception\n_of_ something; and that which it is a conception of, is really _in_ the\nfacts, and might, under some supposable circumstances, or by some\nsupposable extension of the faculties which we actually possess, have\nbeen detected in them. And not only is this always in itself possible,\nbut it actually happens, in almost all cases in which the obtaining of\nthe right conception is a matter of any considerable difficulty. For if\nthere be no new conception required; if one of those already familiar to\nmankind will serve the purpose, the accident of being the first to whom\nthe right one occurs, may happen to almost anybody; at least in the case\nof a set of phenomena which the whole scientific world are engaged in\nattempting to connect. The honour, in Kepler's case, was that of the\naccurate, patient, and toilsome calculations by which he compared the\nresults that followed from his different guesses, with the observations\nof Tycho Brahe; but the merit was very small of guessing an ellipse; the\nonly wonder is that men had not guessed it before, nor could they have\nfailed to do so if there had not existed an obstinate _\u00e0 priori_\nprejudice that the heavenly bodies must move, if not in a circle, in\nsome combination of circles.\n\nThe really difficult cases are those in which the conception destined to\ncreate light and order out of darkness and confusion, has to be sought\nfor among the very phenomena which it afterwards serves to arrange. Why,\naccording to Dr. Whewell himself, did the ancients fail in discovering\nthe laws of mechanics, that is, of equilibrium and of the communication\nof motion? Because they had not, or at least had not clearly, the ideas\nor conceptions of pressure and resistance, momentum, and uniform and\naccelerating force. And whence could they have obtained these ideas,\nexcept from the very facts of equilibrium and motion? The tardy\ndevelopment of several of the physical sciences, for example of optics,\nelectricity, magnetism, and the higher generalizations of chemistry, he\nascribes to the fact that mankind had not yet possessed themselves of\nthe Idea of Polarity, that is, the idea of opposite properties in\nopposite directions. But what was there to suggest such an idea, until,\nby a separate examination of several of these different branches of\nknowledge, it was shown that the facts of each of them did present, in\nsome instances at least, the curious phenomenon of opposite properties\nin opposite directions? The thing was superficially manifest only in two\ncases, those of the magnet, and of electrified bodies; and there the\nconception was encumbered with the circumstance of material poles, or\nfixed points in the body itself, in which points this opposition of\nproperties seemed to be inherent. The first comparison and abstraction\nhad led only to this conception of poles; and if anything corresponding\nto that conception had existed in the phenomena of chemistry or optics,\nthe difficulty now justly considered so great, would have been extremely\nsmall. The obscurity rose from the fact, that the polarities in\nchemistry and optics were distinct species, though of the same genus,\nwith the polarities in electricity and magnetism: and that in order to\nassimilate the phenomena to one another, it was necessary to compare a\npolarity without poles, such for instance as is exemplified in the\npolarization of light, and the polarity with (apparent) poles, which we\nsee in the magnet; and to recognise that these polarities, while\ndifferent in many other respects, agree in the one character which is\nexpressed by the phrase, opposite properties in opposite directions.\nFrom the result of such a comparison it was that the minds of scientific\nmen formed this new general conception: between which, and the first\nconfused feeling of an analogy between some of the phenomena of light\nand those of electricity and magnetism, there is a long interval, filled\nup by the labours and more or less sagacious suggestions of many\nsuperior minds.\n\nThe conceptions, then, which we employ for the colligation and\nmethodization of facts, do not develop themselves from within, but are\nimpressed upon the mind from without; they are never obtained otherwise\nthan by way of comparison and abstraction, and, in the most important\nand the most numerous cases, are evolved by abstraction from the very\nphenomena which it is their office to colligate. I am far, however, from\nwishing to imply that it is not often a very difficult thing to perform\nthis process of abstraction well, or that the success of an inductive\noperation does not, in many cases, principally depend on the skill with\nwhich we perform it. Bacon was quite justified in designating as one of\nthe principal obstacles to good induction, general conceptions wrongly\nformed, \"notiones temer\u00e8 \u00e0 rebus abstract\u00e6:\" to which Dr. Whewell adds,\nthat not only does bad abstraction make bad induction, but that in order\nto perform induction well, we must have abstracted well; our general\nconceptions must be \"clear\" and \"appropriate\" to the matter in hand.\n\n\n\u00a7 3. In attempting to show what the difficulty in this matter really is,\nand how it is surmounted, I must beg the reader, once for all, to bear\nthis in mind; that although in discussing the opinions of a different\nschool of philosophy, I am willing to adopt their language, and to\nspeak, therefore, of connecting facts through the instrumentality of a\nconception, this technical phraseology means neither more nor less than\nwhat is commonly called comparing the facts with one another and\ndetermining in what they agree. Nor has the technical expression even\nthe advantage of being metaphysically correct. The facts are not\n_connected_, except in a merely metaphorical acceptation of the term.\nThe _ideas_ of the facts may become connected, that is, we may be led to\nthink of them together; but this consequence is no more than what may be\nproduced by any casual association. What really takes place, is, I\nconceive, more philosophically expressed by the common word Comparison,\nthan by the phrases \"to connect\" or \"to superinduce.\" For, as the\ngeneral conception is itself obtained by a comparison of particular\nphenomena, so, when obtained, the mode in which we apply it to other\nphenomena is again by comparison. We compare phenomena with each other\nto get the conception, and we then compare those and other phenomena\n_with_ the conception. We get the conception of an animal (for instance)\nby comparing different animals, and when we afterwards see a creature\nresembling an animal, we compare it with our general conception of an\nanimal; and if it agrees with that general conception, we include it in\nthe class. The conception becomes the type of comparison.\n\nAnd we need only consider what comparison is, to see that where the\nobjects are more than two, and still more when they are an indefinite\nnumber, a type of some sort is an indispensable condition of the\ncomparison. When we have to arrange and classify a great number of\nobjects according to their agreements and differences, we do not make a\nconfused attempt to compare all with all. We know that two things are as\nmuch as the mind can easily attend to at a time, and we therefore fix\nupon one of the objects, either at hazard or because it offers in a\npeculiarly striking manner some important character, and, taking this as\nour standard, compare it with one object after another. If we find a\nsecond object which presents a remarkable agreement with the first,\ninducing us to class them together, the question instantly arises, in\nwhat particular circumstances do they agree? and to take notice of these\ncircumstances is already a first stage of abstraction, giving rise to a\ngeneral conception. Having advanced thus far, when we now take in hand a\nthird object we naturally ask ourselves the question, not merely whether\nthis third object agrees with the first, but whether it agrees with it\nin the same circumstances in which the second did? in other words,\nwhether it agrees with the general conception which has been obtained by\nabstraction from the first and second? Thus we see the tendency of\ngeneral conceptions, as soon as formed, to substitute themselves as\ntypes, for whatever individual objects previously answered that purpose\nin our comparisons. We may, perhaps, find that no considerable number of\nother objects agree with this first general conception; and that we must\ndrop the conception, and beginning again with a different individual\ncase, proceed by fresh comparisons to a different general conception.\nSometimes, again, we find that the same conception will serve, by merely\nleaving out some of its circumstances; and by this higher effort of\nabstraction, we obtain a still more general conception; as in the case\nformerly referred to, the scientific world rose from the conception of\npoles to the general conception of opposite properties in opposite\ndirections; or as those South-Sea islanders, whose conception of a\nquadruped had been abstracted from hogs (the only animals of that\ndescription which they had seen), when they afterwards compared that\nconception with other quadrupeds, dropped some of the circumstances,\nand arrived at the more general conception which Europeans associate\nwith the term.\n\nThese brief remarks contain, I believe, all that is well-grounded in the\ndoctrine, that the conception by which the mind arranges and gives unity\nto phenomena must be furnished by the mind itself, and that we find the\nright conception by a tentative process, trying first one and then\nanother until we hit the mark. The conception is not furnished _by_ the\nmind until it has been furnished _to_ the mind; and the facts which\nsupply it are sometimes extraneous facts, but more often the very facts\nwhich we are attempting to arrange by it. It is quite true, however,\nthat in endeavouring to arrange the facts, at whatever point we begin,\nwe never advance three steps without forming a general conception, more\nor less distinct and precise; and that this general conception becomes\nthe clue which we instantly endeavour to trace through the rest of the\nfacts, or rather, becomes the standard with which we thenceforth compare\nthem. If we are not satisfied with the agreements which we discover\namong the phenomena by comparing them with this type, or with some still\nmore general conception which by an additional stage of abstraction we\ncan form from the type; we change our path, and look out for other\nagreements: we recommence the comparison from a different\nstarting-point, and so generate a different set of general conceptions.\nThis is the tentative process which Dr. Whewell speaks of; and which has\nnot unnaturally suggested the theory, that the conception is supplied by\nthe mind itself: since the different conceptions which the mind\nsuccessively tries, it either already possessed from its previous\nexperience, or they were supplied to it in the first stage of the\ncorresponding act of comparison; so that, in the subsequent part of the\nprocess, the conception manifested itself as something compared with the\nphenomena, not evolved from them.\n\n\n\u00a7 4. If this be a correct account of the instrumentality of general\nconceptions in the comparison which necessarily precedes Induction, we\nshall easily be able to translate into our own language what Dr. Whewell\nmeans by saying that conceptions, to be subservient to Induction, must\nbe \"clear\" and \"appropriate.\"\n\nIf the conception corresponds to a real agreement among the phenomena;\nif the comparison which we have made of a set of objects has led us to\nclass them according to real resemblances and differences; the\nconception which does this cannot fail to be appropriate, for some\npurpose or other. The question of appropriateness is relative to the\nparticular object we have in view. As soon as, by our comparison, we\nhave ascertained some agreement, something which can be predicated in\ncommon of a number of objects; we have obtained a basis on which an\ninductive process is capable of being founded. But the agreements, or\nthe ulterior consequences to which those agreements lead, may be of very\ndifferent degrees of importance. If, for instance, we only compare\nanimals according to their colour, and class those together which are\ncoloured alike, we form the general conceptions of a white animal, a\nblack animal, &c., which are conceptions legitimately formed; and if an\ninduction were to be attempted concerning the causes of the colours of\nanimals, this comparison would be the proper and necessary preparation\nfor such an induction, but would not help us towards a knowledge of the\nlaws of any other of the properties of animals: while if, with Cuvier,\nwe compare and class them according to the structure of the skeleton,\nor, with Blainville, according to the nature of their outward\ninteguments, the agreements and differences which are observable in\nthese respects are not only of much greater importance in themselves,\nbut are marks of agreements and differences in many other important\nparticulars of the structure and mode of life of the animals. If,\ntherefore, the study of their structure and habits be our object, the\nconceptions generated by these last comparisons are far more\n\"appropriate\" than those generated by the former. Nothing, other than\nthis, can be meant by the appropriateness of a conception.\n\nWhen Dr. Whewell says that the ancients, or the schoolmen, or any modern\ninquirers, missed discovering the real law of a phenomenon because they\napplied to it an inappropriate instead of an appropriate conception; he\ncan only mean that in comparing various instances of the phenomenon, to\nascertain in what those instances agreed, they missed the important\npoints of agreement; and fastened upon such as were either imaginary,\nand not agreements at all, or if real agreements, were comparatively\ntrifling, and had no connexion with the phenomenon, the law of which was\nsought.\n\nAristotle, philosophizing on the subject of motion, remarked that\ncertain motions apparently take place spontaneously; bodies fall to the\nground, flame ascends, bubbles of air rise in water, &c.: and these he\ncalled natural motions; while others not only never take place without\nexternal incitement, but even when such incitement is applied, tend\nspontaneously to cease; which, to distinguish them from the former, he\ncalled violent motions. Now, in comparing the so-called natural motions\nwith one another, it appeared to Aristotle that they agreed in one\ncircumstance, namely, that the body which moved (or seemed to move)\nspontaneously, was moving _towards its own place_; meaning thereby the\nplace from whence it originally came, or the place where a great\nquantity of matter similar to itself was assembled. In the other class\nof motions, as when bodies are thrown up in the air, they are, on the\ncontrary, moving _from_ their own place. Now, this conception of a body\nmoving towards its own place may justly be considered inappropriate;\nbecause, though it expresses a circumstance really found in some of the\nmost familiar instances of motion apparently spontaneous, yet, first,\nthere are many other cases of such motion, in which that circumstance is\nabsent: the motion, for instance, of the earth and planets. Secondly,\neven when it is present, the motion, on closer examination, would often\nbe seen not to be spontaneous: as, when air rises in water, it does not\nrise by its own nature, but is pushed up by the superior weight of the\nwater which presses upon it. Finally, there are many cases in which the\nspontaneous motion takes place in the contrary direction to what the\ntheory considers as the body's own place; for instance, when a fog rises\nfrom a lake, or when water dries up. The agreement, therefore, which\nAristotle selected as his principle of classification, did not extend to\nall cases of the phenomenon he wanted to study, spontaneous motion;\nwhile it did include cases of the absence of the phenomenon, cases of\nmotion not spontaneous. The conception was hence \"inappropriate.\" We may\nadd that, in the case in question, no conception would be appropriate;\nthere is no agreement which runs through all the cases of spontaneous or\napparently spontaneous motion and no others: they cannot be brought\nunder one law: it is a case of Plurality of Causes.[4]\n\n\n\u00a7 5. So much for the first of Dr. Whewell's conditions, that conceptions\nmust be appropriate. The second is, that they shall be \"clear:\" and let\nus consider what this implies. Unless the conception corresponds to a\nreal agreement, it has a worse defect than that of not being clear; it\nis not applicable to the case at all. Among the phenomena, therefore,\nwhich we are attempting to connect by means of the conception, we must\nsuppose that there really is an agreement, and that the conception is a\nconception of that agreement. In order, then, that it may be clear, the\nonly requisite is, that we shall know exactly in what the agreement\nconsists; that it shall have been carefully observed, and accurately\nremembered. We are said not to have a clear conception of the\nresemblance among a set of objects, when we have only a general feeling\nthat they resemble, without having analysed their resemblance, or\nperceived in what points it consists, and fixed in our memory an exact\nrecollection of those points. This want of clearness, or, as it may be\notherwise called, this vagueness, in the general conception, may be\nowing either to our having no accurate knowledge of the objects\nthemselves, or merely to our not having carefully compared them. Thus a\nperson may have no clear idea of a ship because he has never seen one,\nor because he remembers but little, and that faintly, of what he has\nseen. Or he may have a perfect knowledge and remembrance of many ships\nof various kinds, frigates among the rest, but he may have no clear but\nonly a confused idea of a frigate, because he has never been told, and\nhas not compared them sufficiently to have remarked and remembered, in\nwhat particular points a frigate differs from some other kind of ship.\n\nIt is not, however, necessary, in order to have clear ideas, that we\nshould know all the common properties of the things which we class\ntogether. That would be to have our conception of the class complete as\nwell as clear. It is sufficient if we never class things together\nwithout knowing exactly why we do so,--without having ascertained\nexactly what agreements we are about to include in our conception; and\nif, after having thus fixed our conception, we never vary from it, never\ninclude in the class anything which has not those common properties, nor\nexclude from it anything which has. A clear conception means a\ndeterminate conception; one which does not fluctuate, which is not one\nthing to-day and another to-morrow, but remains fixed and invariable,\nexcept when, from the progress of our knowledge, or the correction of\nsome error, we consciously add to it or alter it. A person of clear\nideas, is a person who always knows in virtue of what properties his\nclasses are constituted; what attributes are connoted by his general\nnames.\n\nThe principal requisites, therefore, of clear conceptions, are habits of\nattentive observation, an extensive experience, and a memory which\nreceives and retains an exact image of what is observed. And in\nproportion as any one has the habit of observing minutely and comparing\ncarefully a particular class of phenomena, and an accurate memory for\nthe results of the observation and comparison, so will his conceptions\nof that class of phenomena be clear; provided he has the indispensable\nhabit, (naturally, however, resulting from those other endowments,) of\nnever using general names without a precise connotation.\n\nAs the clearness of our conceptions chiefly depends on the _carefulness_\nand _accuracy_ of our observing and comparing faculties, so their\nappropriateness, or rather the chance we have of hitting upon the\nappropriate conception in any case, mainly depends on the _activity_ of\nthe same faculties. He who by habit, grounded on sufficient natural\naptitude, has acquired a readiness in accurately observing and comparing\nphenomena, will perceive so many more agreements and will perceive them\nso much more rapidly than other people, that the chances are much\ngreater of his perceiving, in any instance, the agreement on which the\nimportant consequences depend.\n\n\n\u00a7 6. It is of so much importance that the part of the process of\ninvestigating truth, discussed in this chapter, should be rightly\nunderstood, that I think it is desirable to restate the results we have\narrived at, in a somewhat different mode of expression.\n\nWe cannot ascertain general truths, that is, truths applicable to\nclasses, unless we have formed the classes in such a manner that general\ntruths can be affirmed of them. In the formation of any class, there is\ninvolved a conception of it as a class, that is, a conception of certain\ncircumstances as being those which characterize the class, and\ndistinguish the objects composing it from all other things. When we know\nexactly what these circumstances are, we have a clear idea (or\nconception) of the class, and of the meaning of the general name which\ndesignates it. The primary condition implied in having this clear idea,\nis that the class be really a class; that it correspond to a real\ndistinction; that the things it includes really do agree with one\nanother in certain particulars, and differ, in those same particulars,\nfrom all other things. A person without clear ideas, is one who\nhabitually classes together, under the same general names, things which\nhave no common properties, or none which are not possessed also by other\nthings; or who, if the usage of other people prevents him from actually\nmisclassing things, is unable to state to himself the common properties\nin virtue of which he classes them rightly.\n\nBut it is not the sole requisite of classification that the classes\nshould be real classes, framed by a legitimate mental process. Some\nmodes of classing things are more valuable than others for human uses,\nwhether of speculation or of practice; and our classifications are not\nwell made, unless the things which they bring together not only agree\nwith each other in something which distinguishes them from all other\nthings, but agree with each other and differ from other things in the\nvery circumstances which are of primary importance for the purpose\n(theoretical or practical) which we have in view, and which constitutes\nthe problem before us. In other words, our conceptions, though they may\nbe clear, are not _appropriate_ for our purpose, unless the properties\nwe comprise in them are those which will help us towards what we wish to\nunderstand--_i. e._, either those which go deepest into the nature of\nthe things, if our object be to understand that, or those which are most\nclosely connected with the particular property which we are endeavouring\nto investigate.\n\nWe cannot, therefore, frame good general conceptions beforehand. That\nthe conception we have obtained is the one we want, can only be known\nwhen we have done the work for the sake of which we wanted it; when we\ncompletely understand the general character of the phenomena, or the\nconditions of the particular property with which we concern ourselves.\nGeneral conceptions formed without this thorough knowledge, are Bacon's\n\"notiones temer\u00e8 \u00e0 rebus abstract\u00e6.\" Yet such premature conceptions we\nmust be continually making up, in our progress to something better. They\nare an impediment to the progress of knowledge, only when they are\npermanently acquiesced in. When it has become our habit to group things\nin wrong classes--in groups which either are not really classes, having\nno distinctive points of agreement (absence of _clear_ ideas), or which\nare not classes of which anything important to our purpose can be\npredicated (absence of _appropriate_ ideas); and when, in the belief\nthat these badly made classes are those sanctioned by Nature, we refuse\nto exchange them for others, and cannot or will not make up our general\nconceptions from any other elements; in that case all the evils which\nBacon ascribes to his \"notiones temer\u00e8 abstract\u00e6\" really occur. This was\nwhat the ancients did in physics, and what the world in general does in\nmorals and politics to the present day.\n\nIt would thus, in my view of the matter, be an inaccurate mode of\nexpression to say, that obtaining appropriate conceptions is a condition\nprecedent to generalization. Throughout the whole process of comparing\nphenomena with one another for the purpose of generalization, the mind\nis trying to make up a conception; but the conception which it is trying\nto make up is that of the really important point of agreement in the\nphenomena. As we obtain more knowledge of the phenomena themselves, and\nof the conditions on which their important properties depend, our views\non this subject naturally alter; and thus we advance from a less to a\nmore \"appropriate\" general conception, in the progress of our\ninvestigations.\n\nWe ought not, at the same time, to forget that the really important\nagreement cannot always be discovered by mere comparison of the very\nphenomena in question, without the aid of a conception acquired\nelsewhere; as in the case, so often referred to, of the planetary\norbits.\n\nThe search for the agreement of a set of phenomena is in truth very\nsimilar to the search for a lost or hidden object. At first we place\nourselves in a sufficiently commanding position, and cast our eyes round\nus, and if we can see the object it is well; if not, we ask ourselves\nmentally what are the places in which it may be hid, in order that we\nmay there search for it: and so on, until we imagine the place where it\nreally is. And here too we require to have had a previous conception, or\nknowledge, of those different places. As in this familiar process, so in\nthe philosophical operation which it illustrates, we first endeavour to\nfind the lost object or recognise the common attribute, without\nconjecturally invoking the aid of any previously acquired conception, or\nin other words, of any hypothesis. Having failed in this, we call upon\nour imagination for some hypothesis of a possible place, or a possible\npoint of resemblance, and then look, to see whether the facts agree with\nthe conjecture.\n\nFor such cases something more is required than a mind accustomed to\naccurate observation and comparison. It must be a mind stored with\ngeneral conceptions, previously acquired, of the sorts which bear\naffinity to the subject of the particular inquiry. And much will also\ndepend on the natural strength and acquired culture of what has been\ntermed the scientific imagination; on the faculty possessed of mentally\narranging known elements into new combinations, such as have not yet\nbeen observed in nature, though not contradictory to any known laws.\n\nBut the variety of intellectual habits, the purposes which they serve,\nand the modes in which they may be fostered and cultivated, are\nconsiderations belonging to the Art of Education: a subject far wider\nthan Logic, and which this treatise does not profess to discuss. Here,\ntherefore, the present chapter may properly close.\n\n\n\n\nCHAPTER III.\n\nOF NAMING, AS SUBSIDIARY TO INDUCTION.\n\n\n\u00a7 1. It does not belong to the present undertaking to dwell on the\nimportance of language as a medium of human intercourse, whether for\npurposes of sympathy or of information. Nor does our design admit of\nmore than a passing allusion to that great property of names, on which\ntheir functions as an intellectual instrument are, in reality,\nultimately dependent; their potency as a means of forming, and of\nriveting, associations among our other ideas: a subject on which an able\nthinker[5] has thus written:--\n\n\"Names are impressions of sense, and as such take the strongest hold on\nthe mind, and of all other impressions can be most easily recalled and\nretained in view. They therefore serve to give a point of attachment to\nall the more volatile objects of thought and feeling. Impressions that\nwhen passed might be dissipated for ever, are, by their connexion with\nlanguage, always within reach. Thoughts, of themselves, are perpetually\nslipping out of the field of immediate mental vision; but the name\nabides with us, and the utterance of it restores them in a moment. Words\nare the custodiers of every product of mind less impressive than\nthemselves. All extensions of human knowledge, all new generalizations,\nare fixed and spread, even unintentionally, by the use of words. The\nchild growing up learns, along with the vocables of his mother-tongue,\nthat things which he would have believed to be different, are, in\nimportant points, the same. Without any formal instruction, the language\nin which we grow up teaches us all the common philosophy of the age. It\ndirects us to observe and know things which we should have overlooked;\nit supplies us with classifications ready made, by which things are\narranged (as far as the light of by-gone generations admits) with the\nobjects to which they bear the greatest total resemblance. The number of\ngeneral names in a language, and the degree of generality of those\nnames, afford a test of the knowledge of the era, and of the\nintellectual insight which is the birthright of any one born into it.\"\n\nIt is not, however, of the functions of Names, considered generally,\nthat we have here to treat, but only of the manner and degree in which\nthey are directly instrumental to the investigation of truth; in other\nwords, to the process of induction.\n\n\n\u00a7 2. Observation and Abstraction, the operations which formed the\nsubject of the two foregoing chapters, are conditions indispensable to\ninduction; there can be no induction where they are not. It has been\nimagined that Naming is also a condition equally indispensable. There\nare thinkers who have held that language is not solely, according to a\nphrase generally current, _an_ instrument of thought, but _the_\ninstrument: that names, or something equivalent to them, some species of\nartificial signs, are necessary to reasoning; that there could be no\ninference, and consequently no induction, without them. But if the\nnature of reasoning was correctly explained in the earlier part of the\npresent work, this opinion must be held to be an exaggeration, though of\nan important truth. If reasoning be from particulars to particulars, and\nif it consist in recognising one fact as a mark of another, or a mark of\na mark of another, nothing is required to render reasoning possible,\nexcept senses and association: senses to perceive that two facts are\nconjoined; association, as the law by which one of those two facts\nraises up the idea of the other.[6] For these mental phenomena, as well\nas for the belief or expectation which follows, and by which we\nrecognise as having taken place, or as about to take place, that of\nwhich we have perceived a mark, there is evidently no need of language.\nAnd this inference of one particular fact from another is a case of\ninduction. It is of this sort of induction that brutes are capable: it\nis in this shape that uncultivated minds make almost all their\ninductions, and that we all do so in the cases in which familiar\nexperience forces our conclusions upon us without any active process of\ninquiry on our part, and in which the belief or expectation follows the\nsuggestion of the evidence, with the promptitude and certainty of an\ninstinct.[7]\n\n\n\u00a7 3. But though inference of an inductive character is possible without\nthe use of signs, it could never, without them, be carried much beyond\nthe very simple cases which we have just described, and which form, in\nall probability, the limit of the reasonings of those animals to whom\nconventional language is unknown. Without language, or something\nequivalent to it, there could only be as much reasoning from experience\nas can take place without the aid of general propositions. Now, though\nin strictness we may reason from past experience to a fresh individual\ncase without the intermediate stage of a general proposition, yet\nwithout general propositions we should seldom remember what past\nexperience we have had, and scarcely ever what conclusions that\nexperience will warrant. The division of the inductive process into two\nparts, the first ascertaining what is a mark of the given fact, the\nsecond whether in the new case that mark exists, is natural, and\nscientifically indispensable. It is, indeed, in a majority of cases,\nrendered necessary by mere distance of time. The experience by which we\nare to guide our judgments may be other people's experience, little of\nwhich can be communicated to us otherwise than by language: when it is\nour own, it is generally experience long past; unless, therefore, it\nwere recorded by means of artificial signs, little of it (except in\ncases involving our intenser sensations or emotions, or the subjects of\nour daily and hourly contemplation) would be retained in the memory. It\nis hardly necessary to add, that when the inductive inference is of any\nbut the most direct and obvious nature--when it requires several\nobservations or experiments, in varying circumstances, and the\ncomparison of one of these with another--it is impossible to proceed a\nstep, without the artificial memory which words bestow. Without words,\nwe should, if we had often seen A and B in immediate and obvious\nconjunction, expect B whenever we saw A; but to discover their\nconjunction when not obvious, or to determine whether it is really\nconstant or only casual, and whether there is reason to expect it under\nany given change of circumstances, is a process far too complex to be\nperformed without some contrivance to make our remembrance of our own\nmental operations accurate. Now, language is such a contrivance. When\nthat instrument is called to our aid, the difficulty is reduced to that\nof making our remembrance of the meaning of words accurate. This being\nsecured, whatever passes through our minds may be remembered accurately,\nby putting it carefully into words, and committing the words either to\nwriting or to memory.\n\nThe function of Naming, and particularly of General Names, in Induction,\nmay be recapitulated as follows. Every inductive inference which is good\nat all, is good for a whole class of cases: and, that the inference may\nhave any better warrant of its correctness than the mere clinging\ntogether of two ideas, a process of experimentation and comparison is\nnecessary; in which the whole class of cases must be brought to view,\nand some uniformity in the course of nature evolved and ascertained,\nsince the existence of such an uniformity is required as a\njustification for drawing the inference in even a single case. This\nuniformity, therefore, may be ascertained once for all; and if, being\nascertained, it can be remembered, it will serve as a formula for\nmaking, in particular cases, all such inferences as the previous\nexperience will warrant. But we can only secure its being remembered, or\ngive ourselves even a chance of carrying in our memory any considerable\nnumber of such uniformities, by registering them through the medium of\npermanent signs; which (being, from the nature of the case, signs not of\nan individual fact, but of an uniformity, that is, of an indefinite\nnumber of facts similar to one another) are general signs; universals;\ngeneral names, and general propositions.\n\n\n\u00a7 4. And here I cannot omit to notice an oversight committed by some\neminent thinkers; who have said that the cause of our using general\nnames is the infinite multitude of individual objects, which, making it\nimpossible to have a name for each, compels us to make one name serve\nfor many. This is a very limited view of the function of general names.\nEven if there were a name for every individual object, we should require\ngeneral names as much as we now do. Without them we could not express\nthe result of a single comparison, nor record any one of the\nuniformities existing in nature; and should be hardly better off in\nrespect to Induction than if we had no names at all. With none but names\nof individuals, (or in other words, proper names,) we might, by\npronouncing the name, suggest the idea of the object, but we could not\nassert any proposition; except the unmeaning ones formed by predicating\ntwo proper names one of another. It is only by means of general names\nthat we can convey any information, predicate any attribute, even of an\nindividual, much more of a class. Rigorously speaking we could get on\nwithout any other general names than the abstract names of attributes;\nall our propositions might be of the form \"such an individual object\npossesses such an attribute,\" or \"such an attribute is always (or never)\nconjoined with such another attribute.\" In fact, however, mankind have\nalways given general names to objects as well as attributes, and indeed\nbefore attributes: but the general names given to objects imply\nattributes, derive their whole meaning from attributes; and are chiefly\nuseful as the language by means of which we predicate the attributes\nwhich they connote.\n\nIt remains to be considered what principles are to be adhered to in\ngiving general names, so that these names, and the general propositions\nin which they fill a place, may conduce most to the purposes of\nInduction.\n\n\n\n\nCHAPTER IV.\n\nOF THE REQUISITES OF A PHILOSOPHICAL LANGUAGE, AND THE PRINCIPLES OF\nDEFINITION.\n\n\n\u00a7 1. In order that we may possess a language perfectly suitable for the\ninvestigation and expression of general truths, there are two principal,\nand several minor, requisites. The first is, that every general name\nshould have a meaning, steadily fixed, and precisely determined. When,\nby the fulfilment of this condition, such names as we possess are fitted\nfor the due performance of their functions, the next requisite, and the\nsecond in order of importance, is that we should possess a name wherever\none is needed; wherever there is anything to be designated by it, which\nit is of importance to express.\n\nThe former of these requisites is that to which our attention will be\nexclusively directed in the present chapter.\n\n\n\u00a7 2. Every general name, then, must have a certain and knowable meaning.\nNow the meaning (as has so often been explained) of a general\nconnotative name, resides in the connotation; in the attribute on\naccount of which, and to express which, the name is given. Thus, the\nname animal being given to all things which possess the attributes of\nsensation and voluntary motion, the word connotes those attributes\nexclusively, and they constitute the whole of its meaning. If the name\nbe abstract, its denotation is the same with the connotation of the\ncorresponding concrete: it designates directly the attribute, which the\nconcrete term implies. To give a precise meaning to general names is,\nthen, to fix with steadiness the attribute or attributes connoted by\neach concrete general name, and denoted by the corresponding abstract.\nSince abstract names, in the order of their creation, do not precede\nbut follow concrete ones, as is proved by the etymological fact that\nthey are almost always derived from them; we may consider their meaning\nas determined by, and dependent on, the meaning of their concrete: and\nthus the problem of giving a distinct meaning to general language, is\nall included in that of giving a precise connotation to all concrete\ngeneral names.\n\nThis is not difficult in the case of new names; of the technical terms\ncreated by scientific inquirers for the purposes of science or art. But\nwhen a name is in common use, the difficulty is greater; the problem in\nthis case not being that of choosing a convenient connotation for the\nname, but of ascertaining and fixing the connotation with which it is\nalready used. That this can ever be a matter of doubt, is a sort of\nparadox. But the vulgar (including in that term all who have not\naccurate habits of thought) seldom know exactly what assertion they\nintend to make, what common property they mean to express, when they\napply the same name to a number of different things. All which the name\nexpresses with them, when they predicate it of an object, is a confused\nfeeling of resemblance between that object and some of the other things\nwhich they have been accustomed to denote by the name. They have applied\nthe name Stone to various objects previously seen; they see a new\nobject, which appears to them somewhat like the former, and they call it\na stone, without asking themselves in what respect it is like, or what\nmode or degree of resemblance the best authorities, or even they\nthemselves, require as a warrant for using the name. This rough general\nimpression of resemblance is, however, made up of particular\ncircumstances of resemblance; and into these it is the business of the\nlogician to analyse it; to ascertain what points of resemblance among\nthe different things commonly called by the name, have produced in the\ncommon mind this vague feeling of likeness; have given to the things the\nsimilarity of aspect, which has made them a class, and has caused the\nsame name to be bestowed upon them.\n\nBut though general names are imposed by the vulgar without any more\ndefinite connotation than that of a vague resemblance; general\npropositions come in time to be made, in which predicates are applied to\nthose names, that is, general assertions are made concerning the _whole_\nof the things which are denoted by the name. And since by each of these\npropositions some attribute, more or less precisely conceived, is of\ncourse predicated, the ideas of these various attributes thus become\nassociated with the name, and in a sort of uncertain way it comes to\nconnote them; there is a hesitation to apply the name in any new case in\nwhich any of the attributes familiarly predicated of the class do not\nexist. And thus, to common minds, the propositions which they are in the\nhabit of hearing or uttering concerning a class, make up in a loose way\na sort of connotation for the class-name. Let us take, for instance, the\nword Civilized. How few could be found, even among the most educated\npersons, who would undertake to say exactly what the term Civilized\nconnotes. Yet there is a feeling in the minds of all who use it, that\nthey are using it with a meaning; and this meaning is made up, in a\nconfused manner, of everything which they have heard or read that\ncivilized men, or civilized communities, are, or may be expected to be.\n\nIt is at this stage, probably, in the progress of a concrete name, that\nthe corresponding abstract name generally comes into use. Under the\nnotion that the concrete name must of course convey a meaning, or in\nother words, that there is some property common to all things which it\ndenotes, people give a name to this common property; from the concrete\nCivilized, they form the abstract Civilization. But since most people\nhave never compared the different things which are called by the\nconcrete name, in such a manner as to ascertain what properties these\nthings have in common, or whether they have any; each is thrown back\nupon the marks by which he himself has been accustomed to be guided in\nhis application of the term: and these, being merely vague hearsays and\ncurrent phrases, are not the same in any two persons, nor in the same\nperson at different times. Hence the word (as Civilization, for example)\nwhich professes to be the designation of the unknown common property,\nconveys scarcely to any two minds the same idea. No two persons agree in\nthe things they predicate of it; and when it is itself predicated of\nanything, no other person knows, nor does the speaker himself know with\nprecision, what he means to assert. Many other words which could be\nnamed, as the word _honour_, or the word _gentleman_, exemplify this\nuncertainty still more strikingly.\n\nIt needs scarcely be observed, that general propositions of which no one\ncan tell exactly what they assert, cannot possibly have been brought to\nthe test of a correct induction. Whether a name is to be used as an\ninstrument of thinking, or as a means of communicating the result of\nthought, it is imperative to determine exactly the attribute or\nattributes which it is to express: to give it, in short, a fixed and\nascertained connotation.\n\n\n\u00a7 3. It would, however, be a complete misunderstanding of the proper\noffice of a logician in dealing with terms already in use, if we were to\nthink that because a name has not at present an ascertained connotation,\nit is competent to any one to give it such a connotation at his own\nchoice. The meaning of a term actually in use is not an arbitrary\nquantity to be fixed, but an unknown quantity to be sought.\n\nIn the first place, it is obviously desirable to avail ourselves, as far\nas possible, of the associations already connected with the name; not\nenjoining the employment of it in a manner which conflicts with all\nprevious habits, and especially not so as to require the rupture of\nthose strongest of all associations between names, which are created by\nfamiliarity with propositions in which they are predicated of one\nanother. A philosopher would have little chance of having his example\nfollowed, if he were to give such a meaning to his terms as should\nrequire us to call the North American Indians a civilized people, or the\nhigher classes in France or England savages; or to say that civilized\npeople live by hunting, and savages by agriculture. Were there no other\nreason, the extreme difficulty of effecting so complete a revolution in\nspeech would be more than a sufficient one. The endeavour should be,\nthat all generally received propositions into which the term enters,\nshould be at least as true after its meaning is fixed, as they were\nbefore; and that the concrete name, therefore, should not receive such a\nconnotation as shall prevent it from denoting things which, in common\nlanguage, it is currently affirmed of. The fixed and precise connotation\nwhich it receives, should not be in deviation from, but in agreement (as\nfar as it goes) with, the vague and fluctuating connotation which the\nterm already had.\n\nTo fix the connotation of a concrete name, or the denotation of the\ncorresponding abstract, is to define the name. When this can be done\nwithout rendering any received assertions inadmissible, the name can be\ndefined in accordance with its received use, which is vulgarly called\ndefining not the name but the thing. What is meant by the improper\nexpression of defining a thing, (or rather a class of things--for nobody\ntalks of defining an individual,) is to define the name, subject to the\ncondition that it shall denote those things. This, of course, supposes a\ncomparison of the things, feature by feature and property by property,\nto ascertain what attributes they agree in; and not unfrequently an\noperation strictly inductive, for the purpose of ascertaining some\nunobvious agreement, which is the cause of the obvious agreements.\n\nFor, in order to give a connotation to a name, consistently with its\ndenoting certain objects, we have to make our selection from among the\nvarious attributes in which those objects agree. To ascertain in what\nthey do agree is, therefore, the first logical operation requisite. When\nthis has been done as far as is necessary or practicable, the question\narises, which of these common attributes shall be selected to be\nassociated with the name. For if the class which the name denotes be a\nKind, the common properties are innumerable; and even if not, they are\noften extremely numerous. Our choice is first limited by the preference\nto be given to properties which are well known, and familiarly\npredicated of the class; but even these are often too numerous to be all\nincluded in the definition, and, besides, the properties most generally\nknown may not be those which serve best to mark out the class from all\nothers. We should therefore select from among the common properties, (if\namong them any such are to be found,) those on which it has been\nascertained by experience, or proved by deduction, that many others\ndepend; or at least which are sure marks of them, and from whence,\ntherefore, many others will follow by inference. We thus see that to\nframe a good definition of a name already in use, is not a matter of\nchoice but of discussion, and discussion not merely respecting the usage\nof language, but respecting the properties of things, and even the\norigin of those properties. And hence every enlargement of our knowledge\nof the objects to which the name is applied, is liable to suggest an\nimprovement in the definition. It is impossible to frame a perfect set\nof definitions on any subject, until the theory of the subject is\nperfect: and as science makes progress, its definitions are also\nprogressive.\n\n\n\u00a7 4. The discussion of Definitions, in so far as it does not turn on the\nuse of words but on the properties of things, Dr. Whewell calls the\nExplication of Conceptions. The act of ascertaining, better than before,\nin what particulars any phenomena which are classed together agree, he\ncalls in his technical phraseology, unfolding the general conception in\nvirtue of which they are so classed. Making allowance for what appears\nto me the darkening and misleading tendency of this mode of expression,\nseveral of his remarks are so much to the purpose, that I shall take the\nliberty of transcribing them.\n\nHe observes,[8] that many of the controversies which have had an\nimportant share in the formation of the existing body of science, have\n\"assumed the form of a battle of Definitions. For example, the inquiry\nconcerning the laws of falling bodies, led to the question whether the\nproper definition of a _uniform force_ is that it generates a velocity\nproportional to the _space_ from rest, or to the _time_. The controversy\nof the _vis viva_ was what was the proper definition of the _measure of\nforce_. A principal question in the classification of minerals is, what\nis the definition of a _mineral species_. Physiologists have endeavoured\nto throw light on their subject by defining _organization_, or some\nsimilar term.\" Questions of the same nature are still open respecting\nthe definitions of Specific Heat, Latent Heat, Chemical Combination, and\nSolution.\n\n\"It is very important for us to observe, that these controversies have\nnever been questions of insulated and _arbitrary_ definitions, as men\nseem often tempted to imagine them to have been. In all cases there is a\ntacit assumption of some proposition which is to be expressed by means\nof the definition, and which gives it its importance. The dispute\nconcerning the definition thus acquires a real value, and becomes a\nquestion concerning true and false. Thus in the discussion of the\nquestion, What is a uniform force? it was taken for granted that gravity\nis a uniform force. In the debate of the _vis viva_, it was assumed that\nin the mutual action of bodies the whole effect of the force is\nunchanged. In the zoological definition of species, (that it consists of\nindividuals which have, or may have, sprung from the same parents,) it\nis presumed that individuals so related resemble each other more than\nthose which are excluded by such a definition; or, perhaps, that species\nso defined have permanent and definite differences. A definition of\norganization, or of some other term, which was not employed to express\nsome principle, would be of no value.\n\n\"The establishment, therefore, of a right definition of a term, may be a\nuseful step in the explication of our conceptions; but this will be the\ncase then only when we have under our consideration some proposition in\nwhich the term is employed. For then the question really is, how the\nconception shall be understood and defined in order that the proposition\nmay be true.\n\n\"To unfold our conceptions by means of definitions has never been\nserviceable to science, except when it has been associated with an\nimmediate use of the definitions. The endeavour to define a Uniform\nForce was combined with the assertion that gravity is a uniform force:\nthe attempt to define Accelerating Force was immediately followed by\nthe doctrine that accelerating forces may be compounded: the process of\ndefining Momentum was connected with the principle that momenta gained\nand lost are equal: naturalists would have given in vain the definition\nof Species which we have quoted, if they had not also given the\ncharacters of species so separated.... Definition may be the best mode\nof explaining our conception, but that which alone makes it worth while\nto explain it in any mode, is the opportunity of using it in the\nexpression of truth. When a definition is propounded to us as a useful\nstep in knowledge, we are always entitled to ask what principle it\nserves to enunciate.\"\n\nIn giving, then, an exact connotation to the phrase, \"an uniform force,\"\nthe condition was understood, that the phrase should continue to denote\ngravity. The discussion, therefore, respecting the definition, resolved\nitself into this question, What is there of an uniform nature in the\nmotions produced by gravity? By observations and comparisons, it was\nfound, that what was uniform in those motions was the ratio of the\nvelocity acquired to the time elapsed; equal velocities being added in\nequal times. An uniform force, therefore, was defined, a force which\nadds equal velocities in equal times. So, again, in defining momentum.\nIt was already a received doctrine, that when two objects impinge upon\none another, the momentum lost by the one is equal to that gained by the\nother. This proportion it was deemed necessary to preserve, not from the\nmotive (which operates in many other cases) that it was firmly fixed in\npopular belief; for the proposition in question had never been heard of\nby any but the scientifically instructed. But it was felt to contain a\ntruth: even a superficial observation of the phenomena left no doubt\nthat in the propagation of motion from one body to another, there was\nsomething of which the one body gained precisely what the other lost;\nand the word momentum had been invented to express this unknown\nsomething. The settlement, therefore, of the definition of momentum,\ninvolved the determination of the question, What is that of which a\nbody, when it sets another body in motion, loses exactly as much as it\ncommunicates? And when experiment had shown that this _something_ was\nthe product of the velocity of the body by its mass, or quantity of\nmatter, this became the definition of momentum.\n\nThe following remarks,[9] therefore, are perfectly just: \"The business\nof definition is part of the business of discovery.... To define, so\nthat our definition shall have any scientific value, requires no small\nportion of that sagacity by which truth is detected.... When it has been\nclearly seen what ought to be our definition, it must be pretty well\nknown what truth we have to state. The definition, as well as the\ndiscovery, supposes a decided step in our knowledge to have been made.\nThe writers on Logic, in the middle ages, made Definition the last stage\nin the progress of knowledge; and in this arrangement at least, the\nhistory of science, and the philosophy derived from the history, confirm\ntheir speculative views.\" For in order to judge finally how the name\nwhich denotes a class may best be defined, we must know all the\nproperties common to the class, and all the relations of causation or\ndependence among those properties.\n\nIf the properties which are fittest to be selected as marks of other\ncommon properties are also obvious and familiar, and especially if they\nbear a great part in producing that general air of resemblance which was\nthe original inducement to the formation of the class, the definition\nwill then be most felicitous. But it is often necessary to define the\nclass by some property not familiarly known, provided that property be\nthe best mark of those which are known. M. de Blainville, for instance,\nfounded his definition of life on the process of decomposition and\nrecomposition which incessantly takes place in every living body, so\nthat the particles composing it are never for two instants the same.\nThis is by no means one of the most obvious properties of living bodies;\nit might escape altogether the notice of an unscientific observer. Yet\ngreat authorities (independently of M. de Blainville, who is himself a\nfirst-rate authority) have thought that no other property so well\nanswers the conditions required for the definition.\n\n\n\u00a7 5. Having laid down the principles which ought for the most part to be\nobserved in attempting to give a precise connotation to a term in use, I\nmust now add, that it is not always practicable to adhere to those\nprinciples, and that even when practicable, it is occasionally not\ndesirable.\n\nCases in which it is impossible to comply with all the conditions of a\nprecise definition of a name in agreement with usage, occur very\nfrequently. There is often no one connotation capable of being given to\na word, so that it shall still denote everything it is accustomed to\ndenote; or that all the propositions into which it is accustomed to\nenter, and which have any foundation in truth, shall remain true.\nIndependently of accidental ambiguities, in which the different meanings\nhave no connexion with one another; it continually happens that a word\nis used in two or more senses derived from each other, but yet radically\ndistinct. So long as a term is vague, that is, so long as its\nconnotation is not ascertained and permanently fixed, it is constantly\nliable to be applied by _extension_ from one thing to another, until it\nreaches things which have little, or even no, resemblance to those which\nwere first designated by it.\n\nSuppose, says Dugald Stewart, in his _Philosophical Essays_,[10] \"that\nthe letters A, B, C, D, E, denote a series of objects; that A possesses\nsome one quality in common with B; B a quality in common with C; C a\nquality in common with D; D a quality in common with E; while at the\nsame time, no quality can be found which belongs in common to any\n_three_ objects in the series. Is it not conceivable, that the affinity\nbetween A and B may produce a transference of the name of the first to\nthe second; and that, in consequence of the other affinities which\nconnect the remaining objects together, the same name may pass in\nsuccession from B to C; from C to D; and from D to E? In this manner, a\ncommon appellation will arise between A and E, although the two objects\nmay, in their nature and properties, be so widely distant from each\nother, that no stretch of imagination can conceive how the thoughts were\nled from the former to the latter. The transitions, nevertheless, may\nhave been all so easy and gradual, that, were they successfully detected\nby the fortunate ingenuity of a theorist, we should instantly recognise,\nnot only the verisimilitude, but the truth of the conjecture: in the\nsame way as we admit, with the confidence of intuitive conviction, the\ncertainty of the well-known etymological process which connects the\nLatin preposition _e_ or _ex_ with the English substantive _stranger_,\nthe moment that the intermediate links of the chain are submitted to our\nexamination.\"[11]\n\nThe applications which a word acquires by this gradual extension of it\nfrom one set of objects to another, Stewart, adopting an expression from\nMr. Payne Knight, calls its _transitive_ applications; and after briefly\nillustrating such of them as are the result of local or casual\nassociations, he proceeds as follows:[12]--\n\n\"But although by far the greater part of the transitive or derivative\napplications of words depend on casual and unaccountable caprices of the\nfeelings or the fancy, there are certain cases in which they open a very\ninteresting field of philosophical speculation. Such are those, in which\nan analogous transference of the corresponding term may be remarked\nuniversally, or very generally, in other languages; and in which, of\ncourse, the uniformity of the result must be ascribed to the essential\nprinciples of the human frame. Even in such cases, however, it will by\nno means be always found, on examination, that the various applications\nof the same term have arisen from any common quality or qualities in the\nobjects to which they relate. In the greater number of instances, they\nmay be traced to some natural and universal associations of ideas,\nfounded in the common faculties, common organs, and common condition of\nthe human race.... According to the different degrees of intimacy and\nstrength in the associations on which the _transitions_ of language are\nfounded, very different effects may be expected to arise. Where the\nassociation is slight and casual, the several meanings will remain\ndistinct from each other, and will often, in process of time, assume the\nappearance of capricious varieties in the use of the same arbitrary\nsign. _Where the association is so natural and habitual as to become\nvirtually indissoluble, the transitive meanings will coalesce in one\ncomplex conception; and every new transition will become a more\ncomprehensive generalization of the term in question._\"\n\nI solicit particular attention to the law of mind expressed in the last\nsentence, and which is the source of the perplexity so often experienced\nin detecting these transitions of meaning. Ignorance of that law is the\nshoal on which some of the most powerful intellects which have adorned\nthe human race have been stranded. The inquiries of Plato into the\ndefinitions of some of the most general terms of moral speculation are\ncharacterized by Bacon as a far nearer approach to a true inductive\nmethod than is elsewhere to be found among the ancients, and are,\nindeed, almost perfect examples of the preparatory process of comparison\nand abstraction: but, from being unaware of the law just mentioned, he\noften wasted the powers of this great logical instrument on inquiries in\nwhich it could realize no result, since the phenomena, whose common\nproperties he so elaborately endeavoured to detect, had not really any\ncommon properties. Bacon himself fell into the same error in his\nspeculations on the nature of heat, in which he evidently confounded\nunder the name hot, classes of phenomena which had no property in\ncommon. Stewart certainly overstates the matter when he speaks of \"a\nprejudice which has descended to modern times from the scholastic ages,\nthat when a word admits of a variety of significations, these different\nsignifications must all be species of the same genus, and must\nconsequently include some essential idea common to every individual to\nwhich the generic term can be applied:\"[13] for both Aristotle and his\nfollowers were well aware that there are such things as ambiguities of\nlanguage, and delighted in distinguishing them. But they never suspected\nambiguity in the cases where (as Stewart remarks) the association on\nwhich the transition of meaning was founded is so natural and habitual,\nthat the two meanings blend together in the mind, and a real transition\nbecomes an apparent generalization. Accordingly they wasted infinite\npains in endeavouring to find a definition which would serve for several\ndistinct meanings at once: as in an instance noticed by Stewart himself,\nthat of \"causation; the ambiguity of the word which, in the Greek\nlanguage, corresponds to the English word _cause_, having suggested to\nthem the vain attempt of tracing the common idea which, in the case of\nany _effect_, belongs to the _efficient_, to the _matter_, to the\n_form_, and to the _end_. The idle generalities\" (he adds) \"we meet with\nin other philosophers, about the ideas of the _good_, the _fit_, and the\n_becoming_, have taken their rise from the same undue influence of\npopular epithets on the speculations of the learned.\"[14]\n\nAmong the words which have undergone so many successive transitions of\nmeaning that every trace of a property common to all the things they are\napplied to, or at least common and also peculiar to those things, has\nbeen lost, Stewart considers the word Beautiful to be one. And (without\nattempting to decide a question which in no respect belongs to logic) I\ncannot but feel, with him, considerable doubt, whether the word\nbeautiful connotes the same property when we speak of a beautiful\ncolour, a beautiful face, a beautiful scene, a beautiful character, and\na beautiful poem. The word was doubtless extended from one of these\nobjects to another on account of a resemblance between them, or more\nprobably, between the emotions they excited; and, by this progressive\nextension, it has at last reached things very remote from those objects\nof sight to which there is no doubt that it was first appropriated; and\nit is at least questionable whether there is now any property common to\nall the things which, consistently with usage, may be called beautiful,\nexcept the property of agreeableness, which the term certainly does\nconnote, but which cannot be all that people usually intend to express\nby it, since there are many agreeable things which are never called\nbeautiful. If such be the case, it is impossible to give to the word\nBeautiful any fixed connotation, such that it shall denote all the\nobjects which in common use it now denotes, but no others. A fixed\nconnotation, however, it ought to have; for, so long as it has not, it\nis unfit to be used as a scientific term, and is a perpetual source of\nfalse analogies and erroneous generalizations.\n\nThis, then, constitutes a case in exemplification of our remark, that\neven when there is a property common to all the things denoted by a\nname, to erect that property into the definition and exclusive\nconnotation of the name is not always desirable. The various things\ncalled beautiful unquestionably resemble one another in being agreeable;\nbut to make this the definition of beauty, and so extend the word\nBeautiful to all agreeable things, would be to drop altogether a portion\nof meaning which the word really, though indistinctly, conveys, and to\ndo what depends on us towards causing those qualities of the objects\nwhich the word previously, though vaguely, pointed at, to be overlooked\nand forgotten. It is better, in such a case, to give a fixed connotation\nto the term by restricting, than by extending its use; rather excluding\nfrom the epithet Beautiful some things to which it is commonly\nconsidered applicable, than leaving out of its connotation any of the\nqualities by which, though occasionally lost sight of, the general mind\nmay have been habitually guided in the commonest and most interesting\napplications of the term. For there is no question that when people\ncall anything beautiful, they think they are asserting more than that it\nis merely agreeable. They think they are ascribing a peculiar _sort_ of\nagreeableness, analogous to that which they find in some other of the\nthings to which they are accustomed to apply the same name. If,\ntherefore, there be any peculiar sort of agreeableness which is common\nthough not to all, yet to the principal things which are called\nbeautiful, it is better to limit the denotation of the term to those\nthings, than to leave that kind of quality without a term to connote it,\nand thereby divert attention from its peculiarities.\n\n\n\u00a7 6. The last remark exemplifies a rule of terminology, which is of\ngreat importance, and which has hardly yet been recognised as a rule,\nbut by a few thinkers of the present century. In attempting to rectify\nthe use of a vague term by giving it a fixed connotation, we must take\ncare not to discard (unless advisedly, and on the ground of a deeper\nknowledge of the subject) any portion of the connotation which the word,\nin however indistinct a manner, previously carried with it. For\notherwise language loses one of its inherent and most valuable\nproperties, that of being the conservator of ancient experience; the\nkeeper-alive of those thoughts and observations of former ages, which\nmay be alien to the tendencies of the passing time. This function of\nlanguage is so often overlooked or undervalued, that a few observations\non it appear to be extremely required.\n\nEven when the connotation of a term has been accurately fixed, and still\nmore if it has been left in the state of a vague unanalysed feeling of\nresemblance; there is a constant tendency in the word, through familiar\nuse, to part with a portion of its connotation. It is a well-known law\nof the mind, that a word originally associated with a very complex\ncluster of ideas, is far from calling up all those ideas in the mind,\nevery time the word is used: it calls up only one or two, from which the\nmind runs on by fresh associations to another set of ideas, without\nwaiting for the suggestion of the remainder of the complex cluster. If\nthis were not the case, processes of thought could not take place with\nanything like the rapidity which we know they possess. Very often,\nindeed, when we are employing a word in our mental operations, we are so\nfar from waiting until the complex idea which corresponds to the meaning\nof the word is consciously brought before us in all its parts, that we\nrun on to new trains of ideas by the other associations which the mere\nword excites, without having realized in our imagination any part\nwhatever of the meaning: thus using the word, and even using it well and\naccurately, and carrying on important processes of reasoning by means of\nit, in an almost mechanical manner; so much so, that some\nmetaphysicians, generalizing from an extreme case, have fancied that all\nreasoning is but the mechanical use of a set of terms according to a\ncertain form. We may discuss and settle the most important interests of\ntowns or nations, by the application of general theorems or practical\nmaxims previously laid down, without having had consciously suggested to\nus, once in the whole process, the houses and green fields, the thronged\nmarket-places and domestic hearths, of which not only those towns and\nnations consist, but which the words town and nation confessedly mean.\n\nSince, then, general names come in this manner to be used (and even to\ndo a portion of their work well) without suggesting to the mind the\nwhole of their meaning, and often with the suggestion of a very small,\nor no part at all of that meaning; we cannot wonder that words so used\ncome in time to be no longer capable of suggesting any other of the\nideas appropriated to them, than those with which the association is\nmost immediate and strongest, or most kept up by the incidents of life:\nthe remainder being lost altogether; unless the mind, by often\nconsciously dwelling on them, keeps up the association. Words naturally\nretain much more of their meaning to persons of active imagination, who\nhabitually represent to themselves things in the concrete, with the\ndetail which belongs to them in the actual world. To minds of a\ndifferent description, the only antidote to this corruption of language\nis predication. The habit of predicating of the name, all the various\nproperties which it originally connoted, keeps up the association\nbetween the name and those properties.\n\nBut in order that it may do so, it is necessary that the predicates\nshould themselves retain their association with the properties which\nthey severally connote. For the propositions cannot keep the meaning of\nthe words alive, if the meaning of the propositions themselves should\ndie. And nothing is more common than for propositions to be mechanically\nrepeated, mechanically retained in the memory, and their truth\nundoubtingly assented to and relied on, while yet they carry no meaning\ndistinctly home to the mind; and while the matter of fact or law of\nnature which they originally expressed is as much lost sight of, and\npractically disregarded, as if it never had been heard of at all. In\nthose subjects which are at the same time familiar and complicated, and\nespecially in those which are so in as great a degree as moral and\nsocial subjects are, it is a matter of common remark how many important\npropositions are believed and repeated from habit, while no account\ncould be given, and no sense is practically manifested, of the truths\nwhich they convey. Hence it is, that the traditional maxims of old\nexperience, though seldom questioned, have often so little effect on the\nconduct of life; because their meaning is never, by most persons, really\nfelt, until personal experience has brought it home. And thus also it is\nthat so many doctrines of religion, ethics, and even politics, so full\nof meaning and reality to first converts, have manifested (after the\nassociation of that meaning with the verbal formulas has ceased to be\nkept up by the controversies which accompanied their first introduction)\na tendency to degenerate rapidly into lifeless dogmas; which tendency,\nall the efforts of an education expressly and skilfully directed to\nkeeping the meaning alive, are barely sufficient to counteract.\n\nConsidering, then, that the human mind, in different generations,\noccupies itself with different things, and in one age is led by the\ncircumstances which surround it to fix more of its attention upon one of\nthe properties of a thing, in another age upon another; it is natural\nand inevitable that in every age a certain portion of our recorded and\ntraditional knowledge, not being continually suggested by the pursuits\nand inquiries with which mankind are at that time engrossed, should fall\nasleep, as it were, and fade from the memory. It would be in danger of\nbeing totally lost, if the propositions or formulas, the results of the\nprevious experience, did not remain, as forms of words it may be, but of\nwords that once really conveyed, and are still supposed to convey, a\nmeaning: which meaning, though suspended, may be historically traced,\nand when suggested, may be recognised by minds of the necessary\nendowments as being still matter of fact, or truth. While the formulas\nremain, the meaning may at any time revive; and as on the one hand the\nformulas progressively lose the meaning they were intended to convey,\nso, on the other, when this forgetfulness has reached its height and\nbegun to produce obvious consequences, minds arise which from the\ncontemplation of the formulas rediscover the truth, when truth it was,\nwhich was contained in them, and announce it again to mankind, not as a\ndiscovery, but as the meaning of that which they have been taught, and\nstill profess to believe.\n\nThus there is a perpetual oscillation in spiritual truths, and in\nspiritual doctrines of any significance, even when not truths. Their\nmeaning is almost always in a process either of being lost or of being\nrecovered. Whoever has attended to the history of the more serious\nconvictions of mankind--of the opinions by which the general conduct of\ntheir lives is, or as they conceive ought to be, more especially\nregulated--is aware that even when recognising verbally the same\ndoctrines, they attach to them at different periods a greater or a less\nquantity, and even a different kind, of meaning. The words in their\noriginal acceptation connoted, and the propositions expressed, a\ncomplication of outward facts and inward feelings, to different portions\nof which the general mind is more particularly alive in different\ngenerations of mankind. To common minds, only that portion of the\nmeaning is in each generation suggested, of which that generation\npossesses the counterpart in its own habitual experience. But the words\nand propositions lie ready to suggest to any mind duly prepared the\nremainder of the meaning. Such individual minds are almost always to be\nfound: and the lost meaning, revived by them, again by degrees works its\nway into the general mind.\n\nThe arrival of this salutary reaction may however be materially\nretarded, by the shallow conceptions and incautious proceedings of mere\nlogicians. It sometimes happens that towards the close of the downward\nperiod, when the words have lost part of their significance, and have\nnot yet begun to recover it, persons arise whose leading and favourite\nidea is the importance of clear conceptions and precise thought, and the\nnecessity, therefore, of definite language. These persons, in examining\nthe old formulas, easily perceive that words are used in them without a\nmeaning; and if they are not the sort of persons who are capable of\nrediscovering the lost signification, they naturally enough dismiss the\nformula, and define the name without reference to it. In so doing they\nfasten down the name to what it connotes in common use at the time when\nit conveys the smallest quantity of meaning; and introduce the practice\nof employing it, consistently and uniformly, according to that\nconnotation. The word in this way acquires an extent of denotation far\nbeyond what it had before; it becomes extended to many things to which\nit was previously, in appearance capriciously, refused. Of the\npropositions in which it was formerly used, those which were true in\nvirtue of the forgotten part of its meaning are now, by the clearer\nlight which the definition diffuses, seen not to be true according to\nthe definition; which, however, is the recognised and sufficiently\ncorrect expression of all that is perceived to be in the mind of any one\nby whom the term is used at the present day. The ancient formulas are\nconsequently treated as prejudices; and people are no longer taught as\nbefore, though not to understand them, yet to believe that there is\ntruth in them. They no longer remain in the general mind surrounded by\nrespect, and ready at any time to suggest their original meaning.\nWhatever truths they contain are not only, in these circumstances,\nrediscovered far more slowly, but, when rediscovered, the prejudice\nwith which novelties are regarded is now, in some degree at least,\nagainst them, instead of being on their side.\n\nAn example may make these remarks more intelligible. In all ages, except\nwhere moral speculation has been silenced by outward compulsion, or\nwhere the feelings which prompt to it still continue to be satisfied by\nthe traditional doctrines of an established faith, one of the subjects\nwhich have most occupied the minds of thinking persons is the inquiry,\nWhat is virtue? or, What is a virtuous character? Among the different\ntheories on the subject which have, at different times, grown up and\nobtained partial currency, every one of which reflected as in the\nclearest mirror, the express image of the age which gave it birth; there\nwas one, according to which virtue consists in a correct calculation of\nour own personal interests, either in this world only, or also in\nanother. To make this theory plausible, it was of course necessary that\nthe only beneficial actions which people in general were accustomed to\nsee, or were therefore accustomed to praise, should be such as were, or\nat least might without contradicting obvious facts be supposed to be,\nthe result of a prudential regard to self-interest; so that the words\nreally connoted no more, in common acceptation, than was set down in the\ndefinition.\n\nSuppose, now, that the partisans of this theory had contrived to\nintroduce a consistent and undeviating use of the term according to this\ndefinition. Suppose that they had seriously endeavoured, and had\nsucceeded in the endeavour, to banish the word disinterestedness from\nthe language; had obtained the disuse of all expressions attaching odium\nto selfishness or commendation to self-sacrifice, or which implied\ngenerosity or kindness to be anything but doing a benefit in order to\nreceive a greater personal advantage in return. Need we say, that this\nabrogation of the old formulas for the sake of preserving clear ideas\nand consistency of thought, would have been a great evil? while the very\ninconsistency incurred by the coexistence of the formulas with\nphilosophical opinions which seemed to condemn them as absurdities,\noperated as a stimulus to the re-examination of the subject; and thus\nthe very doctrines originating in the oblivion into which a part of the\ntruth had fallen, were rendered indirectly, but powerfully, instrumental\nto its revival.\n\nThe doctrine of the Coleridge school, that the language of any people\namong whom culture is of old date, is a sacred deposit, the property of\nall ages, and which no one age should consider itself empowered to\nalter--borders indeed, as thus expressed, on an extravagance; but it is\ngrounded on a truth, frequently overlooked by that class of logicians\nwho think more of having a clear than of having a comprehensive meaning;\nand who perceive that every age is adding to the truths which it has\nreceived from its predecessors, but fail to see that a counter process\nof losing truths already possessed, is also constantly going on, and\nrequiring the most sedulous attention to counteract it. Language is the\ndepository of the accumulated body of experience to which all former\nages have contributed their part, and which is the inheritance of all\nyet to come. We have no right to prevent ourselves from transmitting to\nposterity a larger portion of this inheritance than we may ourselves\nhave profited by. However much we may be able to improve on the\nconclusions of our forefathers, we ought to be careful not inadvertently\nto let any of their premises slip through our fingers. It may be good to\nalter the meaning of a word, but it is bad to let any part of the\nmeaning drop. Whoever seeks to introduce a more correct use of a term\nwith which important associations are connected, should be required to\npossess an accurate acquaintance with the history of the particular\nword, and of the opinions which in different stages of its progress it\nserved to express. To be qualified to define the name, we must know all\nthat has ever been known of the properties of the class of objects which\nare, or originally were, denoted by it. For if we give it a meaning\naccording to which any proposition will be false which has ever been\ngenerally held to be true, it is incumbent on us to be sure that we know\nand have considered all which those, who believed the proposition,\nunderstood by it.\n\n\n\n\nCHAPTER V.\n\nON THE NATURAL HISTORY OF THE VARIATIONS IN THE MEANING OF TERMS.\n\n\n\u00a7 1. It is not only in the mode which has now been pointed out, namely\nby gradual inattention to a portion of the ideas conveyed, that words in\ncommon use are liable to shift their connotation. The truth is, that the\nconnotation of such words is perpetually varying; as might be expected\nfrom the manner in which words in common use acquire their connotation.\nA technical term, invented for purposes of art or science, has, from the\nfirst, the connotation given to it by its inventor; but a name which is\nin every one's mouth before any one thinks of defining it, derives its\nconnotation only from the circumstances which are habitually brought to\nmind when it is pronounced. Among these circumstances, the properties\ncommon to the things denoted by the name, have naturally a principal\nplace; and would have the sole place, if language were regulated by\nconvention rather than by custom and accident. But besides these common\nproperties, which if they exist are _certainly_ present whenever the\nname is employed, any other circumstance may _casually_ be found along\nwith it, so frequently as to become associated with it in the same\nmanner, and as strongly, as the common properties themselves. In\nproportion as this association forms itself, people give up using the\nname in cases in which those casual circumstances do not exist. They\nprefer using some other name, or the same name with some adjunct, rather\nthan employ an expression which will call up an idea they do not want to\nexcite. The circumstance originally casual, thus becomes regularly a\npart of the connotation of the word.\n\nIt is this continual incorporation of circumstances originally\naccidental, into the permanent signification of words, which is the\ncause that there are so few exact synonymes. It is this also which\nrenders the dictionary meaning of a word, by universal remark so\nimperfect an exponent of its real meaning. The dictionary meaning is\nmarked out in a broad, blunt way, and probably includes all that was\noriginally necessary for the correct employment of the term; but in\nprocess of time so many collateral associations adhere to words, that\nwhoever should attempt to use them with no other guide than the\ndictionary, would confound a thousand nice distinctions and subtle\nshades of meaning which dictionaries take no account of; as we notice in\nthe use of a language in conversation or writing by a foreigner not\nthoroughly master of it. The history of a word, by showing the causes\nwhich determine its use, is in these cases a better guide to its\nemployment than any definition; for definitions can only show its\nmeaning at the particular time, or at most the series of its successive\nmeanings, but its history may show the law by which the succession was\nproduced. The word _gentleman_, for instance, to the correct employment\nof which a dictionary would be no guide, originally meant simply a man\nborn in a certain rank. From this it came by degrees to connote all such\nqualities or adventitious circumstances as were usually found to belong\nto persons of that rank. This consideration at once explains why in one\nof its vulgar acceptations it means any one who lives without labour, in\nanother without manual labour, and in its more elevated signification it\nhas in every age signified the conduct, character, habits, and outward\nappearance, in whomsoever found, which, according to the ideas of that\nage, belonged or were expected to belong to persons born and educated in\na high social position.\n\nIt continually happens that of two words, whose dictionary meanings are\neither the same or very slightly different, one will be the proper word\nto use in one set of circumstances, another in another, without its\nbeing possible to show how the custom of so employing them originally\ngrew up. The accident that one of the words was used and not the other\non a particular occasion or in a particular social circle, will be\nsufficient to produce so strong an association between the word and some\nspeciality of circumstances, that mankind abandon the use of it in any\nother case, and the speciality becomes part of its signification. The\ntide of custom first drifts the word on the shore of a particular\nmeaning, then retires and leaves it there.\n\nAn instance in point is the remarkable change which, in the English\nlanguage at least, has taken place in the signification of the word\n_loyalty_. That word originally meant in English, as it still means in\nthe language from whence it came, fair, open dealing, and fidelity to\nengagements; in that sense the quality it expressed was part of the\nideal chivalrous or knightly character. By what process, in England, the\nterm became restricted to the single case of fidelity to the throne, I\nam not sufficiently versed in the history of courtly language to be able\nto pronounce. The interval between a _loyal chevalier_ and a loyal\nsubject is certainly great. I can only suppose that the word was, at\nsome period, the favourite term at court to express fidelity to the oath\nof allegiance; until at length those who wished to speak of any other,\nand as it was probably deemed, inferior sort of fidelity, either did not\nventure to use so dignified a term, or found it convenient to employ\nsome other in order to avoid being misunderstood.\n\n\n\u00a7 2. Cases are not unfrequent in which a circumstance, at first casually\nincorporated into the connotation of a word which originally had no\nreference to it, in time wholly supersedes the original meaning, and\nbecomes not merely a part of the connotation, but the whole of it. This\nis exemplified in the word pagan, _paganus_; which originally, as its\netymology imports, was equivalent to _villager_; the inhabitant of a\n_pagus_, or village. At a particular era in the extension of\nChristianity over the Roman empire, the adherents of the old religion,\nand the villagers or country people, were nearly the same body of\nindividuals, the inhabitants of the towns having been earliest\nconverted; as in our own day, and at all times, the greater activity of\nsocial intercourse renders them the earliest recipients of new opinions\nand modes, while old habits and prejudices linger longest among the\ncountry people: not to mention that the towns were more immediately\nunder the direct influence of the government, which at that time had\nembraced Christianity. From this casual coincidence, the word _paganus_\ncarried with it, and began more and more steadily to suggest, the idea\nof a worshipper of the ancient divinities; until at length it suggested\nthat idea so forcibly that people who did not desire to suggest the idea\navoided using the word. But when _paganus_ had come to connote\nheathenism, the very unimportant circumstance, with reference to that\nfact, of the place of residence, was soon disregarded in the employment\nof the word. As there was seldom any occasion for making separate\nassertions respecting heathens who lived in the country, there was no\nneed for a separate word to denote them; and pagan came not only to mean\nheathen, but to mean that exclusively.\n\nA case still more familiar to most readers is that of the word _villain_\nor _villein_. This term, as everybody knows, had in the middle ages a\nconnotation as strictly defined as a word could have, being the proper\nlegal designation for those persons who were the subjects of the less\nonerous forms of feudal bondage. The scorn of the semibarbarous military\naristocracy for these their abject dependants, rendered the act of\nlikening any person to this class of people a mark of the greatest\ncontumely: the same scorn led them to ascribe to the same people all\nmanner of hateful qualities, which doubtless also, in the degrading\nsituation in which they were held, were often not unjustly imputed to\nthem. These circumstances combined to attach to the term villain, ideas\nof crime and guilt in so forcible a manner, that the application of the\nepithet even to those to whom it legally belonged became an affront, and\nwas abstained from whenever no affront was intended. From that time\nguilt was part of the connotation; and soon became the whole of it,\nsince mankind were not prompted by any urgent motive to continue making\na distinction in their language between bad men of servile station and\nbad men of any other rank in life.\n\nThese and similar instances in which the original signification of a\nterm is totally lost--another and an entirely distinct meaning being\nfirst engrafted upon the former, and finally substituted for it--afford\nexamples of the double movement which is always taking place in\nlanguage: two counter-movements, one of Generalization, by which words\nare perpetually losing portions of their connotation, and becoming of\nless meaning and more general acceptation; the other of Specialization,\nby which other, or even these same words, are continually taking on\nfresh connotation; acquiring additional meaning, by being restricted in\ntheir employment to a part only of the occasions on which they might\nproperly be used before. This double movement is of sufficient\nimportance in the natural history of language, (to which natural history\nthe artificial modifications ought always to have some degree of\nreference,) to justify our dwelling a little longer on the nature of the\ntwofold phenomenon, and the causes to which it owes its existence.\n\n\n\u00a7 3. To begin with the movement of generalization. It is unnecessary to\ndwell on the changes in the meaning of names which take place merely\nfrom their being used ignorantly, by persons who, not having properly\nmastered the received connotation of a word, apply it in a looser and\nwider sense than belongs to it. This, however, is a real source of\nalterations in the language; for when a word, from being often employed\nin cases where one of the qualities which it connotes does not exist,\nceases to suggest that quality with certainty, then even those who are\nunder no mistake as to the proper meaning of the word, prefer expressing\nthat meaning in some other way, and leave the original word to its fate.\nThe word 'Squire as standing for an owner of a landed estate; Parson, as\ndenoting not the rector of the parish, but clergymen in general; Artist,\nto denote only a painter or sculptor; are cases in point.[15]\nIndependently, however, of the generalization of names through their\nignorant misuse, there is a tendency in the same direction, consistently\nwith a perfect knowledge of their meaning; arising from the fact, that\nthe number of things known to us, and of which we feel a desire to\nspeak, multiply faster than the names for them. Except on subjects for\nwhich there has been constructed a scientific terminology, with which\nunscientific persons do not meddle, great difficulty is generally found\nin bringing a new name into use; and independently of that difficulty,\nit is natural to prefer giving to a new object a name which at least\nexpresses its resemblance to something already known, since by\npredicating of it a name entirely new we at first convey no information.\nIn this manner the name of a species often becomes the name of a genus;\nas _salt_, for example, or _oil_; the former of which words originally\ndenoted only the muriate of soda, the latter, as its etymology\nindicates, only olive oil; but which now denote large and diversified\nclasses of substances resembling these in some of their qualities, and\nconnote only those common qualities, instead of the whole of the\ndistinctive properties of olive oil and sea salt. The words _glass_ and\n_soap_ are used by modern chemists in a similar manner, to denote genera\nof which the substances vulgarly so called are single species. And it\noften happens, as in those instances, that the term keeps its special\nsignification in addition to its more general one, and becomes\nambiguous, that is, two names instead of one.\n\nThese changes, by which words in ordinary use become more and more\ngeneralized, and less and less expressive, take place in a still greater\ndegree with the words which express the complicated phenomena of mind\nand society. Historians, travellers, and in general those who speak or\nwrite concerning moral and social phenomena with which they are not\nfamiliarly acquainted, are the great agents in this modification of\nlanguage. The vocabulary of all except unusually instructed as well as\nthinking persons, is, on such subjects, eminently scanty. They have a\ncertain small set of words to which they are accustomed, and which they\nemploy to express phenomena the most heterogeneous, because they have\nnever sufficiently analysed the facts to which those words correspond in\ntheir own country, to have attached perfectly definite ideas to the\nwords. The first English conquerors of Bengal, for example, carried with\nthem the phrase _landed proprietor_ into a country where the rights of\nindividuals over the soil were extremely different in degree, and even\nin nature, from those recognised in England. Applying the term with all\nits English associations in such a state of things; to one who had only\na limited right they gave an absolute right, from another because he had\nnot an absolute right they took away all right, drove whole classes of\npeople to ruin and despair, filled the country with banditti, created a\nfeeling that nothing was secure, and produced, with the best intentions,\na disorganization of society which had not been produced in that country\nby the most ruthless of its barbarian invaders. Yet the usage of persons\ncapable of so gross a misapprehension, determines the meaning of\nlanguage; and the words they thus misuse grow in generality, until the\ninstructed are obliged to acquiesce; and to employ those words (first\nfreeing them from vagueness by giving them a definite connotation) as\ngeneric terms, subdividing the genera into species.\n\n\n\u00a7 4. While the more rapid growth of ideas than of names thus creates a\nperpetual necessity for making the same names serve, even if\nimperfectly, on a greater number of occasions; a counter-operation is\ngoing on, by which names become on the contrary restricted to fewer\noccasions, by taking on, as it were, additional connotation, from\ncircumstances not originally included in the meaning, but which have\nbecome connected with it in the mind by some accidental cause. We have\nseen above, in the words _pagan_ and _villain_, remarkable examples of\nthe specialization of the meaning of words from casual associations, as\nwell as of the generalization of it in a new direction, which often\nfollows.\n\nSimilar specializations are of frequent occurrence in the history even\nof scientific nomenclature. \"It is by no means uncommon,\" says Dr.\nParis, in his _Pharmacologia_,[16] \"to find a word which is used to\nexpress general characters subsequently become the name of a specific\nsubstance in which such characters are predominant; and we shall find\nthat some important anomalies in nomenclature may be thus explained. The\nterm [Greek: Arsenikon], from which the word Arsenic is derived, was an\nancient epithet applied to those natural substances which possessed\nstrong and acrimonious properties, and as the poisonous quality of\narsenic was found to be remarkably powerful, the term was especially\napplied to Orpiment, the form in which this metal most usually occurred.\nSo the term _Verbena_ (quasi _Herbena_) originally denoted all those\nherbs that were held sacred on account of their being employed in the\nrites of sacrifice, as we learn from the poets; but as _one_ herb was\nusually adopted upon these occasions, the word Verbena came to denote\nthat particular herb _only_, and it is transmitted to us to this day\nunder the same title, viz. Verbena or Vervain, and indeed until lately\nit enjoyed the medical reputation which its sacred origin conferred upon\nit, for it was worn suspended around the neck as an amulet. _Vitriol_,\nin the original application of the word, denoted _any_ crystalline body\nwith a certain degree of transparency (_vitrum_); it is hardly necessary\nto observe that the term is now appropriated to a particular species: in\nthe same manner, Bark, which is a general term, is applied to express\n_one_ genus, and by way of eminence, it has the article _The_ prefixed,\nas _The_ bark: the same observation will apply to the word Opium, which,\nin its primitive sense, signifies _any_ juice ([Greek: opos], _Succus_),\nwhile it now only denotes _one_ species, viz. that of the poppy. So,\nagain, _Elaterium_ was used by Hippocrates to signify various internal\napplications, especially purgatives, of a violent and drastic nature\n(from the word [Greek: elaun\u00f4], _agito_, _moveo_, _stimulo_), but by\nsucceeding authors it was exclusively applied to denote the active\nmatter which subsides from the juice of the wild cucumber. The word\n_Fecula_, again, originally meant to imply _any_ substance which was\nderived by spontaneous subsidence from a liquid (from _f\u00e6x_, the grounds\nor settlement of _any_ liquor); afterwards it was applied to Starch,\nwhich is deposited in this manner by agitating the flour of wheat in\nwater; and lastly, it has been applied to a peculiar vegetable\nprinciple, which, like starch, is insoluble in cold, but completely\nsoluble in boiling water, with which it forms a gelatinous solution.\nThis indefinite meaning of the word _fecula_ has created numerous\nmistakes in pharmaceutic chemistry; Elaterium, for instance, is said to\nbe _fecula_, and, in the original sense of the word, it is properly so\ncalled, inasmuch as it is procured from a vegetable juice by spontaneous\nsubsidence, but in the limited and modern acceptation of the term, it\nconveys an erroneous idea; for instead of the active principle of the\njuice residing in _fecula_, it is a peculiar proximate principle, _sui\ngeneris_, to which I have ventured to bestow the name of _Elatin_. For\nthe same reason, much doubt and obscurity involve the meaning of the\nword _Extract_, because it is applied _generally_ to any substance\nobtained by the evaporation of a vegetable solution, and _specifically_\nto a peculiar proximate principle, possessed of certain characters, by\nwhich it is distinguished from every other elementary body.\"\n\nA generic term is always liable to become thus limited to a single\nspecies, or even individual, if people have occasion to think and speak\nof that individual or species much oftener than of anything else which\nis contained in the genus. Thus by cattle, a stage-coachman will\nunderstand horses; beasts, in the language of agriculturists, stands for\noxen; and birds, with some sportsmen, for partridges only. The law of\nlanguage which operates in these trivial instances, is the very same in\nconformity to which the terms [Greek: Theos], Deus, and God, were\nadopted from Polytheism by Christianity, to express the single object of\nits own adoration. Almost all the terminology of the Christian Church\nis made up of words originally used in a much more general acceptation:\n_Ecclesia_, Assembly; _Bishop_, Episcopus, Overseer; _Priest_,\nPresbyter, Elder; _Deacon_, Diaconus, Administrator; _Sacrament_, a vow\nof allegiance; _Evangelium_, good tidings; and some words, as\n_Minister_, are still used both in the general and in the limited sense.\nIt would be interesting to trace the progress by which _author_ came, in\nits most familiar sense, to signify a writer, and [Greek: poi\u00eat\u00eas], or\nmaker, a poet.\n\nOf the incorporation into the meaning of a term, of circumstances\naccidentally connected with it at some particular period, as in the case\nof Pagan, instances might easily be multiplied. Physician ([Greek:\nphysikos], or naturalist) became, in England, synonymous with a healer\nof diseases, because until a comparatively late period medical\npractitioners were the only naturalists. _Clerc_, or clericus, a\nscholar, came to signify an ecclesiastic, because the clergy were for\nmany centuries the only scholars.\n\nOf all ideas, however, the most liable to cling by association to\nanything with which they have ever been connected by proximity, are\nthose of our pleasures and pains, or of the things which we habitually\ncontemplate as sources of our pleasures or pains. The additional\nconnotation, therefore, which a word soonest and most readily takes on,\nis that of agreeableness or painfulness, in their various kinds and\ndegrees: of being a good or bad thing; desirable or to be avoided; an\nobject of hatred, of dread, contempt, admiration, hope, or love.\nAccordingly there is hardly a single name, expressive of any moral or\nsocial fact calculated to call forth strong affections either of a\nfavourable or of a hostile nature, which does not carry with it\ndecidedly and irresistibly a connotation of those strong affections, or,\nat the least, of approbation or censure; insomuch that to employ those\nnames in conjunction with others by which the contrary sentiments were\nexpressed, would produce the effect of a paradox, or even a\ncontradiction in terms. The baneful influence of a connotation thus\nacquired, on the prevailing habits of thought, especially in morals and\npolitics, has been well pointed out on many occasions by Bentham. It\ngives rise to the fallacy of \"question-begging names.\" The very property\nwhich we are inquiring whether a thing possesses or not, has become so\nassociated with the name of the thing as to be part of its meaning,\ninsomuch that by merely uttering the name we assume the point which was\nto be made out: one of the most frequent sources of apparently\nself-evident propositions.\n\nWithout any further multiplication of examples to illustrate the changes\nwhich usage is continually making in the signification of terms, I shall\nadd, as a practical rule, that the logician, not being able to prevent\nsuch transformations, should submit to them with a good grace when they\nare irrevocably effected, and if a definition is necessary, define the\nword according to its new meaning; retaining the former as a second\nsignification, if it is needed, and if there is any chance of being able\nto preserve it either in the language of philosophy or in common use.\nLogicians cannot _make_ the meaning of any but scientific terms: that of\nall other words is made by the collective human race. But logicians can\nascertain clearly what it is which, working obscurely, has guided the\ngeneral mind to a particular employment of a name; and when they have\nfound this, they can clothe it in such distinct and permanent terms,\nthat mankind shall see the meaning which before they only felt, and\nshall not suffer it to be afterwards forgotten or misapprehended.\n\n\n\n\nCHAPTER VI.\n\nTHE PRINCIPLES OF A PHILOSOPHICAL LANGUAGE FURTHER CONSIDERED.\n\n\n\u00a7 1. We have, thus far, considered only one of the requisites of a\nlanguage adapted for the investigation of truth; that its terms shall\neach of them convey a determinate and unmistakeable meaning. There are,\nhowever, as we have already remarked, other requisites; some of them\nimportant only in the second degree, but one which is fundamental, and\nbarely yields in point of importance, if it yields at all, to the\nquality which we have already discussed at so much length. That the\nlanguage may be fitted for its purposes, not only should every word\nperfectly express its meaning, but there should be no important meaning\nwithout its word. Whatever we have occasion to think of often, and for\nscientific purposes, ought to have a name appropriated to it.\n\nThis requisite of philosophical language may be considered under three\ndifferent heads; that number of separate conditions being involved in\nit.\n\n\n\u00a7 2. First: there ought to be all such names, as are needful for making\nsuch a record of individual observations that the words of the record\nshall exactly show what fact it is which has been observed. In other\nwords, there should be an accurate Descriptive Terminology.\n\nThe only things which we can observe directly being our own sensations,\nor other feelings, a complete descriptive language would be one in which\nthere should be a name for every variety of elementary sensation or\nfeeling. Combinations of sensations or feelings may always be described,\nif we have a name for each of the elementary feelings which compose\nthem; but brevity of description, and clearness (which often depends\nvery much on brevity,) are greatly promoted by giving distinctive names\nnot to the elements alone, but also to all combinations which are of\nfrequent recurrence. On this occasion I cannot do better than quote from\nDr. Whewell[17] some of the excellent remarks which he has made on this\nimportant branch of our subject.\n\n\"The meaning of [descriptive] technical terms can be fixed in the first\ninstance only by convention, and can be made intelligible only by\npresenting to the senses that which the terms are to signify. The\nknowledge of a colour by its name can only be taught through the eye. No\ndescription can convey to a hearer what we mean by _apple-green_ or\n_French-grey_. It might, perhaps, be supposed that, in the first\nexample, the term _apple_, referring to so familiar an object,\nsufficiently suggests the colour intended. But it may easily be seen\nthat this is not true; for apples are of many different hues of green,\nand it is only by a conventional selection that we can appropriate the\nterm to one special shade. When this appropriation is once made, the\nterm refers to the sensation, and not to the parts of the term; for\nthese enter into the compound merely as a help to the memory, whether\nthe suggestion be a natural connexion as in 'apple-green,' or a casual\none as in 'French-grey.' In order to derive due advantage from technical\nterms of this kind, they must be associated _immediately_ with the\nperception to which they belong; and not connected with it through the\nvague usages of common language. The memory must retain the sensation;\nand the technical word must be understood as directly as the most\nfamiliar word, and more distinctly. When we find such terms as\n_tin-white_ or _pinchbeck-brown_, the metallic colour so denoted ought\nto start up in our memory without delay or search.\n\n\"This, which it is most important to recollect with respect to the\nsimpler properties of bodies, as colour and form, is no less true with\nrespect to more compound notions. In all cases the term is fixed to a\npeculiar meaning by convention; and the student, in order to use the\nword, must be completely familiar with the convention, so that he has no\nneed to frame conjectures from the word itself. Such conjectures would\nalways be insecure, and often erroneous. Thus the term _papilionaceous_\napplied to a flower is employed to indicate, not only a resemblance to a\nbutterfly, but a resemblance arising from five petals of a certain\npeculiar shape and arrangement; and even if the resemblance were much\nstronger than it is in such cases, yet, if it were produced in a\ndifferent way, as for example, by one petal, or two only, instead of a\n'standard,' two 'wings,' and a 'keel' consisting of two parts more or\nless united into one, we should be no longer justified in speaking of it\nas a 'papilionaceous' flower.\"\n\nWhen, however, the thing named is, as in this last case, a combination\nof simple sensations, it is not necessary, in order to learn the meaning\nof the word, that the student should refer back to the sensations\nthemselves; it may be communicated to him through the medium of other\nwords; the terms, in short, may be defined. But the names of elementary\nsensations, or elementary feelings of any sort, cannot be defined; nor\nis there any mode of making their signification known but by making the\nlearner experience the sensation, or referring him, through some known\nmark, to his remembrance of having experienced it before. Hence it is\nonly the impressions on the outward senses, or those inward feelings\nwhich are connected in a very obvious and uniform manner with outward\nobjects, that are really susceptible of an exact descriptive language.\nThe countless variety of sensations which arise, for instance, from\ndisease, or from peculiar physiological states, it would be in vain to\nattempt to name; for as no one can judge whether the sensation I have is\nthe same with his, the name cannot have, to us two, real community of\nmeaning. The same may be said, to a considerable extent, of purely\nmental feelings. But in some of the sciences which are conversant with\nexternal objects, it is scarcely possible to surpass the perfection to\nwhich this quality of a philosophical language has been carried.\n\n\"The formation[18] of an exact and extensive descriptive language for\nbotany has been executed with a degree of skill and felicity, which,\nbefore it was attained, could hardly have been dreamt of as attainable.\nEvery part of a plant has been named; and the form of every part, even\nthe most minute, has had a large assemblage of descriptive terms\nappropriated to it, by means of which the botanist can convey and\nreceive knowledge of form and structure, as exactly as if each minute\npart were presented to him vastly magnified. This acquisition was part\nof the Linn\u00e6an reform.... 'Tournefort,' says Decandolle, 'appears to\nhave been the first who really perceived the utility of fixing the sense\nof terms in such a way as always to employ the same word in the same\nsense, and always to express the same idea by the same words; but it was\nLinn\u00e6us who really created and fixed this botanical language, and this\nis his fairest claim to glory, for by this fixation of language he has\nshed clearness and precision over all parts of the science.'\n\n\"It is not necessary here to give any detailed account of the terms of\nbotany. The fundamental ones have been gradually introduced, as the\nparts of plants were more carefully and minutely examined. Thus the\nflower was necessarily distinguished into the _calyx_, the _corolla_,\nthe _stamens_, and the _pistils_; the sections of the corolla were\ntermed _petals_ by Columna; those of the calyx were called _sepals_ by\nNecker. Sometimes terms of greater generality were devised; as\n_perianth_, to include the calyx and corolla, whether one or both of\nthese were present; _pericarp_, for the part enclosing the grain, of\nwhatever kind it be, fruit, nut, pod, &c. And it may easily be imagined,\nthat descriptive terms may, by definition and combination, become very\nnumerous and distinct. Thus leaves may be called _pinnatifid_,\n_pinnatipartite_, _pinnatisect_, _pinnatilobate_, _palmatifid_,\n_palmatipartite_, &c., and each of these words designates different\ncombinations of the modes and extent of the divisions of the leaf with\nthe divisions of its outline. In some cases, arbitrary numerical\nrelations are introduced into the definition: thus, a leaf is called\n_bilobate_, when it is divided into two parts by a notch; but if the\nnotch go to the middle of its length, it is _bifid_; if it go near the\nbase of the leaf, it is _bipartite_; if to the base, it is _bisect_.\nThus, too, a pod of a cruciferous plant is a _siliqua_, if it is four\ntimes as long as it is broad, but if it be shorter than this it is a\n_silicula_. Such terms being established, the form of the very complex\nleaf or frond of a fern (Hymenophyllum Wilsoni) is exactly conveyed by\nthe following phrase:--'fronds rigid pinnate, pinn\u00e6 recurved\nsubunilateral, pinnatifid, the segments linear undivided or bifid\nspinuloso-serrate.'\n\n\"Other characters, as well as form, are conveyed with the like\nprecision: Colour by means of a classified scale of colours.... This was\ndone with most precision by Werner, and his scale of colours is still\nthe most usual standard of naturalists. Werner also introduced a more\nexact terminology with regard to other characters which are important in\nmineralogy, as lustre, hardness. But Mohs improved upon this step by\ngiving a numerical scale of hardness, in which talc is 1, gypsum 2, calc\nspar 3, and so on.... Some properties, as specific gravity, by their\ndefinition give at once a numerical measure; and others, as crystalline\nform, require a very considerable array of mathematical calculation and\nreasoning, to point out their relations and gradations.\"\n\n\n\u00a7 3. Thus far of Descriptive Terminology, or of the language requisite\nfor placing on record our observation of individual instances. But when\nwe proceed from this to Induction, or rather to that comparison of\nobserved instances which is the preparatory step towards it, we stand in\nneed of an additional and a different sort of general names.\n\nWhenever, for purposes of Induction, we find it necessary to introduce\n(in Dr. Whewell's phraseology) some new general conception; that is,\nwhenever the comparison of a set of phenomena leads to the recognition\nin them of some common circumstance, which, our attention not having\nbeen directed to it on any former occasion, is to us a new phenomenon;\nit is of importance that this new conception, or this new result of\nabstraction, should have a name appropriated to it; especially if the\ncircumstance it involves be one which leads to many consequences, or\nwhich is likely to be found also in other classes of phenomena. No\ndoubt, in most cases of the kind, the meaning might be conveyed by\njoining together several words already in use. But when a thing has to\nbe often spoken of, there are more reasons than the saving of time and\nspace, for speaking of it in the most concise manner possible. What\ndarkness would be spread over geometrical demonstrations, if wherever\nthe word _circle_ is used, the definition of a circle were inserted\ninstead of it. In mathematics and its applications, where the nature of\nthe processes demands that the attention should be strongly\nconcentrated, but does not require that it should be widely diffused,\nthe importance of concentration also in the expressions has always been\nduly felt; and a mathematician no sooner finds that he shall often have\noccasion to speak of the same two things together, than he at once\ncreates a term to express them whenever combined: just as, in his\nalgebraical operations, he substitutes for _(a^m + b^n) p/q_, or for\n_a/b + b/c + c/d_ + &c., the single letter P, Q, or S; not solely to\nshorten his symbolical expressions, but to simplify the purely\nintellectual part of his operations, by enabling the mind to give its\nexclusive attention to the relation between the quantity S and the other\nquantities which enter into the equation, without being distracted by\nthinking unnecessarily of the parts of which S is itself composed.\n\nBut there is another reason, in addition to that of promoting\nperspicuity, for giving a brief and compact name to each of the more\nconsiderable results of abstraction which are obtained in the course of\nour intellectual phenomena. By naming them, we fix our attention upon\nthem; we keep them more constantly before the mind. The names are\nremembered, and being remembered, suggest their definition; while if\ninstead of specific and characteristic names, the meaning had been\nexpressed by putting together a number of other names, that particular\ncombination of words already in common use for other purposes would have\nhad nothing to make itself remembered by. If we want to render a\nparticular combination of ideas permanent in the mind, there is nothing\nwhich clenches it like a name specially devoted to express it. If\nmathematicians had been obliged to speak of \"that to which a quantity,\nin increasing or diminishing, is always approaching nearer, so that the\ndifference becomes less than any assignable quantity, but to which it\nnever becomes exactly equal,\" instead of expressing all this by the\nsimple phrase, \"the limit of a quantity,\" we should probably have long\nremained without most of the important truths which have been discovered\nby means of the relation between quantities of various kinds and their\nlimits. If instead of speaking of _momentum_, it had been necessary to\nsay, \"the product of the number of units of velocity in the velocity by\nthe number of units of mass in the mass,\" many of the dynamical truths\nnow apprehended by means of this complex idea would probably have\nescaped notice, for want of recalling the idea itself with sufficient\nreadiness and familiarity. And on subjects less remote from the topics\nof popular discussion, whoever wishes to draw attention to some new or\nunfamiliar distinction among things, will find no way so sure as to\ninvent or select suitable names for the express purpose of marking it.\n\nA volume devoted to explaining what the writer means by civilization,\ndoes not raise so vivid a conception of it as the single expression,\nthat Civilization is a different thing from Cultivation; the compactness\nof that brief designation for the contrasted quality being an equivalent\nfor a long discussion. So, if we would impress forcibly upon the\nunderstanding and memory the distinction between the two different\nconceptions of a representative government, we cannot more effectually\ndo so than by saying that Delegation is not Representation. Hardly any\noriginal thoughts on mental or social subjects ever make their way among\nmankind, or assume their proper importance in the minds even of their\ninventors, until aptly-selected words or phrases have, as it were,\nnailed them down and held them fast.\n\n\n\u00a7 4. Of the three essential parts of a philosophical language, we have\nnow mentioned two: a terminology suited for describing with precision\nthe individual facts observed; and a name for every common property of\nany importance or interest, which we detect by comparing those facts:\nincluding (as the concretes corresponding to those abstract terms) names\nfor the classes which we artificially construct in virtue of those\nproperties, or as many of them, at least, as we have frequent occasion\nto predicate anything of.\n\nBut there is a sort of classes, for the recognition of which no such\nelaborate process is necessary; because each of them is marked out from\nall others not by some one property, the detection of which may depend\non a difficult act of abstraction, but by its properties generally. I\nmean, the Kinds of things, in the sense which, in this treatise, has\nbeen specially attached to that term. By a Kind, it will be remembered,\nwe mean one of those classes which are distinguished from all others not\nby one or a few definite properties, but by an unknown multitude of\nthem: the combination of properties on which the class is grounded,\nbeing a mere index to an indefinite number of other distinctive\nattributes. The class horse is a Kind, because the things which agree in\npossessing the characters by which we recognise a horse, agree in a\ngreat number of other properties, as we know, and, it cannot be doubted,\nin many more than we know. Animal, again, is a Kind, because no\ndefinition that could be given of the name animal could either exhaust\nthe properties common to all animals, or supply premises from which the\nremainder of those properties could be inferred. But a combination of\nproperties which does not give evidence of the existence of any other\nindependent peculiarities, does not constitute a Kind. White horse,\ntherefore, is not a Kind; because horses which agree in whiteness, do\nnot agree in anything else, except the qualities common to all horses,\nand whatever may be the causes or effects of that particular colour.\n\nOn the principle that there should be a name for everything which we\nhave frequent occasion to make assertions about, there ought evidently\nto be a name for every Kind; for as it is the very meaning of a Kind\nthat the individuals composing it have an indefinite multitude of\nproperties in common, it follows that, if not with our present\nknowledge, yet with that which we may hereafter acquire, the Kind is a\nsubject to which there will have to be applied many predicates. The\nthird component element of a philosophical language, therefore, is that\nthere shall be a name for every Kind. In other words, there must not\nonly be a terminology, but also a nomenclature.\n\nThe words Nomenclature and Terminology are employed by most authors\nalmost indiscriminately; Dr. Whewell being, as far as I am aware, the\nfirst writer who has regularly assigned to the two words different\nmeanings. The distinction however which he has drawn between them being\nreal and important, his example is likely to be followed; and (as is apt\nto be the case when such innovations in language are felicitously made)\na vague sense of the distinction is found to have influenced the\nemployment of the terms in common practice, before the expediency had\nbeen pointed out of discriminating them philosophically. Every one would\nsay that the reform effected by Lavoisier and Guyton-Morveau in the\nlanguage of chemistry consisted in the introduction of a new\nnomenclature, not of a new terminology. Linear, lanceolate, oval, or\noblong, serrated, dentate, or crenate leaves, are expressions forming\npart of the terminology of botany, while the names \"Viola odorata,\" and\n\"Ulex Europ\u00e6us,\" belong to its nomenclature.\n\nA nomenclature may be defined, the collection of the names of all the\nKinds with which any branch of knowledge is conversant; or more\nproperly, of all the lowest Kinds, or _infim\u00e6 species_--those which may\nbe subdivided indeed, but not into Kinds, and which generally accord\nwith what in natural history are termed simply species. Science\npossesses two splendid examples of a systematic nomenclature; that of\nplants and animals, constructed by Linn\u00e6us and his successors, and that\nof chemistry, which we owe to the illustrious group of chemists who\nflourished in France towards the close of the eighteenth century. In\nthese two departments, not only has every known species, or lowest Kind,\na name assigned to it, but when new lowest Kinds are discovered, names\nare at once given to them on an uniform principle. In other sciences the\nnomenclature is not at present constructed on any system, either because\nthe species to be named are not numerous enough to require one, (as in\ngeometry for example,) or because no one has yet suggested a suitable\nprinciple for such a system, as in mineralogy; in which the want of a\nscientifically constructed nomenclature is now the principal cause which\nretards the progress of the science.\n\n\n\u00a7 5. A word which carries on its face that it belongs to a nomenclature,\nseems at first sight to differ from other concrete general names in\nthis--that its meaning does not reside in its connotation, in the\nattributes implied in it, but in its denotation, that is, in the\nparticular group of things which it is appointed to designate; and\ncannot, therefore, be unfolded by means of a definition, but must be\nmade known in another way. This opinion, however, appears to me\nerroneous. Words belonging to a nomenclature differ, I conceive, from\nother words mainly in this, that besides the ordinary connotation, they\nhave a peculiar one of their own: besides connoting certain attributes,\nthey also connote that those attributes are distinctive of a Kind. The\nterm \"peroxide of iron,\" for example, belonging by its form to the\nsystematic nomenclature of chemistry, bears on its face that it is the\nname of a peculiar Kind of substance. It moreover connotes, like the\nname of any other class, some portion of the properties common to the\nclass; in this instance the property of being a compound of iron and the\nlargest dose of oxygen with which iron will combine. These two things,\nthe fact of being such a compound, and the fact of being a Kind,\nconstitute the connotation of the name peroxide of iron. When we say of\nthe substance before us, that it is the peroxide of iron, we thereby\nassert, first, that it is a compound of iron and a maximum of oxygen,\nand next, that the substance so composed is a peculiar Kind of\nsubstance.\n\nNow, this second part of the connotation of any word belonging to a\nnomenclature is as essential a portion of its meaning as the first part,\nwhile the definition only declares the first: and hence the appearance\nthat the signification of such terms cannot be conveyed by a definition:\nwhich appearance, however, is fallacious. The name Viola odorata denotes\na Kind, of which a certain number of characters, sufficient to\ndistinguish it, are enunciated in botanical works. This enumeration of\ncharacters is surely, as in other cases, a definition of the name. No,\nsay some, it is not a definition, for the name Viola odorata does not\nmean those characters; it means that particular group of plants, and the\ncharacters are selected from among a much greater number, merely as\nmarks by which to recognise the group. But to this I reply, that the\nname does not mean that group, for it would be applied to that group no\nlonger than while the group is believed to be an _infima species_; if it\nwere to be discovered that several distinct Kinds have been confounded\nunder this one name, no one would any longer apply the name Viola\nodorata to the whole of the group, but would apply it, if retained at\nall, to one only of the Kinds contained therein. What is imperative,\ntherefore, is not that the name shall denote one particular collection\nof objects, but that it shall denote a Kind, and a lowest Kind. The form\nof the name declares that, happen what will, it is to denote an _infima\nspecies_; and that, therefore, the properties which it connotes, and\nwhich are expressed in the definition, are to be connoted by it no\nlonger than while we continue to believe that those properties, when\nfound together, indicate a Kind, and that the whole of them are found in\nno more than one Kind.\n\nWith the addition of this peculiar connotation, implied in the form of\nevery word which belongs to a systematic nomenclature; the set of\ncharacters which is employed to discriminate each Kind from all other\nKinds (and which is a real definition) constitutes as completely as in\nany other case the whole meaning of the term. It is no objection to say\nthat (as is often the case in natural history) the set of characters\nmay be changed, and another substituted as being better suited for the\npurpose of distinction, while the word, still continuing to denote the\nsame group of things, is not considered to have changed its meaning. For\nthis is no more than may happen in the case of any other general name:\nwe may, in reforming its connotation, leave its denotation untouched;\nand it is generally desirable to do so. The connotation, however, is not\nthe less for this the real meaning, for we at once apply the name\nwherever the characters set down in the definition are found; and that\nwhich exclusively guides us in applying the term, must constitute its\nsignification. If we find, contrary to our previous belief, that the\ncharacters are not peculiar to one species, we cease to use the term\ncoextensively with the characters; but then it is because the other\nportion of the connotation fails; the condition that the class must be a\nKind. The connotation, therefore, is still the meaning; the set of\ndescriptive characters is a true definition; and the meaning is\nunfolded, not indeed (as in other cases) by the definition alone, but by\nthe definition and the form of the word taken together.\n\n\n\u00a7 6. We have now analysed what is implied in the two principal\nrequisites of a philosophical language; first, precision, or\ndefiniteness, and secondly, completeness. Any further remarks on the\nmode of constructing a nomenclature must be deferred until we treat of\nClassification; the mode of naming the Kinds of things being necessarily\nsubordinate to the mode of arranging those Kinds into larger classes.\nWith respect to the minor requisites of terminology, some of them are\nwell stated and illustrated in the \"Aphorisms concerning the Language of\nScience,\" included in Dr. Whewell's _Philosophy of the Inductive\nSciences_. These, as being of secondary importance in the peculiar point\nof view of Logic, I shall not further refer to, but shall confine my\nobservations to one more quality, which, next to the two already treated\nof, appears to be the most valuable which the language of science can\npossess. Of this quality a general notion may be conveyed by the\nfollowing aphorism:\n\nWhenever the nature of the subject permits our reasoning processes to\nbe, without danger, carried on mechanically, the language should be\nconstructed on as mechanical principles as possible; while in the\ncontrary case, it should be so constructed that there shall be the\ngreatest possible obstacles to a merely mechanical use of it.\n\nI am aware that this maxim requires much explanation, which I shall at\nonce proceed to give. And first, as to what is meant by using a language\nmechanically. The complete or extreme case of the mechanical use of\nlanguage, is when it is used without any consciousness of a meaning, and\nwith only the consciousness of using certain visible or audible marks in\nconformity to technical rules previously laid down. This extreme case is\nnowhere realized except in the figures of arithmetic and the symbols of\nalgebra, a language unique in its kind, and approaching as nearly to\nperfection, for the purposes to which it is destined, as can, perhaps,\nbe said of any creation of the human mind. Its perfection consists in\nthe completeness of its adaptation to a purely mechanical use. The\nsymbols are mere counters, without even the semblance of a meaning apart\nfrom the convention which is renewed each time they are employed, and\nwhich is altered at each renewal, the same symbol _a_ or _x_ being used\non different occasions to represent things which (except that, like all\nthings, they are susceptible of being numbered) have no property in\ncommon. There is nothing, therefore, to distract the mind from the set\nof mechanical operations which are to be performed upon the symbols,\nsuch as squaring both sides of the equation, multiplying or dividing\nthem by the same or by equivalent symbols, and so forth. Each of these\noperations, it is true, corresponds to a syllogism; represents one step\nof a ratiocination relating not to the symbols, but to the things\nsignified by them. But as it has been found practicable to frame a\ntechnical form, by conforming to which we can make sure of finding the\nconclusion of the ratiocination, our end can be completely attained\nwithout our ever thinking of anything but the symbols. Being thus\nintended to work merely as mechanism, they have the qualities which\nmechanism ought to have. They are of the least possible bulk, so that\nthey take up scarcely any room, and waste no time in their manipulation;\nthey are compact, and fit so closely together that the eye can take in\nthe whole at once of almost every operation which they are employed to\nperform.\n\nThese admirable properties of the symbolical language of mathematics\nhave made so strong an impression on the minds of many thinkers, as to\nhave led them to consider the symbolical language in question as the\nideal type of philosophical language generally; to think that names in\ngeneral, or (as they are fond of calling them) signs, are fitted for the\npurposes of thought in proportion as they can be made to approximate to\nthe compactness, the entire unmeaningness, and the capability of being\nused as counters without a thought of what they represent, which are\ncharacteristic of the _a_ and _b_, the _x_ and _y_, of algebra. This\nnotion has led to sanguine views of the acceleration of the progress of\nscience by means which, I conceive, cannot possibly conduce to that end,\nand forms part of that exaggerated estimate of the influence of signs,\nwhich has contributed in no small degree to prevent the real laws of our\nintellectual operations from being rightly understood.\n\nIn the first place, a set of signs by which we reason without\nconsciousness of their meaning, can be serviceable, at most, only in our\ndeductive operations. In our direct inductions we cannot for a moment\ndispense with a distinct mental image of the phenomena, since the whole\noperation turns on a perception of the particulars in which those\nphenomena agree and differ. But, further, this reasoning by counters is\nonly suitable to a very limited portion even of our deductive processes.\nIn our reasonings respecting numbers, the only general principles which\nwe ever have occasion to introduce, are these, Things which are equal to\nthe same thing are equal to one another, and The sums or differences of\nequal things are equal, with their various corollaries. Not only can no\nhesitation ever arise respecting the applicability of these principles,\nsince they are true of all magnitudes whatever; but every possible\napplication of which they are susceptible, may be reduced to a\ntechnical rule; and such, in fact, the rules of the calculus are. But if\nthe symbols represent any other things than mere numbers, let us say\neven straight or curve lines, we have then to apply theorems of geometry\nnot true of all lines without exception, and to select those which are\ntrue of the lines we are reasoning about. And how can we do this unless\nwe keep completely in mind what particular lines these are? Since\nadditional geometrical truths may be introduced into the ratiocination\nin any stage of its progress, we cannot suffer ourselves, during even\nthe smallest part of it, to use the names mechanically (as we use\nalgebraical symbols) without an image annexed to them. It is only after\nascertaining that the solution of a question concerning lines can be\nmade to depend on a previous question concerning numbers, or in other\nwords after the question has been (to speak technically) reduced to an\nequation, that the unmeaning signs become available, and that the nature\nof the facts themselves to which the investigation relates can be\ndismissed from the mind. Up to the establishment of the equation, the\nlanguage in which mathematicians carry on their reasoning does not\ndiffer in character from that employed by close reasoners on any other\nkind of subject.\n\nI do not deny that every correct ratiocination, when thrown into the\nsyllogistic shape, is conclusive from the mere form of the expression,\nprovided none of the terms used be ambiguous; and this is one of the\ncircumstances which have led some writers to think that if all names\nwere so judiciously constructed and so carefully defined as not to admit\nof any ambiguity, the improvement thus made in language would not only\ngive to the conclusions of every deductive science the same certainty\nwith those of mathematics, but would reduce all reasonings to the\napplication of a technical form, and enable their conclusiveness to be\nrationally assented to after a merely mechanical process, as is\nundoubtedly the case in algebra. But, if we except geometry, the\nconclusions of which are already as certain and exact as they can be\nmade, there is no science but that of number, in which the practical\nvalidity of a reasoning can be apparent to any person who has looked\nonly at the form of the process. Whoever has assented to what was said\nin the last Book concerning the case of the Composition of Causes, and\nthe still stronger case of the entire supersession of one set of laws by\nanother, is aware that geometry and algebra are the only sciences of\nwhich the propositions are categorically true: the general propositions\nof all other sciences are true only hypothetically, supposing that no\ncounteracting cause happens to interfere. A conclusion, therefore,\nhowever correctly deduced, in point of form, from admitted laws of\nnature, will have no other than an hypothetical certainty. At every step\nwe must assure ourselves that no other law of nature has superseded, or\nintermingled its operation with, those which are the premises of the\nreasoning; and how can this be done by merely looking at the words? We\nmust not only be constantly thinking of the phenomena themselves, but we\nmust be constantly studying them; making ourselves acquainted with the\npeculiarities of every case to which we attempt to apply our general\nprinciples.\n\nThe algebraic notation, considered as a philosophical language, is\nperfect in its adaptation to the subjects for which it is commonly\nemployed, namely those of which the investigations have already been\nreduced to the ascertainment of a relation between numbers. But,\nadmirable as it is for its own purpose, the properties by which it is\nrendered such are so far from constituting it the ideal model of\nphilosophical language in general, that the more nearly the language of\nany other branch of science approaches to it, the less fit that language\nis for its own proper functions. On all other subjects, instead of\ncontrivances to prevent our attention from being distracted by thinking\nof the meaning of our signs, we ought to wish for contrivances to make\nit impossible that we should ever lose sight of that meaning even for an\ninstant.\n\nWith this view, as much meaning as possible should be thrown into the\nformation of the word itself; the aids of derivation and analogy being\nmade available to keep alive a consciousness of all that is signified\nby it. In this respect those languages have an immense advantage which\nform their compounds and derivatives from native roots, like the German,\nand not from those of a foreign or dead language, as is so much the case\nwith English, French, and Italian: and the best are those which form\nthem according to fixed analogies, corresponding to the relations\nbetween the ideas to be expressed. All languages do this more or less,\nbut especially, among modern European languages, the German; while even\nthat is inferior to the Greek, in which the relation between the meaning\nof a derivative word and that of its primitive is in general clearly\nmarked by its mode of formation; except in the case of words compounded\nwith prepositions, which are often, in both those languages, extremely\nanomalous.\n\nBut all that can be done, by the mode of constructing words, to prevent\nthem from degenerating into sounds passing through the mind without any\ndistinct apprehension of what they signify, is far too little for the\nnecessity of the case. Words, however well constructed originally, are\nalways tending, like coins, to have their inscription worn off by\npassing from hand to hand; and the only possible mode of reviving it is\nto be ever stamping it afresh, by living in the habitual contemplation\nof the phenomena themselves, and not resting in our familiarity with the\nwords that express them. If any one, having possessed himself of the\nlaws of phenomena as recorded in words, whether delivered to him\noriginally by others, or even found out by himself, is content from\nthenceforth to live among these formul\u00e6, to think exclusively of them,\nand of applying them to cases as they arise, without keeping up his\nacquaintance with the realities from which these laws were\ncollected--not only will he continually fail in his practical efforts,\nbecause he will apply his formul\u00e6 without duly considering whether, in\nthis case and in that, other laws of nature do not modify or supersede\nthem; but the formul\u00e6 themselves will progressively lose their meaning\nto him, and he will cease at last even to be capable of recognising with\ncertainty whether a case falls within the contemplation of his formula\nor not. It is, in short, as necessary, on all subjects not mathematical,\nthat the things on which we reason should be conceived by us in the\nconcrete, and \"clothed in circumstances,\" as it is in algebra that we\nshould keep all individualizing peculiarities sedulously out of view.\n\nWith this remark we close our observations on the Philosophy of\nLanguage.\n\n\n\n\nCHAPTER VII.\n\nOF CLASSIFICATION, AS SUBSIDIARY TO INDUCTION.\n\n\n\u00a7 1. There is, as has been frequently remarked in this work, a\nclassification of things, which is inseparable from the fact of giving\nthem general names. Every name which connotes an attribute, divides, by\nthat very fact, all things whatever into two classes, those which have\nthe attribute and those which have it not; those of which the name can\nbe predicated, and those of which it cannot. And the division thus made\nis not merely a division of such things as actually exist, or are known\nto exist, but of all such as may hereafter be discovered, and even of\nall which can be imagined.\n\nOn this kind of Classification we have nothing to add to what has\npreviously been said. The Classification which requires to be discussed\nas a separate act of the mind, is altogether different. In the one, the\narrangement of objects in groups, and distribution of them into\ncompartments, is a mere incidental effect consequent on the use of names\ngiven for another purpose, namely that of simply expressing some of\ntheir qualities. In the other the arrangement and distribution are the\nmain object, and the naming is secondary to, and purposely conforms\nitself to, instead of governing, that more important operation.\n\nClassification, thus regarded, is a contrivance for the best possible\nordering of the ideas of objects in our minds; for causing the ideas to\naccompany or succeed one another in such a way as shall give us the\ngreatest command over our knowledge already acquired, and lead most\ndirectly to the acquisition of more. The general problem of\nClassification, in reference to these purposes, may be stated as\nfollows: To provide that things shall be thought of in such groups, and\nthose groups in such an order, as will best conduce to the remembrance\nand to the ascertainment of their laws.\n\nClassification thus considered, differs from classification in the wider\nsense, in having reference to real objects exclusively, and not to all\nthat are imaginable: its object being the due co-ordination in our minds\nof those things only, with the properties of which we have actually\noccasion to make ourselves acquainted. But, on the other hand, it\nembraces _all_ really existing objects. We cannot constitute any one\nclass properly, except in reference to a general division of the whole\nof nature; we cannot determine the group in which any one object can\nmost conveniently be placed, without taking into consideration all the\nvarieties of existing objects, all at least which have any degree of\naffinity with it. No one family of plants or animals could have been\nrationally constituted, except as part of a systematic arrangement of\nall plants or animals; nor could such a general arrangement have been\nproperly made, without first determining the exact place of plants and\nanimals in a general division of nature.\n\n\n\u00a7 2. There is no property of objects which may not be taken, if we\nplease, as the foundation for a classification or mental grouping of\nthose objects; and in our first attempts we are likely to select for\nthat purpose properties which are simple, easily conceived, and\nperceptible on a first view, without any previous process of thought.\nThus Tournefort's arrangement of plants was founded on the shape and\ndivisions of the corolla; and that which is commonly called the Linn\u00e6an\n(though Linn\u00e6us also suggested another and more scientific arrangement)\nwas grounded chiefly on the number of the stamens and pistils.\n\nBut these classifications, which are at first recommended by the\nfacility they afford of ascertaining to what class any individual\nbelongs, are seldom much adapted to the ends of that Classification\nwhich is the subject of our present remarks. The Linn\u00e6an arrangement\nanswers the purpose of making us think together of all those kinds of\nplants which possess the same number of stamens and pistils; but to\nthink of them in that manner is of little use, since we seldom have\nanything to affirm in common of the plants which have a given number of\nstamens and pistils. If plants of the class Pentandria, order Monogynia,\nagreed in any other properties, the habit of thinking and speaking of\nthe plants under a common designation would conduce to our remembering\nthose common properties so far as they were ascertained, and would\ndispose us to be on the look-out for such of them as were not yet known.\nBut since this is not the case, the only purpose of thought which the\nLinn\u00e6an classification serves is that of causing us to remember, better\nthan we should otherwise have done, the exact number of stamens and\npistils of every species of plants. Now, as this property is of little\nimportance or interest, the remembering it with any particular accuracy\nis of no moment. And, inasmuch as, by habitually thinking of plants in\nthose groups, we are prevented from habitually thinking of them in\ngroups which have a greater number of properties in common, the effect\nof such a classification, when systematically adhered to, upon our\nhabits of thought, must be regarded as mischievous.\n\nThe ends of scientific classification are best answered, when the\nobjects are formed into groups respecting which a greater number of\ngeneral propositions can be made, and those propositions more important,\nthan could be made respecting any other groups into which the same\nthings could be distributed. The properties, therefore, according to\nwhich objects are classified, should, if possible, be those which are\ncauses of many other properties: or at any rate, which are sure marks of\nthem. Causes are preferable, both as being the surest and most direct of\nmarks, and as being themselves the properties on which it is of most use\nthat our attention should be strongly fixed. But the property which is\nthe cause of the chief peculiarities of a class, is unfortunately seldom\nfitted to serve also as the diagnostic of the class. Instead of the\ncause, we must generally select some of its more prominent effects,\nwhich may serve as marks of the other effects and of the cause.\n\nA classification thus formed is properly scientific or philosophical,\nand is commonly called a Natural, in contradistinction to a Technical\nor Artificial, classification or arrangement. The phrase Natural\nClassification seems most peculiarly appropriate to such arrangements as\ncorrespond, in the groups which they form, to the spontaneous tendencies\nof the mind, by placing together the objects most similar in their\ngeneral aspect: in opposition to those technical systems which,\narranging things according to their agreement in some circumstance\narbitrarily selected, often throw into the same group objects which in\nthe general aggregate of their properties present no resemblance, and\ninto different and remote groups, others which have the closest\nsimilarity. It is one of the most valid recommendations of any\nclassification to the character of a scientific one, that it shall be a\nnatural classification in this sense also; for the test of its\nscientific character is the number and importance of the properties\nwhich can be asserted in common of all objects included in a group; and\nproperties on which the general aspect of the things depends, are, if\nonly on that ground, important, as well as, in most cases, numerous.\nBut, though a strong recommendation, this circumstance is not a _sine\nqu\u00e2 non_; since the most obvious properties of things may be of trifling\nimportance compared with others that are not obvious. I have seen it\nmentioned as a great absurdity in the Linn\u00e6an classification, that it\nplaces (which by the way it does not) the violet by the side of the oak:\nit certainly dissevers natural affinities, and brings together things\nquite as unlike as the oak and the violet are. But the difference,\napparently so wide, which renders the juxtaposition of those two\nvegetables so suitable an illustration of a bad arrangement, depends, to\nthe common eye, mainly on mere size and texture; now if we made it our\nstudy to adopt the classification which would involve the least peril of\nsimilar _rapprochements_, we should return to the obsolete division into\ntrees, shrubs, and herbs, which though of primary importance with regard\nto more general aspect, yet (compared even with so petty and unobvious a\ndistinction as that into dicotyledons and monocotyledons) answers to so\nfew differences in the other properties of plants, that a classification\nfounded on it (independently of the indistinctness of the lines of\ndemarcation) would be as completely artificial and technical as the\nLinn\u00e6an.\n\nOur natural groups, therefore, must often be founded not on the obvious,\nbut on the unobvious properties of things, when these are of greater\nimportance. But in such cases it is essential that there should be some\nother property or set of properties, more readily recognisable by the\nobserver, which coexist with, and may be received as marks of, the\nproperties which are the real groundwork of the classification. A\nnatural arrangement, for example, of animals, must be founded in the\nmain on their internal structure, but (as has been justly remarked) it\nwould be absurd that we should not be able to determine the genus and\nspecies of an animal without first killing it. On this ground, the\npreference, among zoological classifications, is probably due to that of\nM. de Blainville, founded on the differences in the external\ninteguments; differences which correspond, much more accurately than\nmight be supposed, to the really important varieties, both in the other\nparts of the structure, and in the habits and history of the animals.\n\nThis shows, more strongly than ever, how extensive a knowledge of the\nproperties of objects is necessary for making a good classification of\nthem. And as it is one of the uses of such a classification that by\ndrawing attention to the properties on which it is founded, and which if\nthe classification be good are marks of many others, it facilitates the\ndiscovery of those others; we see in what manner our knowledge of\nthings, and our classification of them, tend mutually and indefinitely\nto the improvement of each other.\n\nWe said just now that the classification of objects should follow those\nof their properties which indicate not only the most numerous, but also\nthe most important peculiarities. What is here meant by importance? It\nhas reference to the particular end in view; and the same objects,\ntherefore, may admit with propriety of several different\nclassifications. Each science or art forms its classification of things\naccording to the properties which fall within its special cognizance, or\nof which it must take account in order to accomplish its peculiar\npractical end. A farmer does not divide plants, like a botanist, into\ndicotyledonous and monocotyledonous, but into useful plants and weeds. A\ngeologist divides fossils, not like a zoologist, into families\ncorresponding to those of living species, but into fossils of the\nsecondary and of the tertiary periods, above the coal and below the\ncoal, &c. Whales are or are not fish, according to the purpose for which\nwe are considering them. \"If we are speaking of the internal structure\nand physiology of the animal, we must not call them fish; for in these\nrespects they deviate widely from fishes: they have warm blood, and\nproduce and suckle their young as land quadrupeds do. But this would not\nprevent our speaking of the _whale fishery_, and calling such animals\n_fish_ on all occasions connected with this employment; for the\nrelations thus rising depend upon the animal's living in the water, and\nbeing caught in a manner similar to other fishes. A plea that human laws\nwhich mention fish do not apply to whales, would be rejected at once by\nan intelligent judge.\"[19]\n\nThese different classifications are all good, for the purposes of their\nown particular departments of knowledge or practice. But when we are\nstudying objects not for any special practical end, but for the sake of\nextending our knowledge of the whole of their properties and relations,\nwe must consider as the most important attributes, those which\ncontribute most, either by themselves or by their effects, to render the\nthings like one another, and unlike other things; which give to the\nclass composed of them the most marked individuality; which fill, as it\nwere, the largest space in their existence, and would most impress the\nattention of a spectator who knew all their properties but was not\nspecially interested in any. Classes formed on this principle may be\ncalled, in a more emphatic manner than any others, natural groups.\n\n\n\u00a7 3. On the subject of these groups Dr. Whewell lays down a theory,\ngrounded on an important truth, which he has, in some respects,\nexpressed and illustrated very felicitously; but also, as it appears to\nme, with some admixture of error. It will be advantageous, for both\nthese reasons, to extract the statement of his doctrine in the very\nwords he has used.\n\n\"Natural groups,\" according to this theory,[20] are \"given by Type, not\nby Definition.\" And this consideration accounts for that \"indefiniteness\nand indecision which we frequently find in the descriptions of such\ngroups, and which must appear so strange and inconsistent to any one who\ndoes not suppose these descriptions to assume any deeper ground of\nconnexion than an arbitrary choice of the botanist. Thus in the family\nof the rose-tree, we are told that the _ovules_ are _very rarely_ erect,\nthe _stigmata usually_ simple. Of what use, it might be asked, can such\nloose accounts be? To which the answer is, that they are not inserted in\norder to distinguish the species, but in order to describe the family,\nand the total relations of the ovules and the stigmata of the family are\nbetter known by this general statement. A similar observation may be\nmade with regard to the Anomalies of each group, which occur so\ncommonly, that Mr. Lindley, in his _Introduction to the Natural System\nof Botany_, makes the 'Anomalies' an article in each family. Thus, part\nof the character of the Rosace\u00e6 is, that they have alternate _stipulate_\nleaves, and that the _albumen_ is _obliterated_; but yet in _Lowea_, one\nof the genera of this family, the stipul\u00e6 are _absent_; and the albumen\nis _present_ in another, _Neillia_. This implies, as we have already\nseen, that the artificial character (or _diagnosis_, as Mr. Lindley\ncalls it,) is imperfect. It is, though very nearly, yet not exactly,\ncommensurate with the natural group: and hence in certain cases this\ncharacter is made to yield to the general weight of natural affinities.\n\n\"These views,--of classes determined by characters which cannot be\nexpressed in words,--of propositions which state, not what happens in\nall cases, but only usually,--of particulars which are included in a\nclass, though they transgress the definition of it, may probably\nsurprise the reader. They are so contrary to many of the received\nopinions respecting the use of definitions, and the nature of scientific\npropositions, that they will probably appear to many persons highly\nillogical and unphilosophical. But a disposition to such a judgment\narises in a great measure from this, that the mathematical and\nmathematico-physical sciences have, in a great degree, determined men's\nviews of the general nature and form of scientific truth; while Natural\nHistory has not yet had time or opportunity to exert its due influence\nupon the current habits of philosophizing. The apparent indefiniteness\nand inconsistency of the classifications and definitions of Natural\nHistory belongs, in a far higher degree, to all other except\nmathematical speculations; and the modes in which approximations to\nexact distinctions and general truths have been made in Natural History,\nmay be worthy our attention, even for the light they throw upon the best\nmodes of pursuing truth of all kinds.\n\n\"Though in a Natural group of objects a definition can no longer be of\nany use as a regulative principle, classes are not therefore left quite\nloose, without any certain standard or guide. The class is steadily\nfixed, though not precisely limited; it is given, though not\ncircumscribed; it is determined, not by a boundary line without, but by\na central point within; not by what it strictly excludes, but by what it\neminently includes; by an example, not by a precept; in short, instead\nof a Definition we have a Type for our director.\n\n\"A Type is an example of any class, for instance a species of a genus,\nwhich is considered as eminently possessing the character of the class.\nAll the species which have a greater affinity with this type-species\nthan with any others, form the genus, and are arranged about it,\ndeviating from it in various directions and different degrees. Thus a\ngenus may consist of several species which approach very near the type,\nand of which the claim to a place with it is obvious; while there may be\nother species which straggle further from this central knot, and which\nyet are clearly more connected with it than with any other. And even if\nthere should be some species of which the place is dubious, and which\nappear to be equally bound to two generic types, it is easily seen that\nthis would not destroy the reality of the generic groups, any more than\nthe scattered trees of the intervening plain prevent our speaking\nintelligibly of the distinct forests of two separate hills.\n\n\"The type-species of every genus, the type-genus of every family, is,\nthen, one which possesses all the characters and properties of the genus\nin a marked and prominent manner. The type of the Rose family has\nalternate stipulate leaves, wants the albumen, has the ovules not erect,\nhas the stigmata simple, and besides these features, which distinguish\nit from the exceptions or varieties of its class, it has the features\nwhich make it prominent in its class. It is one of those which possess\nclearly several leading attributes; and thus, though we cannot say of\nany one genus that it _must_ be the type of the family, or of any one\nspecies that it _must_ be the type of the genus, we are still not wholly\nto seek; the type must be connected by many affinities with most of the\nothers of its group; it must be near the centre of the crowd, and not\none of the stragglers.\"\n\nIn this passage (the latter part of which especially I cannot help\nnoticing as an admirable example of philosophic style) Dr. Whewell has\nstated very clearly and forcibly, but (I think) without making all\nnecessary distinctions, one of the principles of a Natural\nClassification. What this principle is, what are its limits, and in what\nmanner he seems to me to have overstepped them, will appear when we have\nlaid down another rule of Natural Arrangement, which appears to me still\nmore fundamental.\n\n\n\u00a7 4. The reader is by this time familiar with the general truth (which I\nrestate so often on account of the great confusion in which it is\ncommonly involved), that there are in nature distinctions of Kind;\ndistinctions not consisting in a given number of definite properties,\n_plus_ the effects which follow from those properties, but running\nthrough the whole nature, through the attributes generally, of the\nthings so distinguished. Our knowledge of the properties of a Kind is\nnever complete. We are always discovering, and expecting to discover,\nnew ones. Where the distinction between two classes of things is not one\nof Kind, we expect to find their properties alike, except where there is\nsome reason for their being different. On the contrary, when the\ndistinction is in Kind, we expect to find the properties different\nunless there be some cause for their being the same. All knowledge of a\nKind must be obtained by observation and experiment upon the Kind\nitself; no inference respecting its properties from the properties of\nthings not connected with it by Kind, goes for more than the sort of\npresumption usually characterized as an analogy, and generally in one of\nits fainter degrees.\n\nSince the common properties of a true Kind, and consequently the general\nassertions which can be made respecting it, or which are certain to be\nmade hereafter as our knowledge extends, are indefinite and\ninexhaustible; and since the very first principle of natural\nclassification is that of forming the classes so that the objects\ncomposing each may have the greatest number of properties in common;\nthis principle prescribes that every such classification shall recognise\nand adopt into itself all distinctions of Kind, which exist among the\nobjects it professes to classify. To pass over any distinctions of Kind,\nand substitute definite distinctions, which, however considerable they\nmay be, do not point to ulterior unknown differences, would be to\nreplace classes with more by classes with fewer attributes in common;\nand would be subversive of the Natural Method of Classification.\n\nAccordingly all natural arrangements, whether the reality of the\ndistinction of Kinds was felt or not by their framers, have been led, by\nthe mere pursuit of their own proper end, to conform themselves to the\ndistinctions of Kind, so far as these had been ascertained at the time.\nThe Species of Plants are not only real Kinds, but are probably,[21]\nall of them, real lowest Kinds, Infim\u00e6 Species; which if we were to\nsubdivide, as of course it is open to us to do, into subclasses, the\nsubdivision would necessarily be founded on _definite_ distinctions, not\npointing (apart from what may be known of their causes or effects) to\nany difference beyond themselves.\n\nIn so far as a natural classification is grounded on real Kinds, its\ngroups are certainly not conventional; it is perfectly true that they do\nnot depend upon an arbitrary choice of the naturalist. But it does not\nfollow, nor, I conceive, is it true, that these classes are determined\nby a type, and not by characters. To determine them by a type would be\nas sure a way of missing the Kind, as if we were to select a set of\ncharacters arbitrarily. They are determined by characters, but these are\nnot arbitrary. The problem is, to find a few definite characters which\npoint to the multitude of indefinite ones. Kinds are Classes between\nwhich there is an impassable barrier; and what we have to seek is, marks\nwhereby we may determine on which side of the barrier an object takes\nits place. The characters which will best do this should be chosen: if\nthey are also important in themselves, so much the better. When we have\nselected the characters, we parcel out the objects according to those\ncharacters, and not, I conceive, according to resemblance to a type. We\ndo not compose the species Ranunculus acris, of all plants which bear a\nsatisfactory degree of resemblance to a model-buttercup, but of those\nwhich possess certain characters selected as marks by which we might\nrecognise the possibility of a common parentage; and the enumeration of\nthose characters is the definition of the species.\n\nThe question next arises, whether, as all Kinds must have a place among\nthe classes, so all the classes in a natural arrangement must be Kinds?\nAnd to this I answer, certainly not. The distinctions of Kinds are not\nnumerous enough to make up the whole of a classification. Very few of\nthe genera of plants, or even of the families, can be pronounced with\ncertainty to be Kinds. The great distinctions of Vascular and Cellular,\nDicotyledonous or Exogenous and Monocotyledonous or Endogenous plants,\nare perhaps differences of Kind; the lines of demarcation which divide\nthose classes seem (though even on this I would not pronounce\npositively) to go through the whole nature of the plants. But the\ndifferent species of a genus, or genera of a family, usually have in\ncommon only a limited number of characters. A Rose does not seem to\ndiffer from a Rubus, or the Umbellifer\u00e6 from the Ranunculace\u00e6, in much\nelse than the characters botanically assigned to those genera or those\nfamilies. Unenumerated differences certainly do exist in some cases;\nthere are families of plants which have peculiarities of chemical\ncomposition, or yield products having peculiar effects on the animal\neconomy. The Crucifer\u00e6 and Fungi contain an unusual proportion of\nnitrogen; the Labiat\u00e6 are the chief sources of essential oils, the\nSolane\u00e6 are very commonly narcotic, &c. In these and similar cases there\nare possibly distinctions of Kind; but it is by no means indispensable\nthat there should be. Genera and Families may be eminently natural,\nthough marked out from one another by properties limited in number;\nprovided those properties are important, and the objects contained in\neach genus or family resemble each other more than they resemble\nanything which is excluded from the genus or family.\n\nAfter the recognition and definition, then, of the _infim\u00e6 species_, the\nnext step is to arrange those _infim\u00e6 species_ into larger groups:\nmaking these groups correspond to Kinds wherever it is possible, but in\nmost cases without any such guidance. And in doing this it is true that\nwe are naturally and properly guided, in most cases at least, by\nresemblance to a type. We form our groups round certain selected Kinds,\neach of which serves as a sort of exemplar of its group. But though the\ngroups are suggested by types, I cannot think that a group when formed\nis _determined_ by the type; that in deciding whether a species belongs\nto the group, a reference is made to the type, and not to the\ncharacters; that the characters \"cannot be expressed in words.\" This\nassertion is inconsistent with Dr. Whewell's own statement of the\nfundamental principle of classification, namely, that \"general\nassertions shall be possible.\" If the class did not possess any\ncharacters in common, what general assertions would be possible\nrespecting it? Except that they all resemble each other more than they\nresemble anything else, nothing whatever could be predicated of the\nclass.\n\nThe truth is, on the contrary, that every genus or family is framed with\ndistinct reference to certain characters, and is composed, first and\nprincipally, of species which agree in possessing all those characters.\nTo these are added, as a sort of appendix, such other species, generally\nin small number, as possess _nearly_ all the properties selected;\nwanting some of them one property, some another, and which, while they\nagree with the rest _almost_ as much as these agree with one another, do\nnot resemble in an equal degree any other group. Our conception of the\nclass continues to be grounded on the characters; and the class might be\ndefined, those things which _either_ possess that set of characters,\n_or_ resemble the things that do so, more than they resemble anything\nelse.\n\nAnd this resemblance itself is not, like resemblance between simple\nsensations, an ultimate fact, unsusceptible of analysis. Even the\ninferior degree of resemblance is created by the possession of common\ncharacters. Whatever resembles the genus Rose more than it resembles any\nother genus, does so because it possesses a greater number of the\ncharacters of that genus, than of the characters of any other genus. Nor\ncan there be any real difficulty in representing, by an enumeration of\ncharacters, the nature and degree of the resemblance which is strictly\nsufficient to include any object in the class. There are always some\nproperties common to all things which are included. Others there often\nare, to which some things, which are nevertheless included, are\nexceptions. But the objects which are exceptions to one character are\nnot exceptions to another: the resemblance which fails in some\nparticulars must be made up for in others. The class, therefore, is\nconstituted by the possession of _all_ the characters which are\nuniversal, and _most_ of those which admit of exceptions. If a plant had\nthe ovules erect, the stigmata divided, possessed the albumen, and was\nwithout stipules, it possibly would not be classed among the Rosace\u00e6.\nBut it may want any one, or more than one of those characters, and not\nbe excluded. The ends of a scientific classification are better answered\nby including it. Since it agrees so nearly, in its known properties,\nwith the sum of the characters of the class, it is likely to resemble\nthat class more than any other in those of its properties which are\nstill undiscovered.\n\nNot only, therefore, are natural groups, no less than any artificial\nclasses, determined by characters; they are constituted in contemplation\nof, and by reason of, characters. But it is in contemplation not of\nthose characters only which are rigorously common to all the objects\nincluded in the group, but of the entire body of characters, all of\nwhich are found in most of those objects, and most of them in all. And\nhence our conception of the class, the image in our minds which is\nrepresentative of it, is that of a specimen complete in all the\ncharacters; most naturally a specimen which, by possessing them all in\nthe greatest degree in which they are ever found, is the best fitted to\nexhibit clearly, and in a marked manner, what they are. It is by a\nmental reference to this standard, not instead of, but in illustration\nof, the definition of the class, that we usually and advantageously\ndetermine whether any individual or species belongs to the class or not.\nAnd this, as it seems to me, is the amount of truth contained in the\ndoctrine of Types.\n\nWe shall see presently that where the classification is made for the\nexpress purpose of a special inductive inquiry, it is not optional, but\nnecessary for fulfilling the conditions of a correct Inductive Method,\nthat we should establish a type-species or genus, namely, the one which\nexhibits in the most eminent degree the particular phenomenon under\ninvestigation. But of this hereafter. It remains, for completing the\ntheory of natural groups, that a few words should be said on the\nprinciples of the nomenclature adapted to them.\n\n\n\u00a7 5. A Nomenclature in science, is, as we have said, a system of the\nnames of Kinds. These names, like other class-names, are defined by the\nenumeration of the characters distinctive of the class. The only merit\nwhich a set of names can have beyond this, is to convey, by the mode of\ntheir construction, as much information as possible: so that a person\nwho knows the thing, may receive all the assistance which the name can\ngive in remembering what he knows, while he who knows it not, may\nreceive as much knowledge respecting it as the case admits of, by merely\nbeing told its name.\n\nThere are two modes of giving to the name of a Kind this sort of\nsignificance. The best, but which unfortunately is seldom practicable,\nis when the word can be made to indicate, by its formation, the very\nproperties which it is designed to connote. The name of a Kind does not,\nof course, connote all the properties of the Kind, since these are\ninexhaustible, but such of them as are sufficient to distinguish it;\nsuch as are sure marks of all the rest. Now, it is very rarely that one\nproperty, or even any two or three properties, can answer this purpose.\nTo distinguish the common daisy from all other species of plants would\nrequire the specification of many characters. And a name cannot, without\nbeing too cumbrous for use, give indication, by its etymology or mode of\nconstruction, of more than a very small number of these. The\npossibility, therefore, of an ideally perfect Nomenclature, is probably\nconfined to the one case in which we are happily in possession of\nsomething nearly approaching to it; the Nomenclature of elementary\nChemistry. The substances, whether simple or compound, with which\nchemistry is conversant, are Kinds, and, as such, the properties which\ndistinguish each of them from the rest are innumerable; but in the case\nof compound substances (the simple ones are not numerous enough to\nrequire a systematic nomenclature), there is one property, the chemical\ncomposition, which is of itself sufficient to distinguish the Kind; and\nis (with certain reservations not yet thoroughly understood) a sure mark\nof all the other properties of the compound. All that was needful,\ntherefore, was to make the name of every compound express, on the first\nhearing, its chemical composition; that is, to form the name of the\ncompound, in some uniform manner, from the names of the simple\nsubstances which enter into it as elements. This was done, most\nskilfully and successfully, by the French chemists. The only thing left\nunexpressed by them was the exact proportion in which the elements were\ncombined; and even this, since the establishment of the atomic theory,\nit has been found possible to express by a simple adaptation of their\nphraseology.\n\nBut where the characters which must be taken into consideration in order\nsufficiently to designate the Kind, are too numerous to be all signified\nin the derivation of the name, and where no one of them is of such\npreponderant importance as to justify its being singled out to be so\nindicated, we may avail ourselves of a subsidiary resource. Though we\ncannot indicate the distinctive properties of the Kind, we may indicate\nits nearest natural affinities, by incorporating into its name the name\nof the proximate natural group of which it is one of the species. On\nthis principle is founded the admirable binary nomenclature of botany\nand zoology. In this nomenclature the name of every species consists of\nthe name of the genus, or natural group next above it, with a word added\nto distinguish the particular species. The last portion of the compound\nname is sometimes taken from some _one_ of the peculiarities in which\nthat species differs from others of the genus; as Clematis\n_integrifolia_, Potentilla _alba_, Viola _palustris_, Artemisia\n_vulgaris_; sometimes from a circumstance of an historical nature, as\nNarcissus _poeticus_, Potentilla _tormentilla_ (indicating that the\nplant was formerly known by the latter name), Exacum _Candollii_ (from\nthe fact that De Candolle was its first discoverer); and sometimes the\nword is purely conventional, as Thlaspi _bursa-pastoris_, Ranunculus\n_thora_; it is of little consequence which; since the second, or as it\nis usually called, the specific name, could at most express,\nindependently of convention, no more than a very small portion of the\nconnotation of the term. But by adding to this the name of the superior\ngenus, we may make the best amends we can for the impossibility of so\ncontriving the name as to express all the distinctive characters of the\nKind. We make it, at all events, express as many of those characters as\nare common to the proximate natural group in which the Kind is included.\nIf even those common characters are so numerous or so little familiar as\nto require a further extension of the same resource, we might, instead\nof a binary, adopt a ternary nomenclature, employing not only the name\nof the genus, but that of the next natural group in order of generality\nabove the genus, commonly called the Family. This was done in the\nmineralogical nomenclature proposed by Professor Mohs. \"The names framed\nby him were not composed of two, but of three elements, designating\nrespectively the Species, the Genus, and the Order; thus he has such\nspecies as _Rhombohedral Lime Haloide_, _Octohedral Fluor Haloide_,\n_Prismatic Hal Baryte_.\"[22] The binary construction, however, has been\nfound sufficient in botany and zoology, the only sciences in which this\ngeneral principle has hitherto been successfully adopted in the\nconstruction of a nomenclature.\n\nBesides the advantage which this principle of nomenclature possesses, in\ngiving to the names of species the greatest quantity of independent\nsignificance which the circumstances of the case admit of, it answers\nthe further end of immensely economizing the use of names, and\npreventing an otherwise intolerable burden on the memory. When the names\nof species become extremely numerous, some artifice (as Dr. Whewell[23]\nobserves) becomes absolutely necessary to make it possible to recollect\nor apply them. \"The known species of plants, for example, were ten\nthousand in the time of Linn\u00e6us, and are now probably sixty thousand. It\nwould be useless to endeavour to frame and employ separate names for\neach of these species. The division of the objects into a subordinated\nsystem of classification enables us to introduce a Nomenclature which\ndoes not require this enormous number of names. Each of the genera has\nits name, and the species are marked by the addition of some epithet to\nthe name of the genus. In this manner about seventeen hundred generic\nnames, with a moderate number of specific names, were found by Linn\u00e6us\nsufficient to designate with precision all the species of vegetables\nknown at his time.\" And though the number of generic names has since\ngreatly increased, it has not increased in anything like the proportion\nof the multiplication of known species.\n\n\n\n\nCHAPTER VIII.\n\nOF CLASSIFICATION BY SERIES.\n\n\n\u00a7 1. Thus far, we have considered the principles of scientific\nclassification so far only as relates to the formation of natural\ngroups; and at this point most of those who have attempted a theory of\nnatural arrangement, including, among the rest, Dr. Whewell, have\nstopped. There remains, however, another, and a not less important\nportion of the theory, which has not yet, as far as I am aware, been\nsystematically treated of by any writer except M. Comte. This is, the\narrangement of the natural groups into a natural series.[24]\n\nThe end of Classification, as an instrument for the investigation of\nnature, is (as before stated) to make us think of those objects\ntogether, which have the greatest number of important common properties;\nand which therefore we have oftenest occasion, in the course of our\ninductions, for taking into joint consideration. Our ideas of objects\nare thus brought into the order most conducive to the successful\nprosecution of inductive inquiries generally. But when the purpose is to\nfacilitate some particular inductive inquiry, more is required. To be\ninstrumental to that purpose, the classification must bring those\nobjects together, the simultaneous contemplation of which is likely to\nthrow most light upon the particular subject. That subject being the\nlaws of some phenomenon or some set of connected phenomena; the very\nphenomenon or set of phenomena in question must be chosen as the\ngroundwork of the classification.\n\nThe requisites of a classification intended to facilitate the study of a\nparticular phenomenon, are, first, to bring into one class all Kinds of\nthings which exhibit that phenomenon, in whatever variety of forms or\ndegrees; and secondly, to arrange those Kinds in a series according to\nthe degree in which they exhibit it, beginning with those which exhibit\nmost of it, and terminating with those which exhibit least. The\nprincipal example, as yet, of such a classification, is afforded by\ncomparative anatomy and physiology, from which, therefore, our\nillustrations shall be taken.\n\n\n\u00a7 2. The object being supposed to be, the investigation of the laws of\nanimal life; the first step, after forming the most distinct conception\nof the phenomenon itself, possible in the existing state of our\nknowledge, is to erect into one great class (that of animals) all the\nknown Kinds of beings where that phenomenon presents itself; in however\nvarious combinations with other properties, and in however different\ndegrees. As some of these Kinds manifest the general phenomenon of\nanimal life in a very high degree, and others in an insignificant\ndegree, barely sufficient for recognition; we must, in the next place,\narrange the various Kinds in a series, following one another according\nto the degrees in which they severally exhibit the phenomenon; beginning\ntherefore with man, and ending with the most imperfect kinds of\nzoophytes.\n\nThis is merely saying that we should put the instances, from which the\nlaw is to be inductively collected, into the order which is implied in\none of the four Methods of Experimental Inquiry discussed in the\npreceding Book; the fourth Method, that of Concomitant Variations. As\nformerly remarked, this is often the only method to which recourse can\nbe had, with assurance of a true conclusion, in cases in which we have\nbut limited means of effecting, by artificial experiments, a separation\nof circumstances usually conjoined. The principle of the method is, that\nfacts which increase or diminish together, and disappear together, are\neither cause and effect, or effects of a common cause. When it has been\nascertained that this relation really subsists between the variations, a\nconnexion between the facts themselves may be confidently laid down,\neither as a law of nature or only as an empirical law, according to\ncircumstances.\n\nThat the application of this Method must be preceded by the formation of\nsuch a series as we have described, is too obvious to need being pointed\nout; and the mere arrangement of a set of objects in a series, according\nto the degrees in which they exhibit some fact of which we are seeking\nthe law, is too naturally suggested by the necessities of our inductive\noperations, to require any lengthened illustration here. But there are\ncases in which the arrangement required for the special purpose, becomes\nthe determining principle of the classification of the same objects for\ngeneral purposes. This will naturally and properly happen, when those\nlaws of the objects which are sought in the special inquiry enact so\nprincipal a part in the general character and history of those\nobjects--exercise so much influence in determining all the phenomena of\nwhich they are either the agents or the theatre--that all other\ndifferences existing among the objects are fittingly regarded as mere\nmodifications of the one phenomenon sought; effects determined by the\nco-operation of some incidental circumstance with the laws of that\nphenomenon. Thus in the case of animated beings, the differences between\none class of animals and another may reasonably be considered as mere\nmodifications of the general phenomenon, animal life; modifications\narising either from the different degrees in which that phenomenon is\nmanifested in different animals, or from the intermixture of the effects\nof incidental causes peculiar to the nature of each, with the effects\nproduced by the general laws of life; those laws still exercising a\npredominant influence over the result. Such being the case, no other\ninductive inquiry respecting animals can be successfully carried on,\nexcept in subordination to the great inquiry into the universal laws of\nanimal life. And the classification of animals best suited to that one\npurpose, is the most suitable to all the other purposes of zoological\nscience.\n\n\n\u00a7 3. To establish a classification of this sort, or even to apprehend it\nwhen established, requires the power of recognising the essential\nsimilarity of a phenomenon, in its minuter degrees and obscurer forms,\nwith what is called the _same_ phenomenon in the greatest perfection of\nits development; that is, of identifying with each other all phenomena\nwhich differ only in degree, and in properties which we suppose to be\ncaused by difference of degree. In order to recognise this identity, or\nin other words, this exact similarity of quality, the assumption of a\ntype-species is indispensable. We must consider as the type of the\nclass, that among the Kinds included in it, which exhibits the\nproperties constitutive of the class, in the highest degree; conceiving\nthe other varieties as instances of degeneracy, as it were, from that\ntype; deviations from it by inferior intensity of the characteristic\nproperty or properties. For every phenomenon is best studied (_c\u00e6teris\nparibus_) where it exists in the greatest intensity. It is there that\nthe effects which either depend on it, or depend on the same causes with\nit, will also exist in the greatest degree. It is there, consequently,\nand only there, that those effects of it, or joint effects with it, can\nbecome fully known to us, so that we may learn to recognise their\nsmaller degrees, or even their mere rudiments, in cases in which the\ndirect study would have been difficult or even impossible. Not to\nmention that the phenomenon in its higher degrees may be attended by\neffects or collateral circumstances which in its smaller degrees do not\noccur at all, requiring for their production in any sensible amount a\ngreater degree of intensity of the cause than is there met with. In man,\nfor example, (the species in which both the phenomenon of animal and\nthat of organic life exist in the highest degree,) many subordinate\nphenomena develop themselves in the course of his animated existence,\nwhich the inferior varieties of animals do not show. The knowledge of\nthese properties may nevertheless be of great avail towards the\ndiscovery of the conditions and laws of the general phenomenon of life,\nwhich is common to man with those inferior animals. And they are, even,\nrightly considered as properties of animated nature itself; because they\nmay evidently be affiliated to the general laws of animated nature;\nbecause we may fairly presume that some rudiments or feeble degrees of\nthose properties would be recognised in all animals by more perfect\norgans, or even by more perfect instruments, than ours; and because\nthose may be correctly termed properties of a class, which a thing\nexhibits exactly in proportion as it belongs to the class, that is, in\nproportion as it possesses the main attributes constitutive of the\nclass.\n\n\n\u00a7 4. It remains to consider how the internal distribution of the series\nmay most properly take place: in what manner it should be divided into\nOrders, Families, and Genera.\n\nThe main principle of division must of course be natural affinity; the\nclasses formed must be natural groups: and the formation of these has\nalready been sufficiently treated of. But the principles of natural\ngrouping must be applied in subordination to the principle of a natural\nseries. The groups must not be so constituted as to place in the same\ngroup things which ought to occupy different points of the general\nscale. The precaution necessary to be observed for this purpose is, that\nthe _primary_ divisions must be grounded not on all distinctions\nindiscriminately, but on those which correspond to variations in the\ndegree of the main phenomenon. The series of Animated Nature should be\nbroken into parts at the points where the variation in the degree of\nintensity of the main phenomenon (as marked by its principal characters,\nSensation, Thought, Voluntary Motion, &c.) begins to be attended by\nconspicuous changes in the miscellaneous properties of the animal. Such\nwell-marked changes take place, for example, where the class Mammalia\nends; at the points where Fishes are separated from Insects, Insects\nfrom Mollusca, &c. When so formed, the primary natural groups will\ncompose the series by mere juxtaposition, without redistribution; each\nof them corresponding to a definite portion of the scale. In like manner\neach family should, if possible, be so subdivided, that one portion of\nit shall stand higher and the other lower, though of course contiguous,\nin the general scale; and only when this is impossible is it allowable\nto ground the remaining subdivisions on characters having no\ndeterminable connexion with the main phenomenon.\n\nWhere the principal phenomenon so far transcends in importance all other\nproperties on which a classification could be grounded, as it does in\nthe case of animated existence, any considerable deviation from the rule\nlast laid down is in general sufficiently guarded against by the first\nprinciple of a natural arrangement, that of forming the groups according\nto the most important characters. All attempts at a scientific\nclassification of animals, since first their anatomy and physiology were\nsuccessfully studied, have been framed with a certain degree of\ninstinctive reference to a natural series, and have accorded in many\nmore points than they have differed, with the classification which would\nmost naturally have been grounded on such a series. But the accordance\nhas not always been complete; and it still is often a matter of\ndiscussion, which of several classifications best accords with the true\nscale of intensity of the main phenomenon. Cuvier, for example, has been\njustly criticized for having formed his natural groups with an undue\ndegree of reference to the mode of alimentation, a circumstance directly\nconnected only with organic life, and not lending to the arrangement\nmost appropriate for the purposes of an investigation of the laws of\nanimal life, since both carnivorous and herbivorous or frugivorous\nanimals are found at almost every degree in the scale of animal\nperfection. Blainville's classification has been considered by high\nauthorities to be free from this defect; as representing correctly, by\nthe mere order of the principal groups, the successive degeneracy of\nanimal nature from its highest to its most imperfect exemplification.\n\n\n\u00a7 5. A classification of any large portion of the field of nature in\nconformity to the foregoing principles, has hitherto been found\npracticable only in one great instance, that of animals. In the case\neven of vegetables, the natural arrangement has not been carried beyond\nthe formation of natural groups. Naturalists have found, and probably\nwill continue to find it impossible to form those groups into any\nseries, the terms of which correspond to real gradations in the\nphenomenon of vegetative or organic life. Such a difference of degree\nmay be traced between the class of Vascular Plants and that of Cellular,\nwhich includes lichens, alg\u00e6, and other substances whose organization is\nsimpler and more rudimentary than that of the higher order of\nvegetables, and which therefore approach nearer to mere inorganic\nnature. But when we rise much above this point, we do not find any\nsufficient difference in the degree in which different plants possess\nthe properties of organization and life. The dicotyledons are of more\ncomplex structure, and somewhat more perfect organization, than the\nmonocotyledons: and some dicotyledonous families, such as the Composit\u00e6,\nare rather more complex in their organization than the rest. But the\ndifferences are not of a marked character, and do not promise to throw\nany particular light upon the conditions and laws of vegetable life and\ndevelopment. If they did, the classification of vegetables would have to\nbe made, like that of animals, with reference to the scale or series\nindicated.\n\nAlthough the scientific arrangements of organic nature afford as yet the\nonly complete example of the true principles of rational classification,\nwhether as to the formation of groups or of series, those principles are\napplicable to all cases in which mankind are called upon to bring the\nvarious parts of any extensive subject into mental co-ordination. They\nare as much to the point when objects are to be classed for purposes of\nart or business, as for those of science. The proper arrangement, for\nexample, of a code of laws, depends on the same scientific conditions as\nthe classifications in natural history; nor could there be a better\npreparatory discipline for that important function, than the study of\nthe principles of a natural arrangement, not only in the abstract, but\nin their actual application to the class of phenomena for which they\nwere first elaborated, and which are still the best school for learning\ntheir use. Of this the great authority on codification, Bentham, was\nperfectly aware: and his early _Fragment on Government_, the admirable\nintroduction to a series of writings unequalled in their department,\ncontains clear and just views (as far as they go) on the meaning of a\nnatural arrangement, such as could scarcely have occurred to any one who\nlived anterior to the age of Linn\u00e6us and Bernard de Jussieu.\n\nFOOTNOTES:\n\n[1] Supra, book iii. ch. ii. \u00a7 3, 4, 5.\n\n[2] Mr. Bailey has given by far the best statement of this theory. \"The\ngeneral name,\" he says, \"raises up the image sometimes of one individual\nof the class formerly seen, sometimes of another, not unfrequently of\nmany individuals in succession; and it sometimes suggests an image made\nup of elements from several different objects, by a latent process of\nwhich I am not conscious.\" (Letters on the Philosophy of the Human Mind,\n1st series, letter 22.) But Mr. Bailey must allow that we carry on\ninductions and ratiocinations respecting the class, by means of this\nidea or conception of some one individual in it. This is all I require.\nThe name of a class calls up some idea, through which we can, to all\nintents and purposes, think of the class as such, and not solely of an\nindividual member of it.\n\n[3] I have entered rather fully into this question in chap. xvii. of _An\nExamination of Sir William Hamilton's Philosophy_, headed \"The Doctrine\nof Concepts or General Notions,\" which contains my last views on the\nsubject.\n\n[4] Other examples of inappropriate conceptions are given by Dr. Whewell\n(_Phil. Ind. Sc._ ii. 185) as follows:--\"Aristotle and his followers\nendeavoured in vain to account for the mechanical relation of forces in\nthe lever, by applying the _inappropriate_ geometrical conceptions of\nthe properties of the circle: they failed in explaining the _form_ of\nthe luminous spot made by the sun shining through a hole, because they\napplied the _inappropriate_ conception of a circular _quality_ in the\nsun's light: they speculated to no purpose about the elementary\ncomposition of bodies, because they assumed the _inappropriate_\nconception of _likeness_ between the elements and the compound, instead\nof the genuine notion of elements merely _determining_ the qualities of\nthe compound.\" But in these cases there is more than an inappropriate\nconception; there is a false conception; one which has no prototype in\nnature, nothing corresponding to it in facts. This is evident in the\nlast two examples, and is equally true in the first; the \"properties of\nthe circle\" which were referred to, being purely fantastical. There is,\ntherefore, an error beyond the wrong choice of a principle of\ngeneralization; there is a false assumption of matters of fact. The\nattempt is made to resolve certain laws of nature into a more general\nlaw, that law not being one which, though real, is inappropriate, but\none wholly imaginary.\n\n[5] Professor Bain.\n\n[6] This sentence having been erroneously understood as if I had meant\nto assert that belief is nothing but an irresistible association, I\nthink it necessary to observe that I express no theory respecting the\nultimate analysis either of reasoning or of belief, two of the most\nobscure points in analytical psychology. I am speaking not of the powers\nthemselves, but of the previous conditions necessary to enable those\npowers to exert themselves: of which conditions I am contending that\nlanguage is not one, senses and association being sufficient without it.\n\n[7] Mr. Bailey agrees with me in thinking that whenever \"from something\nactually present to my senses conjoined with past experience, I feel\nsatisfied that something has happened, or will happen, or is happening,\nbeyond the sphere of my personal observation,\" I may with strict\npropriety be said to reason: and of course to reason inductively, for\ndemonstrative reasoning is excluded by the circumstances of the case.\n(_The Theory of Reasoning_, 2nd ed. p. 27.)\n\n[8] _Novum Organum Renovatum_, pp. 35-37.\n\n[9] _Nov. Org. Renov._, pp. 39, 40.\n\n[10] P. 217, 4to edition.\n\n[11] \"E, ex, extra, extraneus, \u00e9tranger, stranger.\"\n\nAnother etymological example sometimes cited is the derivation of the\nEnglish _uncle_ from the Latin _avus_. It is scarcely possible for two\nwords to bear fewer outward marks of relationship, yet there is but one\nstep between them; _avus_, _avunculus_, _uncle_.\n\nSo _pilgrim_, from _ager_: _per agrum_, _peragrinus_, _peregrinus_,\n_pellegrino_, _pilgrim_.\n\n[12] P. 226-7.\n\n[13] _Essays_, p. 214.\n\n[14] Ibid. 215.\n\n[15] Such cases give a clear insight into the process of the\ndegeneration of languages in periods of history when literary culture\nwas suspended; and we are now in danger of experiencing a similar evil\nthrough the superficial extension of the same culture. So many persons\nwithout anything deserving the name of education have become writers by\nprofession, that written language may almost be said to be principally\nwielded by persons ignorant of the proper use of the instrument, and who\nare spoiling it more and more for those who understand it. Vulgarisms,\nwhich creep in nobody knows how, are daily depriving the English\nlanguage of valuable modes of expressing thought. To take a present\ninstance: the verb _transpire_ formerly conveyed very expressively its\ncorrect meaning, viz. to _become known_ through unnoticed channels--to\nexhale, as it were, into publicity through invisible pores, like a\nvapour or gas disengaging itself. But of late a practice has commenced\nof employing this word, for the sake of finery, as a mere synonym of _to\nhappen_: \"the events which have _transpired_ in the Crimea,\" meaning the\nincidents of the war. This vile specimen of bad English is already seen\nin the despatches of noblemen and viceroys: and the time is apparently\nnot far distant when nobody will understand the word if used in its\nproper sense. It is a great error to think that these corruptions of\nlanguage do no harm. Those who are struggling with the difficulty (and\nwho know by experience how great it already is) of expressing oneself\nclearly with precision, find their resources continually narrowed by\nilliterate writers, who seize and twist from its purpose some form of\nspeech which once served to convey briefly and compactly an unambiguous\nmeaning. It would hardly be believed how often a writer is compelled to\na circumlocution by the single vulgarism, introduced during the last few\nyears, of using the word _alone_ as an adverb, _only_ not being fine\nenough for the rhetoric of ambitious ignorance. A man will say \"to which\nI am not alone bound by honour but also by law,\" unaware that what he\nhas unintentionally said is, that he is _not alone_ bound, some other\nperson being bound with him. Formerly if any one said, \"I am not alone\nresponsible for this,\" he was understood to mean, (what alone his words\nmean in correct English,) that he is not the sole person responsible;\nbut if he now used such an expression, the reader would be confused\nbetween that and two other meanings; that he is not _only responsible_\nbut something more; or that he is responsible _not only for this_ but\nfor something besides. The time is coming when Tennyson's [OE]none could\nnot say \"I will not die alone,\" lest she should be supposed to mean that\nshe would not only die but do something else.\n\nThe blunder of writing _predicate_ for _predict_ has become so widely\ndiffused that it bids fair to render one of the most useful terms in the\nscientific vocabulary of Logic unintelligible. The mathematical and\nlogical term \"to eliminate\" is undergoing a similar destruction. All who\nare acquainted either with the proper use of the word or with its\netymology, know that to eliminate a thing is to thrust it out; but those\nwho know nothing about it, except that it is a fine-looking phrase, use\nit in a sense precisely the reverse, to denote, not turning anything\nout, but bringing it in. They talk of _eliminating_ some truth, or other\nuseful result, from a mass of details. I suspect that this error must at\nfirst have arisen from some confusion between _to eliminate_ and _to\nenucleate_.\n\nThough no such evil consequences as take place in these instances, are\nlikely to arise from the modern freak of writing _sanatory_ instead of\nsanitary, it deserves notice as a charming specimen of pedantry\nengrafted upon ignorance. Those who thus undertake to correct the\nspelling of the classical English writers, are not aware that the\nmeaning of _sanatory_, if there were such a word in the language, would\nhave reference not to the preservation of health, but to the cure of\ndisease.\n\n[16] _Historical Introduction_, vol. i. pp. 66-8.\n\n[17] _History of Scientific Ideas_, ii. 110, 111.\n\n[18] _Hist. Sc. Id._ ii. 111-113.\n\n[19] _Nov. Org. Renov._ pp. 286, 287.\n\n[20] _Hist. Sc. Id._ ii. 120-122.\n\n[21] I say probably, not certainly, because this is not the\nconsideration by which a botanist determines what shall or shall not be\nadmitted as a species. In natural history those objects belong to the\nsame species, which are, or consistently with experience might have\nbeen, produced from the same stock. But this distinction, in most, and\nprobably in all cases, happily accords with the other. It seems to be a\nlaw of physiology, that animals and plants do really, in the\nphilosophical as well as the popular sense, propagate their kind;\ntransmitting to their descendants all the distinctions of Kind (down to\nthe most special or lowest Kind) which they themselves possess.\n\n[22] _Nov. Org. Renov._ p. 274.\n\n[23] _Hist. Sc. Id._ i. 133.\n\n[24] Dr. Whewell, in his reply (_Philosophy of Discovery_, p. 270) says\nthat he \"stopped short of, or rather passed by, the doctrine of a series\nof organized beings,\" because he \"thought it bad and narrow philosophy.\"\nIf he did, it was evidently without understanding this form of the\ndoctrine; for he proceeds to quote a passage from his \"History,\" in\nwhich the doctrine he condemns is designated as that of \"a mere linear\nprogression in nature, which would place each genus in contact only with\nthe preceding and succeeding ones.\" Now the series treated of in the\ntext agrees with this linear progression in nothing whatever but in\nbeing a progression.\n\nIt would surely be possible to arrange all _places_ (for example) in the\norder of their distance from the North Pole, though there would be not\nmerely a plurality, but a whole circle of places at every single\ngradation in the scale.\n\n\n\n\nBOOK V.\n\nON FALLACIES.\n\n\n\"Errare non modo affirmando et negando, sed etiam sentiendo, et in\ntacit\u00e2 hominum cogitatione contingit.\"--HOBBES, _Computatio sive\nLogica_, ch. v.\n\n\"Il leur semble qu'il n'y a qu'\u00e0 douter par fantaisie, et qu'il n'y a\nqu'\u00e0 dire en g\u00e9n\u00e9ral que notre nature est infirme; que notre esprit est\nplein d'aveuglement; qu'il faut avoir un grand soin de se d\u00e9faire de ses\npr\u00e9jug\u00e9s, et autres choses semblables. Ils pensent que cela suffit pour\nne plus se laisser s\u00e9duire \u00e0 ses sens, et pour ne plus se tromper du\ntout. Il ne suffit pas de dire que l'esprit est foible, il faut lui\nfaire sentir ses foiblesses. Ce n'est pas assez de dire qu'il est sujet\n\u00e0 l'erreur, il faut lui d\u00e9couvrir en quoi consistent ses\nerreurs.\"--MALEBRANCHE, _Recherche de la V\u00e9rit\u00e9_.\n\n\n\n\nCHAPTER I.\n\nOF FALLACIES IN GENERAL.\n\n\n\u00a7 1. It is a maxim of the schoolmen, that \"contrariorum eadem est\nscientia:\" we never really know what a thing is, unless we are also able\nto give a sufficient account of its opposite. Conformably to this maxim,\none considerable section, in most treatises on Logic, is devoted to the\nsubject of Fallacies; and the practice is too well worthy of observance,\nto allow of our departing from it. The philosophy of reasoning, to be\ncomplete, ought to comprise the theory of bad as well as of good\nreasoning.\n\nWe have endeavoured to ascertain the principles by which the sufficiency\nof any proof can be tested, and by which the nature and amount of\nevidence needful to prove any given conclusion can be determined\nbeforehand. If these principles were adhered to, then although the\nnumber and value of the truths ascertained would be limited by the\nopportunities, or by the industry, ingenuity, and patience, of the\nindividual inquirer, at least error would not be embraced instead of\ntruth. But the general consent of mankind, founded on their experience,\nvouches for their being far indeed from even this negative kind of\nperfection in the employment of their reasoning powers.\n\nIn the conduct of life--in the practical business of mankind--wrong\ninferences, incorrect interpretations of experience, unless after much\nculture of the thinking faculty, are absolutely inevitable: and with\nmost people, after the highest degree of culture they ever attain, such\nerroneous inferences, producing corresponding errors in conduct, are\nlamentably frequent. Even in the speculations to which eminent\nintellects have systematically devoted themselves, and in reference to\nwhich the collective mind of the scientific world is always at hand to\naid the efforts and correct the aberrations of individuals, it is only\nfrom the more perfect sciences, from those of which the subject-matter\nis the least complicated, that opinions not resting on a correct\ninduction have at length, generally speaking, been expelled. In the\ndepartments of inquiry relating to the more complex phenomena of nature,\nand especially those of which the subject is man, whether as a moral and\nintellectual, a social, or even as a physical being; the diversity of\nopinions still prevalent among instructed persons, and the equal\nconfidence with which those of the most contrary ways of thinking cling\nto their respective tenets, are proof not only that right modes of\nphilosophizing are not yet generally adopted on those subjects, but that\nwrong ones are: that inquirers have not only in general missed the\ntruth, but have often embraced error; that even the most cultivated\nportion of our species have not yet learned to abstain from drawing\nconclusions which the evidence does not warrant.\n\nThe only complete safeguard against reasoning ill, is the habit of\nreasoning well; familiarity with the principles of correct reasoning,\nand practice in applying those principles. It is, however, not\nunimportant to consider what are the most common modes of bad reasoning;\nby what appearances the mind is most likely to be seduced from the\nobservance of true principles of induction; what, in short, are the most\ncommon and most dangerous varieties of Apparent Evidence, whereby\npersons are misled into opinions for which there does not exist evidence\nreally conclusive.\n\nA catalogue of the varieties of apparent evidence which are not real\nevidence, is an enumeration of Fallacies. Without such an enumeration,\ntherefore, the present work would be wanting in an essential point. And\nwhile writers who included in their theory of reasoning nothing more\nthan ratiocination, have, in consistency with this limitation, confined\ntheir remarks to the fallacies which have their seat in that portion of\nthe process of investigation; we, who profess to treat of the whole\nprocess, must add to our directions for performing it rightly, warnings\nagainst performing it wrongly in any of its parts: whether the\nratiocinative or the experimental portion of it be in fault, or the\nfault lie in dispensing with ratiocination and induction altogether.\n\n\n\u00a7 2. In considering the sources of unfounded inference, it is\nunnecessary to reckon the errors which arise, not from a wrong method,\nnor even from ignorance of the right one, but from a casual lapse,\nthrough hurry or inattention, in the application of the true principles\nof induction. Such errors, like the accidental mistakes in casting up a\nsum, do not call for philosophical analysis or classification;\ntheoretical considerations can throw no light upon the means of avoiding\nthem. In the present treatise our attention is required, not to mere\ninexpertness in performing the operation in the right way, (the only\nremedies for which are increased attention and more sedulous practice,)\nbut to the modes of performing it in a way fundamentally wrong; the\nconditions under which the human mind persuades itself that it has\nsufficient grounds for a conclusion which it has not arrived at by any\nof the legitimate methods of induction--which it has not even carelessly\nor overhastily, endeavoured to test by those legitimate methods.\n\n\n\u00a7 3. There is another branch of what may be called the Philosophy of\nError, which must be mentioned here, though only to be excluded from our\nsubject. The sources of erroneous opinions are twofold, moral and\nintellectual. Of these, the moral do not fall within the compass of this\nwork. They may be classed under two general heads; Indifference to the\nattainment of truth, and Bias: of which last the most common case is\nthat in which we are biassed by our wishes; but the liability is almost\nas great to the undue adoption of a conclusion which is disagreeable to\nus, as of one which is agreeable, if it be of a nature to bring into\naction any of the stronger passions. Persons of timid character are the\nmore predisposed to believe any statement, the more it is calculated to\nalarm them. Indeed it is a psychological law, deducible from the most\ngeneral laws of the mental constitution of man, that any strong passion\nrenders us credulous as to the existence of objects suitable to excite\nit.\n\nBut the moral causes of opinions, though with most persons the most\npowerful of all, are but remote causes: they do not act directly, but by\nmeans of the intellectual causes; to which they bear the same relation\nthat the circumstances called, in the theory of medicine, _predisposing_\ncauses, bear to _exciting_ causes. Indifference to truth cannot, in and\nby itself, produce erroneous belief; it operates by preventing the mind\nfrom collecting the proper evidences, or from applying to them the test\nof a legitimate and rigid induction; by which omission it is exposed\nunprotected to the influence of any species of apparent evidence which\noffers itself spontaneously, or which is elicited by that smaller\nquantity of trouble which the mind may be willing to take. As little is\nBias a direct source of wrong conclusions. We cannot believe a\nproposition only by wishing, or only by dreading, to believe it. The\nmost violent inclination to find a set of propositions true, will not\nenable the weakest of mankind to believe them without a vestige of\nintellectual grounds--without any, even apparent, evidence. It acts\nindirectly, by placing the intellectual grounds of belief in an\nincomplete or distorted shape before his eyes. It makes him shrink from\nthe irksome labour of a rigorous induction, when he has a misgiving that\nits result may be disagreeable; and in such examination as he does\ninstitute, it makes him exert that which is in a certain measure\nvoluntary, his attention, unfairly, giving a larger share of it to the\nevidence which seems favourable to the desired conclusion, a smaller to\nthat which seems unfavourable. It operates, too, by making him look out\neagerly for reasons, or apparent reasons, to support opinions which are\nconformable, or resist those which are repugnant, to his interests or\nfeelings; and when the interests or feelings are common to great numbers\nof persons, reasons are accepted and pass current, which would not for a\nmoment be listened to in that character, if the conclusion had nothing\nmore powerful than its reasons to speak in its behalf. The natural or\nacquired partialities of mankind are continually throwing up\nphilosophical theories, the sole recommendation of which consists in\nthe premises they afford for proving cherished doctrines, or justifying\nfavourite feelings: and when any one of these theories has been so\nthoroughly discredited as no longer to serve the purpose, another is\nalways ready to take its place. This propensity, when exercised in\nfavour of any widely-spread persuasion or sentiment, is often decorated\nwith complimentary epithets; and the contrary habit of keeping the\njudgment in complete subordination to evidence, is stigmatized by\nvarious hard names, as scepticism, immorality, coldness,\nhard-heartedness, and similar expressions according to the nature of the\ncase. But though the opinions of the generality of mankind, when not\ndependent on mere habit and inculcation, have their root much more in\nthe inclinations than in the intellect, it is a necessary condition to\nthe triumph of the moral bias that it should first pervert the\nunderstanding. Every erroneous inference, though originating in moral\ncauses, involves the intellectual operation of admitting insufficient\nevidence as sufficient; and whoever was on his guard against all kinds\nof inconclusive evidence which can be mistaken for conclusive, would be\nin no danger of being led into error even by the strongest bias. There\nare minds so strongly fortified on the intellectual side, that they\ncould not blind themselves to the light of truth, however really\ndesirous of doing so; they could not, with all the inclination in the\nworld, pass off upon themselves bad arguments for good ones. If the\nsophistry of the intellect could be rendered impossible, that of the\nfeelings, having no instrument to work with, would be powerless. A\ncomprehensive classification of all those things which, not being\nevidence, are liable to appear such to the understanding, will,\ntherefore, of itself include all errors of judgment arising from moral\ncauses, to the exclusion only of errors of practice committed against\nbetter knowledge.\n\nTo examine, then, the various kinds of apparent evidence which are not\nevidence at all, and of apparently conclusive evidence which do not\nreally amount to conclusiveness, is the object of that part of our\ninquiry into which we are about to enter.\n\nThe subject is not beyond the compass of classification and\ncomprehensive survey. The things, indeed, which are not evidence of any\ngiven conclusion, are manifestly endless, and this negative property,\nhaving no dependence on any positive ones, cannot be made the groundwork\nof a real classification. But the things which, not being evidence, are\nsusceptible of being mistaken for it, are capable of a classification\nhaving reference to the positive property which they possess, of\nappearing to be evidence. We may arrange them, at our choice, on either\nof two principles; according to the cause which makes them appear to be\nevidence, not being so; or according to the particular kind of evidence\nwhich they simulate. The Classification of Fallacies which will be\nattempted in the ensuing chapter, is founded on these considerations\njointly.\n\n\n\n\nCHAPTER II.\n\nCLASSIFICATION OF FALLACIES.\n\n\n\u00a7 1. In attempting to establish certain general distinctions which shall\nmark out from one another the various kinds of Fallacious Evidence, we\npropose to ourselves an altogether different aim from that of several\neminent thinkers, who have given, under the name of Political or other\nFallacies, a mere enumeration of a certain number of erroneous opinions;\nfalse general propositions which happen to be often met with; _loci\ncommunes_ of bad arguments on some particular subject. Logic is not\nconcerned with the false opinions which people happen to entertain, but\nwith the manner in which they come to entertain them. The question is\nnot, what facts have at any time been erroneously supposed to be proof\nof certain other facts, but what property in the facts it was which led\nany one to this mistaken supposition.\n\nWhen a fact is supposed, though incorrectly, to be evidentiary of, or a\nmark of, some other fact, there must be a cause of the error; the\nsupposed evidentiary fact must be connected in some particular manner\nwith the fact of which it is deemed evidentiary,--must stand in some\nparticular relation to it, without which relation it would not be\nregarded in that light. The relation may either be one resulting from\nthe simple contemplation of the two facts side by side with one another,\nor it may depend on some process of mind, by which a previous\nassociation has been established between them. Some peculiarity of\nrelation, however, there must be; the fact which can, even by the\nwildest aberration, be supposed to prove another fact, must stand in\nsome special position with regard to it; and if we could ascertain and\ndefine that special position, we should perceive the origin of the\nerror.\n\nWe cannot regard one fact as evidentiary of another, unless we believe\nthat the two are always, or in the majority of cases, conjoined. If we\nbelieve A to be evidentiary of B, if when we see A we are inclined to\ninfer B from it, the reason is because we believe that wherever A is, B\nalso either always or for the most part exists, either as an antecedent,\na consequent, or a concomitant. If when we see A we are inclined not to\nexpect B--if we believe A to be evidentiary of the absence of B--it is\nbecause we believe that where A is, B either is never, or at least\nseldom, found. Erroneous conclusions, in short, no less than correct\nconclusions, have an invariable relation to a general formula, either\nexpressed or tacitly implied. When we infer some fact from some other\nfact which does not really prove it, we either have admitted, or, if we\nmaintained consistency, ought to admit, some groundless general\nproposition respecting the conjunction of the two phenomena.\n\nFor every property, therefore, in facts, or in our mode of considering\nfacts, which leads us to believe that they are habitually conjoined when\nthey are not, or that they are not when in reality they are, there is a\ncorresponding kind of Fallacy; and an enumeration of fallacies would\nconsist in a specification of those properties in facts, and those\npeculiarities in our mode of considering them, which give rise to this\nerroneous opinion.\n\n\n\u00a7 2. To begin, then; the supposed connexion, or repugnance, between the\ntwo facts, may either be a conclusion from evidence (that is, from some\nother proposition or propositions) or may be admitted without any such\nground; admitted, as the phrase is, on its own evidence; embraced as\nself-evident, as an axiomatic truth. This gives rise to the first great\ndistinction, that between Fallacies of Inference, and Fallacies of\nSimple Inspection. In the latter division must be included not only all\ncases in which a proposition is believed and held for true, literally\nwithout any extrinsic evidence, either of specific experience or general\nreasoning; but those more frequent cases in which simple inspection\ncreates a _presumption_ in favour of a proposition; not sufficient for\nbelief, but sufficient to cause the strict principles of a regular\ninduction to be dispensed with, and creating a predisposition to believe\nit on evidence which would be seen to be insufficient if no such\npresumption existed. This class, comprehending the whole of what may be\ntermed Natural Prejudices, and which I shall call indiscriminately\nFallacies of Simple Inspection or Fallacies _\u00e0 priori_, shall be placed\nat the head of our list.\n\nFallacies of Inference, or erroneous conclusions from supposed evidence,\nmust be subdivided according to the nature of the apparent evidence from\nwhich the conclusions are drawn; or (what is the same thing) according\nto the particular kind of sound argument which the fallacy in question\nsimulates. But there is a distinction to be first drawn, which does not\nanswer to any of the divisions of sound arguments, but arises out of the\nnature of bad ones. We may know exactly what our evidence is, and yet\ndraw a false conclusion from it; we may conceive precisely what our\npremises are, what alleged matters of fact, or general principles, are\nthe foundation of our inference; and yet, because the premises are\nfalse, or because we have inferred from them what they will not support,\nour conclusion may be erroneous. But a case, perhaps even more frequent,\nis that in which the error arises from not conceiving our premises with\ndue clearness, that is, (as shown in the preceding Book,[1]) with due\nfixity: forming one conception of our evidence when we collect or\nreceive it, and another when we make use of it; or unadvisedly, and in\ngeneral unconsciously, substituting, as we proceed, different premises\nin the place of those with which we set out, or a different conclusion\nfor that which we undertook to prove. This gives existence to a class of\nfallacies which may be justly termed (in a phrase borrowed from Bentham)\nFallacies of Confusion; comprehending, among others, all those which\nhave their source in language, whether arising from the vagueness or\nambiguity of our terms, or from casual associations with them.\n\nWhen the fallacy is not one of Confusion, that is, when the proposition\nbelieved, and the evidence on which it is believed, are steadily\napprehended and unambiguously expressed, there remain to be made two\ncross divisions. The Apparent Evidence may be either particular facts,\nor foregone generalizations; that is, the process may simulate either\nsimple Induction, or Deduction; and again, the evidence, whether\nconsisting of supposed facts or of general propositions, may be false in\nitself, or, being true, may fail to bear out the conclusion attempted to\nbe founded on it. This gives us first, Fallacies of Induction and\nFallacies of Deduction, and then a subdivision of each of these,\naccording as the supposed evidence is false, or true but inconclusive.\n\nFallacies of Induction, where the facts on which the induction proceeds\nare erroneous, may be termed Fallacies of Observation. The term is not\nstrictly accurate, or rather, not accurately coextensive with the class\nof fallacies which I propose to designate by it. Induction is not always\ngrounded on facts immediately observed, but sometimes on facts inferred:\nand when these last are erroneous, the error may not be, in the literal\nsense of the term, an instance of bad observation, but of bad inference.\nIt will be convenient, however, to make only one class of all the\ninductions of which the error lies in not sufficiently ascertaining the\nfacts on which the theory is grounded; whether the cause of failure be\nmal-observation, or simple non-observation, and whether the\nmal-observation be direct, or by means of intermediate marks which do\nnot prove what they are supposed to prove. And in the absence of any\ncomprehensive term to denote the ascertainment, by whatever means, of\nthe facts on which an induction is grounded, I will venture to retain\nfor this class of fallacies, under the explanation now given, the title\nof Fallacies of Observation.\n\nThe other class of inductive fallacies, in which the facts are correct,\nbut the conclusion not warranted by them, are properly denominated\nFallacies of Generalization: and these, again, fall into various\nsubordinate classes or natural groups, some of which will be enumerated\nin their proper place.\n\nWhen we now turn to Fallacies of Deduction, namely those modes of\nincorrect argumentation in which the premises, or some of them, are\ngeneral propositions, and the argument a ratiocination; we may of course\nsubdivide these also into two species similar to the two preceding,\nnamely, those which proceed on false premises, and those of which the\npremises, though true, do not support the conclusion. But of these\nspecies, the first must necessarily fall under some one of the heads\nalready enumerated. For the error must be either in those premises which\nare general propositions, or in those which assert individual facts. In\nthe former case it is an Inductive Fallacy, of one or the other class;\nin the latter it is a Fallacy of Observation: unless, in either case,\nthe erroneous premise has been assumed on simple inspection, in which\ncase the fallacy is _\u00e0 priori_. Or finally, the premises, of whichever\nkind they are, may never have been conceived in so distinct a manner as\nto produce any clear consciousness by what means they were arrived at;\nas in the case of what is called reasoning in a circle: and then the\nfallacy is one of Confusion.\n\nThere remain, therefore, as the only class of fallacies having properly\ntheir seat in deduction, those in which the premises of the\nratiocination do not bear out its conclusion; the various cases, in\nshort, of vicious argumentation, provided against by the rules of the\nsyllogism. We shall call these, Fallacies of Ratiocination.\n\nWe have thus five distinguishable classes of fallacy, which may be\nexpressed in the following synoptic table:--\n\n Fallacies\n\n of Simple Inspection 1. Fallacies _\u00e0 priori_.\n\n of Inference\n\n from evidence distinctly\n conceived\n\n Inductive Fallacies 2. Fallacies of Observation.\n 3. Fallacies of Generalization.\n\n Deductive Fallacies 4. Fallacies of Ratiocination.\n\n from evidence indistinctly\n conceived 5. Fallacies of Confusion.\n\n\n\u00a7 3. We must not, however, expect to find that men's actual errors\nalways, or even commonly, fall so unmistakeably under some one of these\nclasses, as to be incapable of being referred to any other. Erroneous\narguments do not admit of such a sharply cut division as valid arguments\ndo. An argument fully stated, with all its steps distinctly set out, in\nlanguage not susceptible of misunderstanding, must, if it be erroneous,\nbe so in some one of these five modes unequivocally: or indeed of the\nfirst four, since the fifth, on such a supposition, would vanish. But it\nis not in the nature of bad reasoning to express itself thus\nunambiguously. When a sophist, whether he is imposing on himself or\nattempting to impose on others, can be constrained to throw his\nsophistry into so distinct a form, it needs, in a large proportion of\ncases, no further exposure.\n\nIn all arguments, everywhere but in the schools, some of the links are\nsuppressed; _\u00e0 fortiori_ when the arguer either intends to deceive, or\nis a lame and inexpert thinker, little accustomed to bring his reasoning\nprocesses to any test: and it is in those steps of the reasoning which\nare made in this tacit and half-conscious, or even wholly unconscious\nmanner, that the error oftenest lurks. In order to detect the fallacy,\nthe proposition thus silently assumed must be supplied; but the\nreasoner, most likely, has never really asked himself what he was\nassuming: his confuter, unless permitted to extort it from him by the\nSocratic mode of interrogation, must himself judge what the suppressed\npremise ought to be in order to support the conclusion. And hence, in\nthe words of Archbishop Whately, \"it must be often a matter of doubt, or\nrather, of arbitrary choice, not only to which genus each _kind_ of\nfallacy should be referred, but even to which kind to refer any one\n_individual_ fallacy; for since, in any course of argument, _one_\npremise is usually suppressed, it frequently happens in the case of a\nfallacy, that the hearers are left to the alternative of supplying\n_either_ a premise which is _not true_, or _else_, one which _does not\nprove_ the conclusion: _e. g._ if a man expatiates on the distress of\nthe country, and thence argues that the government is tyrannical, we\nmust suppose him to assume _either_ that 'every distressed country is\nunder a tyranny,' which is a manifest falsehood, _or_ merely that 'every\ncountry under a tyranny is distressed,' which, however true, proves\nnothing, the middle term being undistributed.\" The former would be\nranked, in our distribution, among fallacies of generalization, the\nlatter among those of ratiocination. \"Which are we to suppose the\nspeaker meant us to understand? Surely\" (if he understood himself) \"just\nwhichever each of his hearers might happen to prefer: some might assent\nto the false premise; others allow the unsound syllogism.\"\n\nAlmost all fallacies, therefore, might in strictness be brought under\nour fifth class, Fallacies of Confusion. A fallacy can seldom be\nabsolutely referred to any of the other classes; we can only say, that\nif all the links were filled up which should be capable of being\nsupplied in a valid argument, it would either stand thus (forming a\nfallacy of one class), or thus (a fallacy of another); or at furthest we\nmay say, that the conclusion is most _likely_ to have originated in a\nfallacy of such and such a class. Thus in the illustration just quoted,\nthe error committed may be traced with most probability to a fallacy of\ngeneralization; that of mistaking an uncertain mark, or piece of\nevidence, for a certain one; concluding from an effect to some one of\nits possible causes, when there are others which would have been equally\ncapable of producing it.\n\nYet, though the five classes run into each other, and a particular error\noften seems to be arbitrarily assigned to one of them rather than to any\nof the rest, there is considerable use in so distinguishing them. We\nshall find it convenient to set apart, as Fallacies of Confusion, those\nof which confusion is the most obvious characteristic; in which no other\ncause can be assigned for the mistake committed, than neglect or\ninability to state the question properly, and to apprehend the evidence\nwith definiteness and precision. In the remaining four classes I shall\nplace not only the cases in which the evidence is clearly seen to be\nwhat it is, and yet a wrong conclusion drawn from it, but also those in\nwhich, although there be confusion, the confusion is not the sole cause\nof the error, but there is some shadow of a ground for it in the nature\nof the evidence itself. And in distributing these cases of partial\nconfusion among the four classes, I shall, when there can be any\nhesitation as to the precise seat of the fallacy, suppose it to be in\nthat part of the process in which, from the nature of the case, and the\ntendencies of the human mind, an error would in the particular\ncircumstances be the most probable.\n\nAfter these observations we shall proceed, without further preamble, to\nconsider the five classes in their order.\n\n\n\n\nCHAPTER III.\n\nFALLACIES OF SIMPLE INSPECTION; OR _\u00c0 PRIORI_ FALLACIES.\n\n\n\u00a7 1. The tribe of errors of which we are to treat in the first instance,\nare those in which no actual inference takes place at all: the\nproposition (it cannot in such cases be called a conclusion) being\nembraced, not as proved, but as requiring no proof; as a self-evident\ntruth; or else as having such intrinsic verisimilitude, that external\nevidence not in itself amounting to proof, is sufficient in aid of the\nantecedent presumption.\n\nAn attempt to treat this subject comprehensively would be a\ntransgression of the bounds prescribed to this work, since it would\nnecessitate the inquiry which, more than any other, is the grand\nquestion of what is called metaphysics, viz. What are the propositions\nwhich may reasonably be received without proof? That there must be some\nsuch propositions all are agreed, since there cannot be an infinite\nseries of proof, a chain suspended from nothing. But to determine what\nthese propositions are, is the _opus magnum_ of the more recondite\nmental philosophy. Two principal divisions of opinion on the subject\nhave divided the schools of philosophy from its first dawn. The one\nrecognises no ultimate premises but the facts of our subjective\nconsciousness; our sensations, emotions, intellectual states of mind,\nand volitions. These, and whatever by strict rules of induction can be\nderived from these, it is possible, according to this theory, for us to\nknow; of all else we must remain in ignorance. The opposite school hold\nthat there are other existences, suggested indeed to our minds by these\nsubjective phenomena, but not inferrible from them, by any process\neither of deduction or of induction; which, however, we must, by the\nconstitution of our mental nature recognise as realities; and\nrealities, too, of a higher order than the phenomena of our\nconsciousness, being the efficient causes and necessary substrata of all\nPhenomena. Among these entities they reckon Substances, whether matter\nor spirit; from the dust under our feet to the soul, and from that to\nDeity. All these, according to them, are preternatural or supernatural\nbeings, having no likeness in experience, though experience is entirely\na manifestation of their agency. Their existence, together with more or\nless of the laws to which they conform in their operations, are, on this\ntheory, apprehended and recognised as real by the mind itself\nintuitively: experience (whether in the form of sensation or of mental\nfeeling) having no other part in the matter than as affording facts\nwhich are consistent with these necessary postulates of reason, and\nwhich are explained and accounted for by them.\n\nAs it is foreign to the purpose of the present treatise to decide\nbetween these conflicting theories, we are precluded from inquiring into\nthe existence, or defining the extent and limits, of knowledge _\u00e0\npriori_, and from characterizing the kind of correct assumption which\nthe fallacy of incorrect assumption, now under consideration, simulates.\nYet since it is allowed on both sides that such assumptions are often\nmade improperly, we may find it practicable, without entering into the\nultimate metaphysical grounds of the discussion, to state some\nspeculative propositions, and suggest some practical cautions,\nrespecting the forms in which such unwarranted assumptions are most\nlikely to be made.\n\n\n\u00a7 2. In the cases in which, according to the thinkers of the ontological\nschool, the mind apprehends, by intuition, things, and the laws of\nthings, not cognizable by our sensitive faculty; those intuitive, or\nsupposed intuitive, perceptions are undistinguishable from what the\nopposite school are accustomed to call ideas of the mind. When they\nthemselves say that they perceive the things by an immediate act of a\nfaculty given for that purpose by their Creator, it would be said of\nthem by their opponents that they find an idea or conception in their\nown minds, and from the idea or conception, infer the existence of a\ncorresponding objective reality. Nor would this be an unfair statement,\nbut a mere version into other words of the account given by many of\nthemselves; and one to which the more clear-sighted of them might, and\ngenerally do, without hesitation, subscribe. Since, therefore, in the\ncases which lay the strongest claims to be examples of knowledge _\u00e0\npriori_, the mind proceeds from the idea of a thing to the reality of\nthe thing itself, we cannot be surprised by finding that illicit\nassumptions _\u00e0 priori_ consist in doing the same thing erroneously: in\nmistaking subjective facts for objective, laws of the percipient mind\nfor laws of the perceived object, properties of the ideas or conceptions\nfor properties of the things conceived.\n\nAccordingly, a large proportion of the erroneous thinking which exists\nin the world proceeds on a tacit assumption, that the same order must\nobtain among the objects in nature which obtains among our ideas of\nthem. That if we always think of two things together, the two things\nmust always exist together. That if one thing makes us think of another\nas preceding or following it, that other must precede it or follow it in\nactual fact. And conversely, that when we cannot conceive two things\ntogether they cannot exist together, and that their combination may,\nwithout further evidence, be rejected from the list of possible\noccurrences.\n\nFew persons, I am inclined to think, have reflected on the great extent\nto which this fallacy has prevailed, and prevails, in the actual beliefs\nand actions of mankind. For a first illustration of it, we may refer to\na large class of popular superstitions. If any one will examine in what\ncircumstances most of those things agree, which in different ages and by\ndifferent portions of the human race have been considered as omens or\nprognostics of some interesting event, whether calamitous or fortunate;\nthey will be found very generally characterized by this peculiarity,\nthat they cause the mind to _think_ of that, of which they are therefore\nsupposed to forebode the actual occurrence. \"Talk of the devil, and he\nwill appear,\" has passed into a proverb. Talk of the devil, that is,\nraise the idea, and the reality will follow. In times when the\nappearance of that personage in a visible form was thought to be no\nunfrequent occurrence, it has doubtless often happened to persons of\nvivid imagination and susceptible nerves, that talking of the devil has\ncaused them to fancy they saw him; as, even in our more incredulous\ndays, listening to ghost stories predisposes us to see ghosts; and thus,\nas a prop to the _\u00e0 priori_ fallacy, there might come to be added an\nauxiliary fallacy of mal-observation, with one of false generalization\ngrounded on it. Fallacies of different orders often herd or cluster\ntogether in this fashion, one smoothing the way for another. But the\norigin of the superstition is evidently that which we have assigned. In\nlike manner it has been universally considered unlucky to speak of\nmisfortune. The day on which any calamity happened has been considered\nan unfortunate day, and there has been a feeling everywhere, and in some\nnations a religious obligation, against transacting any important\nbusiness on that day. For on such a day our thoughts are likely to be of\nmisfortune. For a similar reason, any untoward occurrence in commencing\nan undertaking has been considered ominous of failure; and often,\ndoubtless, has really contributed to it, by putting the persons engaged\nin the enterprise more or less out of spirits: but the belief has\nequally prevailed where the disagreeable circumstance was, independently\nof superstition, too insignificant to depress the spirits by any\ninfluence of its own. All know the story of C\u00e6sar's accidentally\nstumbling in the act of landing on the African coast; and the presence\nof mind with which he converted the direful presage into a favourable\none by exclaiming, \"Africa, I embrace thee.\" Such omens, it is true,\nwere often conceived as warnings of the future, given by a friendly or a\nhostile deity; but this very superstition grew out of a pre-existing\ntendency; the god was supposed to send, as an indication of what was to\ncome, something which people were already disposed to consider in that\nlight. So in the case of lucky or unlucky names. Herodotus tells us how\nthe Greeks, on the way to Mycale, were encouraged in their enterprise by\nthe arrival of a deputation from Samos, one of the members of which was\nnamed Hegesistratus, the leader of armies.\n\nCases may be pointed out in which something which could have no real\neffect but to make persons _think_ of misfortune, was regarded not\nmerely as a prognostic, but as something approaching to an actual cause\nof it. The [Greek: euph\u00eamei] of the Greeks, and _favete linguis_, or\n_bona verba qu\u00e6so_, of the Romans, evince the care with which they\nendeavoured to repress the utterance of any word expressive or\nsuggestive of ill fortune; not from notions of delicate politeness, to\nwhich their general mode of conduct and feeling had very little\nreference, but from _bon\u00e2 fide_ alarm lest the event so suggested to the\nimagination should in fact occur. Some vestige of a similar superstition\nhas been known to exist among uneducated persons even in our own day: it\nis thought an unchristian thing to talk of, or suppose, the death of any\nperson while he is alive. It is known how careful the Romans were to\navoid, by an indirect mode of speech, the utterance of any word directly\nexpressive of death or other calamity: how instead of _mortuus est_ they\nsaid _vixit_; and \"be the event fortunate or _otherwise_\" instead of\n_adverse_. The name Maleventum, of which Salmasius so sagaciously\ndetected the Thessalian origin ([Greek: Maloeis], [Greek: Maloentos]),\nthey changed into the highly propitious denomination, Beneventum; Egesta\ninto Segesta; and Epidamnus, a name so interesting in its associations\nto the reader of Thucydides, they exchanged for Dyrrhachium, to escape\nthe perils of a word suggestive of _damnum_ or detriment.\n\n\"If an hare cross the highway,\" says Sir Thomas Browne,[2] \"there are\nfew above threescore that are not perplexed thereat; which\nnotwithstanding is but an augurial terror, according to that received\nexpression, _Inauspicatum dat iter oblatus lepus_. And the ground of the\nconceit was probably no greater than this, that a fearful animal passing\nby us portended unto us something to be feared; as upon the like\nconsideration the meeting of a fox presaged some future imposture.\" Such\nsuperstitions as these last must be the result of study; they are too\nrecondite for natural or spontaneous growth. But when the attempt was\nonce made to construct a science of predictions, any association, though\never so faint or remote, by which an object could be connected in\nhowever far-fetched a manner with ideas either of prosperity or of\ndanger and misfortune, was enough to determine its being classed among\ngood or evil omens.\n\nAn example of rather a different kind from any of these, but falling\nunder the same principle, is the famous attempt on which so much labour\nand ingenuity were expended by the alchemists, to make gold potable. The\nmotive to this was a conceit that potable gold could be no other than\nthe universal medicine: and why gold? Because it was so precious. It\nmust have all marvellous properties as a physical substance, because the\nmind was already accustomed to marvel at it.\n\nFrom a similar feeling, \"every substance,\" says Dr. Paris,[3] \"whose\norigin is involved in mystery, has at different times been eagerly\napplied to the purposes of medicine. Not long since, one of those\nshowers which are now known to consist of the excrements of insects,\nfell in the north of Italy; the inhabitants regarded it as manna, or\nsome supernatural panacea, and they swallowed it with such avidity, that\nit was only by extreme address that a small quantity was obtained for a\nchemical examination.\" The superstition, in this instance, though\ndoubtless partly of a religious character, probably in part also arose\nfrom the prejudice that a wonderful thing must of course have wonderful\nproperties.\n\n\n\u00a7 3. The instances of _\u00e0 priori_ fallacy which we have hitherto cited\nbelong to the class of vulgar errors, and do not now, nor in any but a\nrude age ever could, impose upon minds of any considerable attainments.\nBut those to which we are about to proceed, have been, and still are,\nall but universally prevalent among thinkers. The same disposition to\ngive objectivity to a law of the mind--to suppose that what is true of\nour ideas of things must be true of the things themselves--exhibits\nitself in many of the most accredited modes of philosophical\ninvestigation, both on physical and on metaphysical subjects. In one of\nits most undisguised manifestations, it embodies itself in two maxims,\nwhich lay claim to axiomatic truth: Things which we cannot think of\ntogether, cannot coexist; and Things which we cannot help thinking of\ntogether, must coexist. I am not sure that the maxims were ever\nexpressed in these precise words, but the history both of philosophy and\nof popular opinions abounds with exemplifications of both forms of the\ndoctrine.\n\nTo begin with the latter of them: Things which we cannot think of except\ntogether, must exist together. This is assumed in the generally received\nand accredited mode of reasoning which concludes that A must accompany B\nin point of fact, because \"it is involved in the idea.\" Such thinkers do\nnot reflect that the idea, being a result of abstraction, ought to\nconform to the facts, and cannot make the facts conform to it. The\nargument is at most admissible as an appeal to authority; a surmise,\nthat what is now part of the idea, must, before it became so, have been\nfound by previous inquirers in the facts. Nevertheless, the philosopher\nwho more than all others made professions of rejecting authority,\nDescartes, constructed his system on this very basis. His favourite\ndevice for arriving at truth, even in regard to outward things, was by\nlooking into his own mind for it. \"Credidi me,\" says his celebrated\nmaxim, \"pro regul\u00e2 generali sumere posse, omne id quod vald\u00e8 dilucid\u00e8 et\ndistinct\u00e8 concipiebam, verum esse;\" whatever can be very clearly\nconceived, must certainly exist; that is, as he afterwards explains it,\nif the idea includes existence. And on this ground he infers that\ngeometrical figures really exist, because they can be distinctly\nconceived. Whenever existence is \"involved in an idea,\" a thing\nconformable to the idea must really exist; which is as much as to say,\nwhatever the idea contains must have its equivalent in the thing; and\nwhat we are not able to leave out of the idea cannot be absent from the\nreality.[4] This assumption pervades the philosophy not only of\nDescartes, but of all the thinkers who received their impulse mainly\nfrom him, in particular the two most remarkable among them, Spinoza and\nLeibnitz, from whom the modern German metaphysical philosophy is\nessentially an emanation. I am indeed disposed to think that the fallacy\nnow under consideration has been the cause of two-thirds of the bad\nphilosophy, and especially of the bad metaphysics, which the human mind\nhas never ceased to produce. Our general ideas contain nothing but what\nhas been put into them, either by our passive experience, or by our\nactive habits of thought; and the metaphysicians in all ages, who have\nattempted to construct the laws of the universe by reasoning from our\nsupposed necessities of thought, have always proceeded, and only could\nproceed, by laboriously finding in their own minds what they themselves\nhad formerly put there, and evolving from their ideas of things what\nthey had first _involved_ in those ideas. In this way all deeply-rooted\nopinions and feelings are enabled to create apparent demonstrations of\ntheir truth and reasonableness, as it were out of their own substance.\n\nThe other form of the fallacy; Things which we cannot think of together\ncannot exist together,--including as one of its branches, that what we\ncannot think of as existing cannot exist at all,--may thus be briefly\nexpressed: Whatever is inconceivable must be false.\n\nAgainst this prevalent doctrine I have sufficiently argued in a former\nBook,[5] and nothing is required in this place but examples. It was\nlong held that Antipodes were impossible because of the difficulty which\nwas found in conceiving persons with their heads in the same direction\nas our feet. And it was one of the received arguments against the\nCopernican system, that we cannot conceive so great a void space as that\nsystem supposes to exist in the celestial regions. When men's\nimaginations had always been used to conceive the stars as firmly set in\nsolid spheres, they naturally found much difficulty in imagining them in\nso different, and, as it doubtless appeared to them, so precarious a\nsituation. But they had no right to mistake the limitation (whether\nnatural, or, as it in fact proved, only artificial) of their own\nfaculties, for an inherent limitation of the possible modes of existence\nin the universe.\n\nIt may be said in objection, that the error in these cases was in the\nminor premise, not the major; an error of fact, not of principle; that\nit did not consist in supposing that what is inconceivable cannot be\ntrue, but in supposing antipodes to be inconceivable, when present\nexperience proves that they can be conceived. Even if this objection\nwere allowed, and the proposition that what is inconceivable cannot be\ntrue were suffered to remain unquestioned as a speculative truth, it\nwould be a truth on which no practical consequence could ever be\nfounded, since, on this showing, it is impossible to affirm of any\nproposition, not being a contradiction in terms, that it is\ninconceivable. Antipodes were really, not fictitiously, inconceivable to\nour ancestors: they are indeed conceivable to us; and as the limits of\nour power of conception have been so largely extended, by the extension\nof our experience and the more varied exercise of our imagination, so\nmay posterity find many combinations perfectly conceivable to them which\nare inconceivable to us. But, as beings of limited experience, we must\nalways and necessarily have limited conceptive powers; while it does not\nby any means follow that the same limitation obtains in the\npossibilities of nature, nor even in her actual manifestations.\n\nRather more than a century and a half ago it was a scientific maxim,\ndisputed by no one, and which no one deemed to require any proof, that\n\"a thing cannot act where it is not.\" With this weapon the Cartesians\nwaged a formidable war against the theory of gravitation, which,\naccording to them, involving so obvious an absurdity, must be rejected\n_in limine_: the sun could not possibly act upon the earth, not being\nthere. It was not surprising that the adherents of the old systems of\nastronomy should urge this objection against the new; but the false\nassumption imposed equally on Newton himself, who in order to turn the\nedge of the objection, imagined a subtle ether which filled up the space\nbetween the sun and the earth, and by its intermediate agency was the\nproximate cause of the phenomena of gravitation. \"It is inconceivable,\"\nsaid Newton, in one of his letters to Dr. Bentley,[6] \"that inanimate\nbrute matter should, without the mediation of something else, which is\nnot material, operate upon and affect other matter _without mutual\ncontact_.... That gravity should be innate, inherent, and essential to\nmatter, so that one body may act on another, at a distance, through a\nvacuum, without the mediation of anything else, by and through which\ntheir action and force may be conveyed from one to another, is to me so\ngreat an absurdity, that I believe no man, who in philosophical matters\nhas a competent faculty of thinking, can ever fall into it.\" This\npassage should be hung up in the cabinet of every cultivator of science\nwho is ever tempted to pronounce a fact impossible because it appears to\nhim inconceivable. In our own day one would be more tempted, though with\nequal injustice, to reverse the concluding observation, and consider the\nseeing any absurdity at all in a thing so simple and natural, to be what\nreally marks the absence of \"a competent faculty of thinking.\" No one\nnow feels any difficulty in conceiving gravity to be, as much as any\nother property is, \"inherent, and essential to matter,\" nor finds the\ncomprehension of it facilitated in the smallest degree by the\nsupposition of an ether (though some recent inquirers do give this as an\nexplanation of it); nor thinks it at all incredible that the celestial\nbodies can and do act where they, in actual bodily presence, are not.\nTo us it is not more wonderful that bodies should act upon one another\n\"without mutual contact,\" than that they should do so when in contact;\nwe are familiar with both these facts, and we find them equally\ninexplicable, but equally easy to believe. To Newton, the one, because\nhis imagination was familiar with it, appeared natural and a matter of\ncourse, while the other, for the contrary reason, seemed too absurd to\nbe credited.\n\nIt is strange that any one, after such a warning, should rely implicitly\non the evidence _\u00e0 priori_ of such propositions as these, that matter\ncannot think; that space, or extension, is infinite; that nothing can be\nmade out of nothing (_ex nihilo nihil fit_). Whether these propositions\nare true or not this is not the place to determine, nor even whether the\nquestions are soluble by the human faculties. But such doctrines are no\nmore self-evident truths, than the ancient maxim that a thing cannot act\nwhere it is not, which probably is not now believed by any educated\nperson in Europe.[7] Matter cannot think; why? because we _cannot\nconceive_ thought to be annexed to any arrangement of material\nparticles. Space is infinite, because having never known any part of it\nwhich had not other parts beyond it, we _cannot conceive_ an absolute\ntermination. _Ex nihilo nihil fit_, because having never known any\nphysical product without a pre-existing physical material, we _cannot_,\nor think we cannot, _imagine_ a creation out of nothing. But these\nthings may in themselves be as conceivable as gravitation without an\nintervening medium, which Newton thought too great an absurdity for any\nperson of a competent faculty of philosophical thinking to admit: and\neven supposing them not conceivable, this, for aught we know, may be\nmerely one of the limitations of our very limited minds, and not in\nnature at all.\n\nNo writer has more directly identified himself with the fallacy now\nunder consideration, or has embodied it in more distinct terms, than\nLeibnitz. In his view, unless a thing was not merely conceivable, but\neven explainable, it could not exist in nature. All _natural_ phenomena,\naccording to him, must be susceptible of being accounted for _\u00e0 priori_.\nThe only facts of which no explanation could be given but the will of\nGod, were miracles properly so called. \"Je reconnais,\" says he,[8]\n\"qu'il n'est pas permis de nier ce qu'on n'entend pas; mais j'ajoute\nqu'on a droit de nier (au moins dans l'ordre naturel) ce qui absolument\nn'est point intelligible ni explicable. Je soutiens aussi ... qu'enfin\nla conception des cr\u00e9atures n'est pas la mesure du pouvoir de Dieu, mais\nque leur conceptivit\u00e9, ou force de concevoir, est la mesure du pouvoir\nde la nature, tout ce qui est conforme \u00e0 l'ordre naturel pouvant \u00eatre\ncon\u00e7u ou entendu par quelque cr\u00e9ature.\"\n\nNot content with assuming that nothing can be true which we are unable\nto conceive, scientific inquirers have frequently given a still further\nextension to the doctrine, and held that, even of things not altogether\ninconceivable, that which we can conceive with the greatest ease is\nlikeliest to be true. It was long an admitted axiom, and is not yet\nentirely discredited, that \"nature always acts by the simplest means,\"\n_i.e._ by those which are most easily conceivable.[9] A large proportion\nof all the errors ever committed in the investigation of the laws of\nnature, have arisen from the assumption that the most familiar\nexplanation or hypothesis must be the truest. One of the most\ninstructive facts in scientific history is the pertinacity with which\nthe human mind clung to the belief that the heavenly bodies must move in\ncircles, or be carried round by the revolution of spheres; merely\nbecause those were in themselves the simplest suppositions: though, to\nmake them accord with the facts which were ever contradicting them more\nand more, it became necessary to add sphere to sphere and circle to\ncircle, until the original simplicity was converted into almost\ninextricable complication.\n\n\n\u00a7 4. We pass to another _\u00e0 priori_ fallacy or natural prejudice, allied\nto the former, and originating as that does, in the tendency to presume\nan exact correspondence between the laws of the mind and those of things\nexternal to it. The fallacy may be enunciated in this general\nform--Whatever can be thought of apart exists apart: and its most\nremarkable manifestation consists in the personification of\nabstractions. Mankind in all ages have had a strong propensity to\nconclude that wherever there is a name, there must be a distinguishable\nseparate entity corresponding to the name; and every complex idea which\nthe mind has formed for itself by operating upon its conceptions of\nindividual things, was considered to have an outward objective reality\nanswering to it. Fate, Chance, Nature, Time, Space, were real beings,\nnay, even gods. If the analysis of qualities in the earlier part of this\nwork be correct, names of qualities and names of substances stand for\nthe very same sets of facts or phenomena; _whiteness_ and _a white\nthing_ are only different phrases, required by convenience for speaking\nof the same external fact under different relations. Not such, however,\nwas the notion which this verbal distinction suggested of old, either to\nthe vulgar or to the scientific. Whiteness was an entity, inhering or\nsticking in the white substance: and so of all other qualities. So far\nwas this carried, that even concrete general terms were supposed to be,\nnot names of indefinite numbers of individual substances, but names of a\npeculiar kind of entities termed Universal Substances. Because we can\nthink and speak of man in general, that is, of all persons in so far as\npossessing the common attributes of the species, without fastening our\nthoughts permanently on some one individual person; therefore man in\ngeneral was supposed to be, not an aggregate of individual persons, but\nan abstract or universal man, distinct from these.\n\nIt may be imagined what havoc metaphysicians trained in these habits\nmade with philosophy, when they came to the largest generalizations of\nall. _Substanti\u00e6 Secund\u00e6_ of any kind were bad enough, but such\nSubstanti\u00e6 Secund\u00e6 as [Greek: to on], for example, and [Greek: to hen],\nstanding for peculiar entities supposed to be inherent in all things\nwhich _exist_, or which are said to be _one_, were enough to put an end\nto all intelligible discussion; especially since, with a just perception\nthat the truths which philosophy pursues are _general_ truths, it was\nsoon laid down that these general substances were the only subjects of\nscience, being immutable, while individual substances cognizable by the\nsenses, being in a perpetual flux, could not be the subject of real\nknowledge. This misapprehension of the import of general language\nconstitutes Mysticism, a word so much oftener written and spoken than\nunderstood. Whether in the Vedas, in the Platonists, or in the\nHegelians, mysticism is neither more nor less than ascribing objective\nexistence to the subjective creations of our own faculties, to ideas or\nfeelings of the mind; and believing that by watching and contemplating\nthese ideas of its own making, it can read in them what takes place in\nthe world without.\n\n\n\u00a7 5. Proceeding with the enumeration of _\u00e0 priori_ fallacies, and\nendeavouring to arrange them with as much reference as possible to their\nnatural affinities, we come to another, which is also nearly allied to\nthe fallacy preceding the last, standing in the same relation to one\nvariety of it as the fallacy last mentioned does to the other. This,\ntoo, represents nature as under incapacities corresponding to those of\nour intellect; but instead of only asserting that nature cannot do a\nthing because we cannot conceive it done, goes the still greater length\nof averring that nature does a particular thing, on the sole ground that\nwe can see no reason why she should not. Absurd as this seems when so\nplainly stated, it is a received principle among scientific authorities\nfor demonstrating _\u00e0 priori_ the laws of physical phenomena. A\nphenomenon must follow a certain law, because we see no reason why it\nshould deviate from that law in one way rather than in another. This is\ncalled the Principle of the Sufficient Reason;[10] and by means of it\nphilosophers often flatter themselves that they are able to establish,\nwithout any appeal to experience, the most general truths of\nexperimental physics.\n\nTake, for example, two of the most elementary of all laws, the law of\ninertia and the first law of motion. A body at rest cannot, it is\naffirmed, begin to move unless acted upon by some external force:\nbecause, if it did, it must either move up or down, forward or backward,\nand so forth; but if no outward force acts upon it, there can be _no\nreason_ for its moving up rather than down, or down rather than up, &c.,\n_ergo_, it will not move at all.\n\nThis reasoning I conceive to be entirely fallacious, as indeed Dr.\nBrown, in his treatise on Cause and Effect, has shown with great\nacuteness and justness of thought. We have before remarked, that almost\nevery fallacy may be referred to different genera by different modes of\nfilling up the suppressed steps; and this particular one may, at our\noption, be brought under _petitio principii_. It supposes that nothing\ncan be a \"sufficient reason\" for a body's moving in one particular\ndirection, except some external force. But this is the very thing to be\nproved. Why not some _internal_ force? Why not the law of the thing's\nown nature? Since these philosophers think it necessary to prove the law\nof inertia, they of course do not suppose _it_ to be self-evident; they\nmust, therefore, be of opinion that, previously to all proof, the\nsupposition of a body's moving by internal impulse is an admissible\nhypothesis; but if so, why is not the hypothesis also admissible, that\nthe internal impulse acts naturally in some one particular direction,\nnot in another? If spontaneous motion might have been the law of matter,\nwhy not spontaneous motion towards the sun, towards the earth, or\ntowards the zenith? Why not, as the ancients supposed, towards a\nparticular place in the universe, appropriated to each particular kind\nof substance? Surely it is not allowable to say that spontaneity of\nmotion is credible in itself, but not credible if supposed to take place\nin any determinate direction.\n\nIndeed, if any one chose to assert that all bodies when uncontrolled set\nout in a direct line towards the north pole, he might equally prove his\npoint by the principle of the Sufficient Reason. By what right is it\nassumed that a state of rest is the particular state which cannot be\ndeviated from without special cause? Why not a state of motion, and of\nsome particular sort of motion? Why may we not say that the natural\nstate of a horse left to himself is to amble, because otherwise he must\neither trot, gallop, or stand still, and because we know no reason why\nhe should do one of these rather than another? If this is to be called\nan unfair use of the \"sufficient reason,\" and the other a fair one,\nthere must be a tacit assumption that a state of rest is more natural to\na horse than a state of ambling. If this means that it is the state\nwhich the animal will assume when left to himself, that is the very\npoint to be proved; and if it does not mean this, it can only mean that\na state of rest is the simplest state, and therefore the most likely to\nprevail in nature, which is one of the fallacies or natural prejudices\nwe have already examined.\n\nSo again of the First Law of Motion; that a body once moving will, if\nleft to itself, continue to move uniformly in a straight line. An\nattempt is made to prove this law by saying, that if not, the body must\ndeviate either to the right or to the left, and that there is no reason\nwhy it should do one more than the other. But who could know,\nantecedently to experience, whether there was a reason or not? Might it\nnot be the nature of bodies, or of some particular bodies, to deviate\ntowards the right? or if the supposition is preferred, towards the east,\nor south? It was long thought that bodies, terrestrial ones at least,\nhad a natural tendency to deflect downwards; and there is no shadow of\nanything objectionable in the supposition, except that it is not true.\nThe pretended proof of the law of motion is even more manifestly\nuntenable than that of the law of inertia, for it is flagrantly\ninconsistent; it assumes that the continuance of motion in the direction\nfirst taken is more natural than deviation either to the right or to the\nleft, but denies that one of these can possibly be more natural than the\nother. All these fancies of the possibility of knowing what is natural\nor not natural by any other means than experience, are, in truth,\nentirely futile. The real and only proof of the laws of motion, or of\nany other law of the universe, is experience; it is simply that no\nother suppositions explain or are consistent with the facts of universal\nnature.\n\nGeometers have, in all ages, been open to the imputation of endeavouring\nto prove the most general facts of the outward world by sophistical\nreasoning, in order to avoid appeals to the senses. Archimedes, says\nProfessor Playfair,[11] established some of the elementary propositions\nof statics by a process in which he \"borrows no principle from\nexperiment, but establishes his conclusion entirely by reasoning _\u00e0\npriori_. He assumes, indeed, that equal bodies, at the ends of the equal\narms of a lever, will balance one another; and also that a cylinder or\nparallelopiped of homogeneous matter, will be balanced about its centre\nof magnitude. These, however, are not inferences from experience; they\nare, properly speaking, conclusions deduced from the principle of the\nSufficient Reason.\" And to this day there are few geometers who would\nnot think it far more scientific to establish these or any other\npremises in this way, than to rest their evidence on that familiar\nexperience which in the case in question might have been so safely\nappealed to.\n\n\n\u00a7 6. Another natural prejudice, of most extensive prevalence, and which\nhad a great share in producing the errors fallen into by the ancients in\ntheir physical inquiries, was this: That the differences in nature must\ncorrespond to our received distinctions; that effects which we are\naccustomed, in popular language, to call by different names, and arrange\nin different classes, must be of different natures, and have different\ncauses. This prejudice, so evidently of the same origin with those\nalready treated of, marks more especially the earliest stage of science,\nwhen it has not yet broken loose from the trammels of every-day\nphraseology. The extraordinary prevalence of the fallacy among the Greek\nphilosophers may be accounted for by their generally knowing no other\nlanguage than their own; from which it was a consequence that their\nideas followed the accidental or arbitrary combinations of that\nlanguage, more completely than can happen among the moderns to any but\nilliterate persons. They had great difficulty in distinguishing between\nthings which their language confounded, or in putting mentally together\nthings which it distinguished; and could hardly combine the objects in\nnature, into any classes but those which were made for them by the\npopular phrases of their own country: or at least could not help\nfancying those classes to be natural, and all others arbitrary and\nartificial. Accordingly, scientific investigation among the Greek\nschools of speculation and their followers in the middle ages, was\nlittle more than a mere sifting and analysing of the notions attached to\ncommon language. They thought that by determining the meaning of words,\nthey could become acquainted with facts. \"They took for granted,\" says\nDr. Whewell,[12] \"that philosophy must result from the relations of\nthose notions which are involved in the common use of language, and they\nproceeded to seek it by studying such notions.\" In his next chapter, Dr.\nWhewell has so well illustrated and exemplified this error, that I shall\ntake the liberty of quoting him at some length.\n\n\"The propensity to seek for principles in the common usages of language\nmay be discerned at a very early period. Thus we have an example of it\nin a saying which is reported of Thales, the founder of Greek\nphilosophy. When he was asked, 'What is the _greatest_ thing?' he\nreplied '_Place_; for all other things are _in_ the world, but the world\nis _in_ it.' In Aristotle we have the consummation of this mode of\nspeculation. The usual point from which he starts in his inquiries is,\nthat _we say_ thus or thus in common language. Thus, when he has to\ndiscuss the question whether there be, in any part of the universe, a\nvoid, or space in which there is nothing, he inquires first in how many\nsenses we say that one thing is _in_ another. He enumerates many of\nthese; we say the part is in the whole, as the finger is _in_ the hand;\nagain we say, the species is in the genus, as man is included _in_\nanimal; again, the government of Greece is _in_ the king; and various\nother senses are described and exemplified, but of all these _the most\nproper_ is when we say a thing is _in_ a vessel, and generally _in\nplace_. He next examines what _place_ is, and comes to this conclusion,\nthat 'if about a body there be another body including it, it is in\nplace, and if not, not.' A body moves when it changes its place; but he\nadds, that if water be in a vessel, the vessel being at rest, the parts\nof the water may still move, for they are included by each other; so\nthat while the whole does not change its place, the parts may change\ntheir place in a circular order. Proceeding then to the question of a\n_void_, he as usual examines the different senses in which the term is\nused, and adopts as the most proper, _place without matter_: with no\nuseful result.\n\n\"Again, in a question concerning mechanical action, he says, 'When a man\nmoves a stone by pushing it with a stick, _we say_ both that the man\nmoves the stone, and that the stick moves the stone, but the latter\n_more properly_.'\n\n\"Again, we find the Greek philosophers applying themselves to extract\ntheir dogmas from the most general and abstract notions which they could\ndetect; for example, from the conception of the Universe as One or as\nMany things. They tried to determine how far we may, or must, combine\nwith these conceptions that of a whole, of parts, of number, of limits,\nof place, of beginning or end, of full or void, of rest, or motion, of\ncause and effect, and the like. The analysis of such conceptions with\nsuch a view, occupies, for instance, almost the whole of Aristotle's\nTreatise on the Heavens.\"\n\nThe following paragraph merits particular attention:--\"Another mode of\nreasoning, very widely applied in these attempts, was the _doctrine of\ncontrarieties_, in which it was assumed, that adjectives or substances\nwhich are in common language, or in some abstract mode of conception,\nopposed to each other, must point at some fundamental antithesis in\nnature, which it is important to study. Thus Aristotle says that the\nPythagoreans, from the contrasts which number suggests, collected ten\nprinciples--Limited and Unlimited, Odd and Even, One and Many, Right and\nLeft, Male and Female, Rest and Motion, Straight and Curved, Light and\nDarkness, Good and Evil, Square and Oblong.... Aristotle himself deduced\nthe doctrine of four elements and other dogmas by oppositions of the\nsame kind.\"\n\nOf the manner in which, from premises obtained in this way, the ancients\nattempted to deduce laws of nature, an example is given in the same work\na few pages further on. \"Aristotle decides that there is no void, on\nsuch arguments as this. In a void there could be no difference of up and\ndown; for as in nothing there are no differences, so there are none in a\nprivation or negation; but a void is merely a privation or negation of\nmatter; therefore, in a void, bodies could not move up and down, which\nit is in their nature to do. It is easily seen\" (Dr. Whewell very justly\nadds) \"that such a mode of reasoning elevates the familiar forms of\nlanguage, and the intellectual connexions of terms, to a supremacy over\nfacts; making truth depend upon whether terms are or are not privative,\nand whether we say that bodies fall _naturally_.\"\n\nThe propensity to assume that the same relations obtain between objects\nthemselves, which obtain between our ideas of them, is here seen in the\nextreme stage of its development. For the mode of philosophizing,\nexemplified in the foregoing instances, assumes no less than that the\nproper way of arriving at knowledge of nature, is to study nature itself\nsubjectively; to apply our observation and analysis not to the facts,\nbut to the common notions entertained of the facts.\n\nMany other equally striking examples may be given of the tendency to\nassume that things which for the convenience of common life are placed\nin different classes, must differ in every respect. Of this nature was\nthe universal and deeply-rooted prejudice of antiquity and the middle\nages, that celestial and terrestrial phenomena must be essentially\ndifferent, and could in no manner or degree depend on the same laws. Of\nthe same kind, also, was the prejudice against which Bacon contended,\nthat nothing produced by nature could be successfully imitated by man:\n\"Calorem solis et ignis toto genere differre; ne scilicet homines\nputent se per opera ignis, aliquid simile iis qu\u00e6 in Natura fiunt,\neducere et formare posse:\" and again, \"Compositionem tantum opus\nHominis, Mistionem vero opus solius Natur\u00e6 esse: ne scilicet homines\nsperent aliquam ex arte Corporum naturalium generationem aut\ntransformationem.\"[13] The grand distinction in the ancient scientific\nspeculations, between natural and violent motions, though not without a\nplausible foundation in the appearances themselves, was doubtless\ngreatly recommended to adoption by its conformity to this prejudice.\n\n\n\u00a7 7. From the fundamental error of the scientific inquirers of\nantiquity, we pass, by a natural association, to a scarcely less\nfundamental one of their great rival and successor, Bacon. It has\nexcited the surprise of philosophers that the detailed system of\ninductive logic, which this extraordinary man laboured to construct, has\nbeen turned to so little direct use by subsequent inquirers, having\nneither continued, except in a few of its generalities, to be recognised\nas a theory, nor having conducted in practice to any great scientific\nresults. But this, though not unfrequently remarked, has scarcely\nreceived any plausible explanation; and some, indeed, have preferred to\nassert that all rules of induction are useless, rather than suppose that\nBacon's rules are grounded on an insufficient analysis of the inductive\nprocess. Such, however, will be seen to be the fact, as soon as it is\nconsidered, that Bacon entirely overlooked Plurality of Causes. All his\nrules tacitly imply the assumption, so contrary to all we now know of\nnature, that a phenomenon cannot have more than one cause.\n\nWhen he is inquiring into what he terms the _forma calidi aut frigidi_,\n_gravis aut levis_, _sicci aut humidi_, and the like, he never for an\ninstant doubts that there is some one thing, some invariable condition\nor set of conditions, which is present in all cases of heat, or cold, or\nwhatever other phenomenon he is considering; the only difficulty being\nto find what it is; which accordingly he tries to do by a process of\nelimination, rejecting or excluding, by negative instances, whatever is\nnot the _forma_ or cause, in order to arrive at what is. But, that this\n_forma_ or cause is _one_ thing, and that it is the same in all hot\nobjects, he has no more doubt of, than another person has that there is\nalways some cause _or other_. In the present state of knowledge it could\nnot be necessary, even if we had not already treated so fully of the\nquestion, to point out how widely this supposition is at variance with\nthe truth. It is particularly unfortunate for Bacon that, falling into\nthis error, he should have fixed almost exclusively upon a class of\ninquiries in which it was especially fatal; namely, inquiries into the\ncauses of the sensible qualities of objects. For his assumption,\ngroundless in every case, is false in a peculiar degree with respect to\nthose sensible qualities. In regard to scarcely any of them has it been\nfound possible to trace any unity of cause, any set of conditions\ninvariably accompanying the quality. The conjunctions of such qualities\nwith one another constitute the variety of Kinds, in which, as already\nremarked, it has not been found possible to trace any law. Bacon was\nseeking for what did not exist. The phenomenon of which he sought for\nthe one cause has oftenest no cause at all, and when it has, depends (as\nfar as hitherto ascertained) on an unassignable variety of distinct\ncauses.\n\nAnd on this rock every one must split, who represents to himself as the\nfirst and fundamental problem of science to ascertain what is the cause\nof a given effect, rather than what are the effects of a given cause. It\nwas shown, in an early stage of our inquiry into the nature of\nInduction,[14] how much more ample are the resources which science\ncommands for the latter than for the former inquiry, since it is upon\nthe latter only that we can throw any direct light by means of\nexperiment; the power of artificially producing an effect, implying a\nprevious knowledge of at least one of its causes. If we discover the\ncauses of effects, it is generally by having previously discovered the\neffects of causes: the greatest skill in devising crucial instances for\nthe former purpose may only end, as Bacon's physical inquiries did, in\nno result at all. Was it that his eagerness to acquire the power of\nproducing for man's benefit effects of practical importance to human\nlife, rendering him impatient of pursuing that end by a circuitous\nroute, made even him, the champion of experiment, prefer the direct\nmode, though one of mere observation, to the indirect, in which alone\nexperiment was possible? Or had even Bacon not entirely cleared his mind\nfrom the notion of the ancients, that \"rerum cognoscere _causas_\" was\nthe sole object of philosophy, and that to inquire into the _effects_ of\nthings belonged to servile and mechanical arts?\n\nIt is worth remarking that, while the only efficient mode of cultivating\nspeculative science was missed from an undue contempt of manual\noperations, the false speculative views thus engendered gave in their\nturn a false direction to such practical and mechanical aims as were\nsuffered to exist. The assumption universal among the ancients and in\nthe middle ages, that there were _principles_ of heat and cold, dryness\nand moisture, &c., led directly to a belief in alchemy; in a\ntransmutation of substances, a change from one Kind into another. Why\nshould it not be possible to make gold? Each of the characteristic\nproperties of gold has its _forma_, its essence, its set of conditions,\nwhich if we could discover, and learn how to realize, we could\nsuperinduce that particular property upon any other substance, upon\nwood, or iron, or lime, or clay. If, then, we could effect this with\nrespect to every one of the essential properties of the precious metal,\nwe should have converted the other substance into gold. Nor did this, if\nonce the premises were granted, appear to transcend the real powers of\nmankind. For daily experience showed that almost every one of the\ndistinctive sensible properties of any object, its consistence, its\ncolour, its taste, its smell, its shape, admitted of being totally\nchanged by fire, or water, or some other chemical agent. The _form\u00e6_ of\nall those qualities seeming, therefore, to be within human power either\nto produce or to annihilate, not only did the transmutation of\nsubstances appear abstractedly possible, but the employment of the\npower, at our choice, for practical ends, seemed by no means\nhopeless.[15]\n\nA prejudice, universal in the ancient world, and from which Bacon was so\nfar from being free, that it pervaded and vitiated the whole practical\npart of his system of logic, may with good reason be ranked high in the\norder of Fallacies of which we are now treating.\n\n\n\u00a7 8. There remains one _\u00e0 priori_ fallacy or natural prejudice, the most\ndeeply-rooted, perhaps, of all which we have enumerated: one which not\nonly reigned supreme in the ancient world, but still possesses almost\nundisputed dominion over many of the most cultivated minds; and some of\nthe most remarkable of the numerous instances by which I shall think it\nnecessary to exemplify it, will be taken from recent thinkers. This is,\nthat the conditions of a phenomenon must, or at least probably will,\nresemble the phenomenon itself.\n\nConformably to what we have before remarked to be of frequent\noccurrence, this fallacy might without much impropriety have been placed\nin a different class, among Fallacies of Generalization: for experience\ndoes afford a certain degree of countenance to the assumption. The cause\ndoes, in very many cases, resemble its effect; like produces like. Many\nphenomena have a direct tendency to perpetuate their own existence, or\nto give rise to other phenomena similar to themselves. Not to mention\nforms actually moulded on one another, as impressions on wax and the\nlike, in which the closest resemblance between the effect and its cause\nis the very law of the phenomenon; all motion tends to continue itself,\nwith its own velocity, and in its own original direction; and the motion\nof one body tends to set others in motion, which is indeed the most\ncommon of the modes in which the motions of bodies originate. We need\nscarcely refer to contagion, fermentation, and the like; or to the\nproduction of effects by the growth or expansion of a germ or rudiment\nresembling on a smaller scale the completed phenomenon, as in the growth\nof a plant or animal from an embryo, that embryo itself deriving its\norigin from another plant or animal of the same kind. Again, the\nthoughts, or reminiscences, which are effects of our past sensations,\nresemble those sensations; feelings produce similar feelings by way of\nsympathy; acts produce similar acts by involuntary or voluntary\nimitation. With so many appearances in its favour, no wonder if a\npresumption naturally grew up, that causes must _necessarily_ resemble\ntheir effects, and that like could _only_ be produced by like.\n\nThis principle of fallacy has usually presided over the fantastical\nattempts to influence the course of nature by conjectural means, the\nchoice of which was not directed by previous observation and experiment.\nThe guess almost always fixed upon some means which possessed features\nof real or apparent resemblance to the end in view. If a charm was\nwanted, as by Ovid's Medea, to prolong life, all long-lived animals, or\nwhat were esteemed such, were collected and brewed into a broth:--\n\n ... nec defuit illic\n Squamea Cinyphii tenuis membrana chelydri\n Vivacisque jecur cervi: quibus insuper addit\n Ora caputque novem cornicis s\u00e6cula pass\u00e6.\n\nA similar notion was embodied in the celebrated medical theory called\nthe \"Doctrine of Signatures,\" \"which is no less,\" says Dr. Paris,[16]\n\"than a belief that every natural substance which possesses any\nmedicinal virtue indicates by an obvious and well-marked external\ncharacter the disease for which it is a remedy, or the object for which\nit should be employed.\" This outward character was generally some\nfeature of resemblance, real or fantastical, either to the effect it\nwas supposed to produce, or to the phenomenon over which its power was\nthought to be exercised. \"Thus the lungs of a fox must be a specific for\nasthma, because that animal is remarkable for its strong powers of\nrespiration. Turmeric has a brilliant yellow colour, which indicates\nthat it has the power of curing the jaundice; for the same reason,\npoppies must relieve diseases of the head; Agaricus those of the\nbladder; _Cassia fistula_ the affections of the intestines, and\nAristolochia the disorders of the uterus: the polished surface and stony\nhardness which so eminently characterize the seeds of the Lithospermum\nofficinale (common gromwell) were deemed a certain indication of their\nefficacy in calculous and gravelly disorders; for a similar reason, the\nroots of the Saxifraga granulata (white saxifrage) gained reputation in\nthe cure of the same disease; and the Euphrasia (eye-bright) acquired\nfame, as an application in complaints of the eye, because it exhibits a\nblack spot in its corolla resembling the pupil. The blood-stone, the\nHeliotropium of the ancients, from the occasional small specks or points\nof a blood-red colour exhibited on its green surface, is even at this\nvery day employed in many parts of England and Scotland, to stop a\nbleeding from the nose; and nettle tea continues a popular remedy for\nthe cure of _Urticaria_. It is also asserted that some substances bear\nthe _signatures_ of the humours, as the petals of the red rose that of\nthe blood, and the roots of rhubarb and the flowers of saffron that of\nthe bile.\"\n\nThe early speculations respecting the chemical composition of bodies\nwere rendered abortive by no circumstance more, than by their invariably\ntaking for granted that the properties of the elements must resemble\nthose of the compounds which were formed from them.\n\nTo descend to more modern instances; it was long thought, and was\nstoutly maintained by the Cartesians and even by Leibnitz against the\nNewtonian system, (nor did Newton himself, as we have seen, contest the\nassumption, but eluded it by an arbitrary hypothesis), that nothing (of\na physical nature at least) could account for motion, except previous\nmotion; the impulse or impact of some other body. It was very long\nbefore the scientific world could prevail upon itself to admit\nattraction and repulsion (_i. e._ spontaneous tendencies of particles to\napproach or recede from one another) as ultimate laws, no more requiring\nto be accounted for than impulse itself, if indeed the latter were not,\nin truth, resolvable into the former. From the same source arose the\ninnumerable hypotheses devised to explain those classes of motions which\nappeared more mysterious than others because there was no obvious mode\nof attributing them to impulse, as for example the voluntary motions of\nthe human body. Such were the interminable systems of vibrations\npropagated along the nerves, or animal spirits rushing up and down\nbetween the muscles and the brain; which, if the facts could have been\nproved, would have been an important addition to our knowledge of\nphysiological laws; but the mere invention, or arbitrary supposition of\nthem, could not unless by the strongest delusion be supposed to render\nthe phenomena of animal life more comprehensible, or less mysterious.\nNothing, however, seemed satisfactory, but to make out that motion was\ncaused by motion; by something like itself. If it was not one kind of\nmotion, it must be another. In like manner it was supposed that the\nphysical qualities of objects must arise from some similar quality, or\nperhaps only some quality bearing the same name, in the particles or\natoms of which the objects were composed; that a sharp taste, for\nexample, must arise from sharp particles. And reversing the inference,\nthe effects produced by a phenomenon must, it was supposed, resemble in\ntheir physical attributes the phenomenon itself. The influences of the\nplanets were supposed to be analogous to their visible peculiarities:\nMars, being of a red colour, portended fire and slaughter; and the like.\n\nPassing from physics to metaphysics, we may notice among the most\nremarkable fruits of this _\u00e0 priori_ fallacy, two closely analogous\ntheories, employed in ancient and modern times to bridge over the chasm\nbetween the world of mind and that of matter: the _species sensibiles_\nof the Epicureans, and the modern doctrine of perception by means of\nideas. These theories are indeed, probably, indebted for their existence\nnot solely to the fallacy in question, but to that fallacy combined\nwith another natural prejudice already adverted to, that a thing cannot\nact where it is not. In both doctrines it is assumed that the phenomenon\nwhich takes place _in us_ when we see or touch an object, and which we\nregard as an effect of that object, or rather as its presence to our\norgans, must of necessity resemble very closely the outward object\nitself. To fulfil this condition, the Epicureans supposed that objects\nwere constantly projecting in all directions impalpable images of\nthemselves, which entered at the eyes and penetrated to the mind; while\nmodern metaphysicians, though they rejected this hypothesis, agreed in\ndeeming it necessary to suppose that not the thing itself, but a mental\nimage or representation of it, was the direct object of perception. Dr.\nReid had to employ a world of argument and illustration to familiarize\npeople with the truth, that the sensations or impressions on our minds\nneed not necessarily be copies of, or bear any resemblance to, the\ncauses which produce them; in opposition to the natural prejudice which\nled people to assimilate the action of bodies upon our senses, and\nthrough them upon our minds, to the transfer of a given form from one\nobject to another by actual moulding. The works of Dr. Reid are even now\nthe most effectual course of study for detaching the mind from the\nprejudice of which this was an example. And the value of the service\nwhich he thus rendered to popular philosophy, is not much diminished\nalthough we may hold, with Brown, that he went too far in imputing the\n\"ideal theory\" as an actual tenet, to the generality of the philosophers\nwho preceded him, and especially to Locke and Hume: for if they did not\nthemselves consciously fall into the error, unquestionably they often\nled their readers into it.\n\nThe prejudice, that the conditions of a phenomenon must resemble the\nphenomenon, is occasionally exaggerated, at least verbally, into a still\nmore palpable absurdity; the conditions of the thing are spoken of as if\nthey _were_ the very thing itself. In Bacon's model-inquiry, which\noccupies so great a space in the _Novum Organum_, the _inquisitio in\nformam calidi_, the conclusion which he favours is that heat is a kind\nof motion; meaning of course not the feeling of heat, but the\nconditions of the feeling; meaning, therefore, only that wherever there\nis heat, there must first be a particular kind of motion; but he makes\nno distinction in his language between these two ideas, expressing\nhimself as if heat, and the conditions of heat, were one and the same\nthing. So Darwin, in the beginning of his _Zoonomia_, says, \"The word\n_idea_ has various meanings in the writers of metaphysic: it is here\nused simply for those notions of external things which our organs of\nsense bring us acquainted with originally,\" (thus far the proposition,\nthough vague, is unexceptionable in meaning,) \"and is defined a\ncontraction, a motion, or configuration, of the fibres which constitute\nthe immediate organ of sense.\" Our _notions_, a configuration of the\nfibres! What kind of logician must he be who thinks that a phenomenon is\n_defined_ to _be_ the condition on which he supposes it to depend?\nAccordingly he says soon after, not that our ideas are caused by, or\nconsequent on, certain organic phenomena, but \"our ideas _are_ animal\nmotions of the organs of sense.\" And this confusion runs through the\nfour volumes of the _Zoonomia_; the reader never knows whether the\nwriter is speaking of the effect, or of its supposed cause; of the idea,\na state of mental consciousness, or of the state of the nerves and brain\nwhich he considers it to presuppose.\n\nI have given a variety of instances in which the natural prejudice, that\ncauses and their effects must resemble one another, has operated in\npractice so as to give rise to serious errors. I shall now go further,\nand produce from writings even of the present or very recent times,\ninstances in which this prejudice is laid down as an established\nprinciple. M. Victor Cousin, in the last of his celebrated lectures on\nLocke, enunciates the maxim in the following unqualified terms. \"Tout ce\nqui est vrai de l'effet est vrai de la cause.\" A doctrine to which,\nunless in some peculiar and technical meaning of the words cause and\neffect, it is not to be imagined that any person would literally adhere:\nbut he who could so write must be far enough from seeing, that the very\nreverse might be the fact; that there is nothing impossible in the\nsupposition that no one property which is true of the effect might be\ntrue of the cause. Without going quite so far in point of expression,\nColeridge, in his _Biographia Literaria_,[17] affirms as an \"evident\ntruth,\" that \"the law of causality holds only between homogeneous\nthings, _i. e._ things having some common property,\" and therefore\n\"cannot extend from one world into another, its opposite:\" hence, as\nmind and matter have no common property, mind cannot act upon matter,\nnor matter upon mind. What is this but the _\u00e0 priori_ fallacy of which\nwe are speaking? The doctrine, like many others of Coleridge, is taken\nfrom Spinoza, in the first book of whose _Ethica (De Deo)_ it stands as\nthe Third Proposition, \"Qu\u00e6 res nihil commune inter se habent, earum una\nalterius causa esse non potest,\" and is there proved from two so-called\naxioms, equally gratuitous with itself: but Spinoza, ever systematically\nconsistent, pursued the doctrine to its inevitable consequence, the\nmateriality of God.\n\nThe same conception of impossibility led the ingenious and subtle mind\nof Leibnitz to his celebrated doctrine of a pre-established harmony. He,\ntoo, thought that mind could not act upon matter, nor matter upon mind,\nand that the two, therefore, must have been arranged by their Maker like\ntwo clocks, which, though unconnected with one another, strike\nsimultaneously, and always point to the same hour. Malebranche's equally\nfamous theory of Occasional Causes was another form of the same\nconception: instead of supposing the clocks originally arranged to\nstrike together, he held that when the one strikes, God interposes, and\nmakes the other strike in correspondence with it.\n\nDescartes, in like manner, whose works are a rich mine of almost every\ndescription of _\u00e0 priori_ fallacy, says that the Efficient Cause must at\nleast have all the perfections of the effect, and for this singular\nreason: \"Si enim ponamus aliquid in ide\u00e2 reperiri quod non fuerit in\nejus caus\u00e2, hoc igitur habet a nihilo;\" of which it is scarcely a parody\nto say, that if there be pepper in the soup there must be pepper in the\ncook who made it, since otherwise the pepper would be without a cause. A\nsimilar fallacy is committed by Cicero in his second book _De Finibus_,\nwhere, speaking in his own person against the Epicureans, he charges\nthem with inconsistency in saying that the pleasures of the mind had\ntheir origin from those of the body, and yet that the former were more\nvaluable, as if the effect could surpass the cause. \"Animi voluptas\noritur propter voluptatem corporis, et major est animi voluptas quam\ncorporis? ita fit ut gratulator l\u00e6tior sit quam is cui gratulatur.\" Even\nthat, surely, is not an impossibility: a person's good fortune has often\ngiven more pleasure to others than it gave to the person himself.\n\nDescartes, with no less readiness, applies the same principle the\nconverse way, and infers the nature of the effects from the assumption\nthat they must, in this or that property or in all their properties,\nresemble their cause. To this class belong his speculations, and those\nof so many others after him, tending to infer the order of the universe,\nnot from observation, but by _\u00e0 priori_ reasoning from supposed\nqualities of the Godhead. This sort of inference was probably never\ncarried to a greater length than it was in one particular instance by\nDescartes, when, as a proof of one of his physical principles, that the\nquantity of motion in the universe is invariable, he had recourse to the\nimmutability of the Divine Nature. Reasoning of a very similar character\nis however nearly as common now as it was in his time, and does duty\nlargely as a means of fencing off disagreeable conclusions. Writers have\nnot yet ceased to oppose the theory of divine benevolence to the\nevidence of physical facts, to the principle of population for example.\nAnd people seem in general to think that they have used a very powerful\nargument, when they have said, that to suppose some proposition true,\nwould be a reflection on the goodness or wisdom of the Deity. Put into\nthe simplest possible terms, their argument is, \"If it had depended on\nme, I would not have made the proposition true, therefore it is not\ntrue.\" Put into other words it stands thus: \"God is perfect, therefore\n(what I think) perfection must obtain in nature.\" But since in reality\nevery one feels that nature is very far from perfect, the doctrine is\nnever applied consistently. It furnishes an argument which (like many\nothers of a similar character) people like to appeal to when it makes\nfor their own side. Nobody is convinced by it, but each appears to think\nthat it puts religion on his side of the question, and that it is a\nuseful weapon of offence for wounding an adversary.\n\nAlthough several other varieties of _\u00e0 priori_ fallacy might probably be\nadded to those here specified, these are all against which it seems\nnecessary to give any special caution. Our object is to open, without\nattempting or affecting to exhaust, the subject. Having illustrated,\ntherefore, this first class of Fallacies at sufficient length, I shall\nproceed to the second.\n\n\n\n\nCHAPTER IV.\n\nFALLACIES OF OBSERVATION.\n\n\n\u00a7 1. From the fallacies which are properly Prejudices, or presumptions\nantecedent to, and superseding, proof, we pass to those which lie in the\nincorrect performance of the proving process. And as Proof, in its\nwidest extent, embraces one or more, or all, of three processes,\nObservation, Generalization, and Deduction; we shall consider in their\norder the errors capable of being committed in these three operations.\nAnd first, of the first mentioned.\n\nA fallacy of misobservation may be either negative or positive; either\nNon-observation or Mal-observation. It is non-observation, when all the\nerror consists in overlooking, or neglecting, facts or particulars which\nought to have been observed. It is mal-observation, when something is\nnot simply unseen, but seen wrong; when the fact or phenomenon, instead\nof being recognised for what it is in reality, is mistaken for something\nelse.\n\n\n\u00a7 2. Non-observation may either take place by overlooking instances, or\nby overlooking some of the circumstances of a given instance. If we were\nto conclude that a fortune-teller was a true prophet, from not adverting\nto the cases in which his predictions had been falsified by the event,\nthis would be non-observation of instances; but if we overlooked or\nremained ignorant of the fact that in cases where the predictions had\nbeen fulfilled, he had been in collusion with some one who had given him\nthe information on which they were grounded, this would be\nnon-observation of circumstances.\n\nThe former case, in so far as the act of induction from insufficient\nevidence is concerned, does not fall under this second class of\nFallacies, but under the third, Fallacies of Generalization. In every\nsuch case, however, there are two defects or errors instead of one:\nthere is the error of treating the insufficient evidence as if it were\nsufficient, which is a Fallacy of the third class; and there is the\ninsufficiency itself; the not having better evidence; which, when such\nevidence, or in other words, when other instances, were to be had, is\nNon-observation: and the erroneous inference, so far as it is to be\nattributed to this cause, is a Fallacy of the second class.\n\nIt belongs not to our purpose to treat of non-observation as arising\nfrom casual inattention, from general slovenliness of mental habits,\nwant of due practice in the use of the observing faculties, or\ninsufficient interest in the subject. The question pertinent to logic\nis--Granting the want of complete competency in the observer, on what\npoints is that insufficiency on his part likely to lead him wrong? or\nrather, what sorts of instances, or of circumstances in any given\ninstance, are most likely to escape the notice of observers generally;\nof mankind at large.\n\n\n\u00a7 3. First, then, it is evident that when the instances on one side of a\nquestion are more likely to be remembered and recorded than those on the\nother; especially if there be any strong motive to preserve the memory\nof the first, but not of the latter; these last are likely to be\noverlooked, and escape the observation of the mass of mankind. This is\nthe recognised explanation of the credit given, in spite of reason and\nevidence, to many classes of impostors: to quack doctors, and\nfortune-tellers in all ages; to the \"cunning man\" of modern times and\nthe oracles of old. Few have considered the extent to which this fallacy\noperates in practice, even in the teeth of the most palpable negative\nevidence. A striking example of it is the faith which the uneducated\nportion of the agricultural classes, in this and other countries,\ncontinue to repose in the prophecies as to weather supplied by almanac\nmakers: though every season affords to them numerous cases of\ncompletely erroneous prediction; but as every season also furnishes some\ncases in which the prediction is fulfilled, this is enough to keep up\nthe credit of the prophet, with people who do not reflect on the number\nof instances requisite for what we have called, in our inductive\nterminology, the Elimination of Chance; since a certain number of casual\ncoincidences not only may but will happen, between any two unconnected\nevents.\n\nColeridge, in one of the essays in the _Friend_, has illustrated the\nmatter we are now considering, in discussing the origin of a proverb,\n\"which, differently worded, is to be found in all the languages of\nEurope,\" viz. \"Fortune favours fools.\" He ascribes it partly to the\n\"tendency to exaggerate all effects that seem disproportionate to their\nvisible cause, and all circumstances that are in any way strongly\ncontrasted with our notions of the persons under them.\" Omitting some\nexplanations which would refer the error to mal-observation, or to the\nother species of non-observation (that of circumstances), I take up the\nquotation farther on. \"Unforeseen coincidences may have greatly helped a\nman, yet if they have done for him only what possibly from his own\nabilities he might have effected for himself, his good luck will excite\nless attention, and the instances be less remembered. That clever men\nshould attain their objects seems natural, and we neglect the\ncircumstances that perhaps produced that success of themselves, without\nthe intervention of skill or foresight; but we dwell on the fact and\nremember it, as something strange, when the same happens to a weak or\nignorant man. So too, though the latter should fail in his undertakings\nfrom concurrences that might have happened to the wisest man, yet his\nfailure being no more than might have been expected and accounted for\nfrom his folly, it lays no hold on our attention, but fleets away among\nthe other undistinguished waves in which the stream of ordinary life\nmurmurs by us, and is forgotten. Had it been as true as it was\nnotoriously false, that those all-embracing discoveries, which have shed\na dawn of _science_ on the _art_ of chemistry, and give no obscure\npromise of some one great constitutive law, in the light of which dwell\ndominion and the power of prophecy; if these discoveries, instead of\nhaving been, as they really were, preconcerted by meditation, and\nevolved out of his own intellect, had occurred by a set of lucky\n_accidents_ to the illustrious father and founder of philosophic\nalchemy; if they had presented themselves to Professor Davy exclusively\nin consequence of his _luck_ in possessing a particular galvanic\nbattery; if this battery, as far as Davy was concerned, had itself been\nan _accident_, and not (as in point of fact it was) desired and obtained\nby him for the purpose of ensuring the testimony of experience to his\nprinciples, and in order to bind down material nature under the\ninquisition of reason, and force from her, as by torture, unequivocal\nanswers to _prepared_ and _preconceived_ questions,--yet still they\nwould not have been talked of or described as instances of _luck_, but\nas the natural results of his admitted genius and known skill. But\nshould an accident have disclosed similar discoveries to a mechanic at\nBirmingham or Sheffield, and if the man should grow rich in consequence,\nand partly by the envy of his neighbours and partly with good reason, be\nconsidered by them as a man _below par_ in the general powers of his\nunderstanding; then, 'O what a lucky fellow! Well, Fortune _does_ favour\nfools--that's for certain!--It is always so!' And forthwith the\nexclaimer relates half a dozen similar instances. Thus accumulating the\none sort of facts and never collecting the other, we do, as poets in\ntheir diction, and quacks of all denominations do in their reasoning,\nput a part for the whole.\"\n\nThis passage very happily sets forth the manner in which, under the\nloose mode of induction which proceeds _per enumerati onem simplicem_,\nnot seeking for instances of such a kind as to be decisive of the\nquestion, but generalizing from any which occur, or rather which are\nremembered, opinions grow up with the apparent sanction of experience,\nwhich have no foundation in the laws of nature at all. \"Itaque recte\nrespondit ille,\" (we may say with Bacon,[18]) \"qui cum suspensa tabula\nin templo ei monstraretur eorum, qui vota solverant, quod naufragii\npericulo elapsi sint, atque interrogando premeretur, anne tum quidem\nDeorum numen agnosceret, qu\u00e6sivit denuo, _At ubi sunt illi depicti qui\npost vota nuncupata perierunt?_ Eadem ratio est fere omnis\nsuperstitionis, ut in Astrologicis, in Somniis, Ominibus, Nemesibus, et\nhujusmodi; in quibus, homines delectati hujusmodi vanitatibus, advertunt\neventus, ubi implentur; ast ubi fallunt, licet multo frequentius, tamen\nnegligunt, et pr\u00e6tereunt.\" And he proceeds to say, that independently of\nthe love of the marvellous, or any other bias in the inclinations, there\nis a natural tendency in the intellect itself to this kind of fallacy;\nsince the mind is more moved by affirmative instances, though negative\nones are of most use in philosophy; \"Is tamen humano intellectui error\nest proprius et perpetuus, ut magis moveatur et excitetur Affirmativis\nquam Negativis; cum rite et ordine \u00e6quum se utrique pr\u00e6bere debeat; quin\ncontra, in omni Axiomate vero constituendo, major vis est instanti\u00e6\nnegativ\u00e6.\"\n\nBut the greatest of all causes of non-observation is a preconceived\nopinion. This it is which, in all ages, has made the whole race of\nmankind, and every separate section of it, for the most part unobservant\nof all facts, however abundant, even when passing under their own eyes,\nwhich are contradictory to any first appearance, or any received tenet.\nIt is worth while to recal occasionally to the oblivious memory of\nmankind some of the striking instances in which opinions that the\nsimplest experiment would have shown to be erroneous, continued to be\nentertained because nobody ever thought of trying that experiment. One\nof the most remarkable of these was exhibited in the Copernican\ncontroversy. The opponents of Copernicus argued that the earth did not\nmove, because if it did, a stone let fall from the top of a high tower\nwould not reach the ground at the foot of the tower, but at a little\ndistance from it, in a contrary direction to the earth's course; in the\nsame manner (said they) as, if a ball is let drop from the mast-head\nwhile the ship is in full sail, it does not fall exactly at the foot of\nthe mast, but nearer to the stern of the vessel. The Copernicans would\nhave silenced these objectors at once if they had _tried_ dropping a\nball from the mast-head, since they would have found that it does fall\nexactly at the foot, as the theory requires: but no; they admitted the\nspurious fact, and struggled vainly to make out a difference between the\ntwo cases. \"The ball was no _part_ of the ship--and the motion forward\nwas not _natural_, either to the ship or to the ball. The stone, on the\nother hand, let fall from the top of the tower, was a _part_ of the\nearth; and therefore, the diurnal and annular revolutions which were\n_natural_ to the earth, were also _natural_ to the stone: the stone\nwould, therefore, retain the same motion with the tower, and strike the\nground precisely at the bottom of it.\"[19]\n\nOther examples, scarcely less striking, are recorded by Dr. Whewell,[20]\nwhere imaginary laws of nature have continued to be received as real,\nmerely because no person had steadily looked at facts which almost every\none had the opportunity of observing. \"A vague and loose mode of looking\nat facts very easily observable, left men for a long time under the\nbelief that a body ten times as heavy as another falls ten times as\nfast; that objects immersed in water are always magnified, without\nregard to the form of the surface; that the magnet exerts an\nirresistible force; that crystal is always found associated with ice;\nand the like. These and many others are examples how blind and careless\nman can be even in observation of the plainest and commonest\nappearances; and they show us that the mere faculties of perception,\nalthough constantly exercised upon innumerable objects, may long fail in\nleading to any exact knowledge.\"\n\nIf even on physical facts, and these of the most obvious character, the\nobserving faculties of mankind can be to this degree the passive slaves\nof their preconceived impressions, we need not be surprised that this\nshould be so lamentably true as all experience attests it to be, on\nthings more nearly connected with their stronger feelings--on moral,\nsocial, and religious subjects. The information which an ordinary\ntraveller brings back from a foreign country, as the result of the\nevidence of his senses, is almost always such as exactly confirms the\nopinions with which he set out. He has had eyes and ears for such things\nonly as he expected to see. Men read the sacred books of their religion,\nand pass unobserved therein, multitudes of things utterly\nirreconcileable with even their own notions of moral excellence. With\nthe same authorities before them, different historians, alike innocent\nof intentional misrepresentation, see only what is favourable to\nProtestants or Catholics, royalists or republicans, Charles I. or\nCromwell; while others, having set out with the preconception that\nextremes must be in the wrong, are incapable of seeing truth and justice\nwhen these are wholly on one side.\n\nThe influence of a preconceived theory is well exemplified in the\nsuperstitions of barbarians respecting the virtues of medicaments and\ncharms. The negroes, among whom coral, as of old among ourselves, is\nworn as an amulet, affirm, according to Dr. Paris,[21] that its colour\n\"is always affected by the state of health of the wearer, it becoming\npaler in disease.\" On a matter open to universal observation, a general\nproposition which has not the smallest vestige of truth is received as a\nresult of experience; the preconceived opinion preventing, it would\nseem, any observation whatever on the subject.\n\n\n\u00a7 4. For illustration of the first species of non-observation, that of\nInstances, what has now been stated may suffice. But there may also be\nnon-observation of some material circumstances, in instances which have\nnot been altogether overlooked--nay, which may be the very instances on\nwhich the whole superstructure of a theory has been founded. As, in the\ncases hitherto examined, a general proposition was too rashly adopted,\non the evidence of particulars, true indeed, but insufficient to support\nit; so in the cases to which we now turn, the particulars themselves\nhave been imperfectly observed, and the singular propositions on which\nthe generalization is grounded, or some at least of those singular\npropositions, are false.\n\nSuch, for instance, was one of the mistakes committed in the celebrated\nphlogistic theory; a doctrine which accounted for combustion by the\nextrication of a substance called phlogiston, supposed to be contained\nin all combustible matter. The hypothesis accorded tolerably well with\nsuperficial appearances: the ascent of flame naturally suggests the\nescape of a substance; and the visible residuum of ashes, in bulk and\nweight, generally falls extremely short of the combustible material. The\nerror was, non-observation of an important portion of the actual\nresidue, namely, the gaseous products of combustion. When these were at\nlast noticed and brought into account, it appeared to be an universal\nlaw, that all substances gain instead of losing weight by undergoing\ncombustion; and, after the usual attempt to accommodate the old theory\nto the new fact by means of an arbitrary hypothesis (that phlogiston had\nthe quality of positive levity instead of gravity), chemists were\nconducted to the true explanation, namely, that instead of a substance\nseparated, there was on the contrary a substance absorbed.\n\nMany of the absurd practices which have been deemed to possess medicinal\nefficacy, have been indebted for their reputation to non-observance of\nsome accompanying circumstance which was the real agent in the cures\nascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby:\n\"Whenever any wound had been inflicted, this powder was applied to the\nweapon that had inflicted it, which was, moreover, covered with\nointment, and dressed two or three times a day. The wound itself, in the\nmeantime, was directed to be brought together, and carefully bound up\nwith clean linen rags, but _above all, to be let alone_ for seven days,\nat the end of which period the bandages were removed, when the wound was\ngenerally found perfectly united. The triumph of the cure was decreed to\nthe mysterious agency of the sympathetic powder which had been so\nassiduously applied to the weapon, whereas it is hardly necessary to\nobserve that the promptness of the cure depended on the total exclusion\nof air from the wound, and upon the sanative operations of nature not\nhaving received any disturbance from the officious interference of art.\nThe result, beyond all doubt, furnished the first hint which led\nsurgeons to the improved practice of healing wounds by what is\ntechnically called the _first intention_.\"[22] \"In all records,\" adds\nDr. Paris, \"of extraordinary cures performed by mysterious agents, there\nis a great desire to conceal the remedies and other curative means which\nwere simultaneously administered with them; thus Oribasius commends in\nhigh terms a necklace of P\u00e6ony root for the cure of epilepsy; but we\nlearn that he always took care to accompany its use with copious\nevacuations, although he assigns to them no share of credit in the cure.\nIn later times we have a good specimen of this species of deception,\npresented to us in a work on Scrofula by Mr. Morley, written, as we are\ninformed, for the sole purpose of restoring the much injured character\nand use of the Vervain; in which the author directs the root of this\nplant to be tied with a yard of white satin riband around the neck,\nwhere it is to remain until the patient is cured; but mark--during this\ninterval he calls to his aid the most active medicines in the materia\nmedica.\"[23]\n\nIn other cases the cures really produced by rest, regimen, and\namusement, have been ascribed to the medicinal, or occasionally to the\nsupernatural, means which were put in requisition. \"The celebrated John\nWesley, while he commemorates the triumph of sulphur and supplication\nover his bodily infirmity, forgets to appreciate the resuscitating\ninfluence of four months' repose from his apostolic labours; and such is\nthe disposition of the human mind to place confidence in the operation\nof mysterious agents, that we find him more disposed to attribute his\ncure to a brown paper plaister of egg and brimstone, than to Dr.\nFothergill's salutary prescription of country air, rest, asses' milk,\nand horse exercise.\"[24]\n\nIn the following example, the circumstance overlooked was of a somewhat\ndifferent character. \"When the yellow fever raged in America, the\npractitioners trusted exclusively to the copious use of mercury; at\nfirst this plan was deemed so universally efficacious, that, in the\nenthusiasm of the moment, it was triumphantly proclaimed that death\nnever took place after the mercury had evinced its effect upon the\nsystem: all this was very true, but it furnished no proof of the\nefficacy of that metal, since the disease in its aggravated form was so\nrapid in its career, that it swept away its victims long before the\nsystem could be brought under mercurial influence, while in its milder\nshape it passed off equally well without any assistance from art.\"[25]\n\nIn these examples the circumstance overlooked was cognizable by the\nsenses. In other cases, it is one the knowledge of which could only be\narrived at by reasoning; but the fallacy may still be classed under the\nhead to which, for want of a more appropriate name, we have given the\nappellation Fallacies of Non-observation. It is not the nature of the\nfaculties which ought to have been employed, but the non-employment of\nthem, which constitutes this Natural Order of Fallacies. Wherever the\nerror is negative, not positive; wherever it consists especially in\n_overlooking_, in being ignorant or unmindful of some fact which, if\nknown and attended to, would have made a difference in the conclusion\narrived at; the error is properly placed in the Class which we are\nconsidering. In this Class, there is not, as in all other fallacies\nthere is, a positive mis-estimate of evidence actually had. The\nconclusion would be just, if the portion which is seen of the case were\nthe whole of it; but there is another portion overlooked, which vitiates\nthe result.\n\nFor instance, there is a remarkable doctrine which has occasionally\nfound a vent in the public speeches of unwise legislators, but which\nonly in one instance that I am aware of has received the sanction of a\nphilosophical writer, namely M. Cousin, who, in his preface to the\n_Gorgias_ of Plato, contending that punishment must have some other and\nhigher justification than the prevention of crime, makes use of this\nargument--that if punishment were only for the sake of example, it would\nbe indifferent whether we punished the innocent or the guilty, since the\npunishment, considered as an example, is equally efficacious in either\ncase. Now we must, in order to go along with this reasoning, suppose,\nthat the person who feels himself under temptation, observing somebody\npunished, concludes himself to be in danger of being punished likewise,\nand is terrified accordingly. But it is forgotten that if the person\npunished is supposed to be innocent, or even if there be any doubt of\nhis guilt, the spectator will reflect that his own danger, whatever it\nmay be, is not contingent on his guiltiness, but threatens him equally\nif he remains innocent, and how therefore is he deterred from guilt by\nthe apprehension of such punishment? M. Cousin supposes that people will\nbe dissuaded from guilt by whatever renders the condition of the guilty\nmore perilous, forgetting that the condition of the innocent (also one\nof the elements in the calculation) is, in the case supposed, made\nperilous in precisely an equal degree. This is a fallacy of overlooking;\nor of non-observation, within the intent of our classification.\n\nFallacies of this description are the great stumbling-block to correct\nthinking in political economy. The economical workings of society afford\nnumerous cases in which the effects of a cause consist of two sets of\nphenomena: the one immediate, concentrated, obvious to all eyes, and\npassing, in common apprehension, for the whole effect; the other widely\ndiffused, or lying deeper under the surface, and which is exactly\ncontrary to the former. Take, for instance, the common notion so\nplausible at the first glance, of the encouragement given to industry by\nlavish expenditure. A, who spends his whole income, and even his\ncapital, in expensive living, is supposed to give great employment to\nlabour. B, who lives on a small portion, and invests the remainder in\nthe funds, is thought to give little or no employment. For everybody\nsees the gains which are made by A's tradesmen, servants, and others,\nwhile his money is spending. B's savings, on the contrary, pass into the\nhands of the person whose stock he purchased, who with it pays a debt he\nowed to some banker, who lends it again to some merchant or\nmanufacturer; and the capital being laid out in hiring spinners and\nweavers, or carriers and the crews of merchant vessels, not only gives\nimmediate employment to at least as much industry as A employs during\nthe whole of his career, but coming back with increase by the sale of\nthe goods which have been manufactured or imported, forms a fund for the\nemployment of the same and perhaps a greater quantity of labour in\nperpetuity. But the observer does not see, and therefore does not\nconsider, what becomes of B's money; he does see what is done with A's:\nhe observes the amount of industry which A's profusion feeds; he\nobserves not the far greater quantity which it prevents from being fed;\nand thence the prejudice, universal to the time of Adam Smith, that\nprodigality encourages industry, and parsimony is a discouragement to\nit.\n\nThe common argument against free trade was a fallacy of the same nature.\nThe purchaser of British silk encourages British industry; the purchaser\nof Lyons silk encourages only French; the former conduct is patriotic,\nthe latter ought to be interdicted by law. The circumstance is\noverlooked, that the purchaser of any foreign commodity necessarily\ncauses, directly or indirectly, the export of an equivalent value of\nsome article of home production (beyond what would otherwise be\nexported), either to the same foreign country or to some other; which\nfact, though from the complication of the circumstances it cannot always\nbe verified by specific observation, no observation can possibly be\nbrought to contradict, while the evidence of reasoning on which it rests\nis irrefragable. The fallacy is, therefore, the same as in the preceding\ncase, that of seeing a part only of the phenomena, and imagining that\npart to be the whole: and may be ranked among Fallacies of\nNon-observation.\n\n\n\u00a7 5. To complete the examination of the second of our five classes, we\nhave now to speak of Mal-observation; in which the error does not lie in\nthe fact that something is unseen, but that something seen is seen\nwrong.\n\nPerception being infallible evidence of whatever is really perceived,\nthe error now under consideration can be committed no otherwise than by\nmistaking for conception what is in fact inference. We have formerly\nshown how intimately the two are blended in almost everything which is\ncalled observation, and still more in every Description.[26] What is\nactually on any occasion perceived by our senses being so minute in\namount, and generally so unimportant a portion of the state of facts\nwhich we wish to ascertain or to communicate; it would be absurd to say\nthat either in our observations, or in conveying their result to others,\nwe ought not to mingle inference with fact; all that can be said is,\nthat when we do so we ought to be aware of what we are doing, and to\nknow what part of the assertion rests on consciousness, and is therefore\nindisputable, what part on inference, and is therefore questionable.\n\nOne of the most celebrated examples of an universal error produced by\nmistaking an inference for the direct evidence of the senses, was the\nresistance made, on the ground of common sense, to the Copernican\nsystem. People fancied they _saw_ the sun rise and set, the stars\nrevolve in circles round the pole. We now know that they saw no such\nthing; what they really saw was a set of appearances, equally\nreconcileable with the theory they held and with a totally different\none. It seems strange that such an instance as this, of the testimony of\nthe senses pleaded with the most entire conviction in favour of\nsomething which was a mere inference of the judgment, and, as it turned\nout, a false inference, should not have opened the eyes of the bigots of\ncommon sense, and inspired them with a more modest distrust of the\ncompetency of mere ignorance to judge the conclusions of cultivated\nthought.\n\nIn proportion to any person's deficiency of knowledge and mental\ncultivation, is generally his inability to discriminate between his\ninferences and the perceptions on which they were grounded. Many a\nmarvellous tale, many a scandalous anecdote, owes its origin to this\nincapacity. The narrator relates, not what he saw or heard, but the\nimpression which he derived from what he saw or heard, and of which\nperhaps the greater part consisted of inference, though the whole is\nrelated not as inference but as matter-of-fact. The difficulty of\ninducing witnesses to restrain within any moderate limits the\nintermixture of their inferences with the narrative of their\nperceptions, is well known to experienced cross-examiners; and still\nmore is this the case when ignorant persons attempt to describe any\nnatural phenomenon. \"The simplest narrative,\" says Dugald Stewart,[27]\n\"of the most illiterate observer involves more or less of hypothesis;\nnay, in general, it will be found that, in proportion to his ignorance,\nthe greater is the number of conjectural principles involved in his\nstatements. A village apothecary (and, if possible, in a still greater\ndegree, an experienced nurse) is seldom able to describe the plainest\ncase, without employing a phraseology of which every word is a theory:\nwhereas a simple and genuine specification of the phenomena which mark a\nparticular disease; a specification unsophisticated by fancy, or by\npreconceived opinions, may be regarded as unequivocal evidence of a mind\ntrained by long and successful study to the most difficult of all arts,\nthat of the faithful _interpretation_ of nature.\"\n\nThe universality of the confusion between perceptions and the inferences\ndrawn from them, and the rarity of the power to discriminate the one\nfrom the other, ceases to surprise us when we consider that in the far\ngreater number of instances the actual perceptions of our senses are of\nno importance or interest to us except as marks from which we infer\nsomething beyond them. It is not the colour and superficial extension\nperceived by the eye that are important to us, but the object, of which\nthose visible appearances testify the presence; and where the sensation\nitself is indifferent, as it generally is, we have no motive to attend\nparticularly to it, but acquire a habit of passing it over without\ndistinct consciousness, and going on at once to the inference. So that\nto know what the sensation actually was, is a study in itself, to which\npainters, for example, have to train themselves by special and\nlong-continued discipline and application. In things further removed\nfrom the dominion of the outward senses, no one who has not great\nexperience in psychological analysis is competent to break this intense\nassociation; and when such analytic habits do not exist in the requisite\ndegree, it is hardly possible to mention any of the habitual judgments\nof mankind on subjects of a high degree of abstraction, from the being\nof a God and the immortality of the soul down to the multiplication\ntable, which are not, or have not been, considered as matter of direct\nintuition. So strong is the tendency to ascribe an intuitive character\nto judgments which are mere inferences, and often false ones. No one can\ndoubt that many a deluded visionary has actually believed that he was\ndirectly inspired from Heaven, and that the Almighty had conversed with\nhim face to face; which yet was only, on his part, a conclusion drawn\nfrom appearances to his senses, or feelings in his internal\nconsciousness, which afforded no warrant for any such belief. A caution,\ntherefore, against this class of errors, is not only needful but\nindispensable; though to determine whether, on any of the great\nquestions of metaphysics, such errors are actually committed, belongs\nnot to this place, but, as I have so often said, to a different science.\n\n\n\n\nCHAPTER V.\n\nFALLACIES OF GENERALIZATION.\n\n\n\u00a7 1. The class of Fallacies of which we are now to speak, is the most\nextensive of all; embracing a greater number and variety of unfounded\ninferences than any of the other classes, and which it is even more\ndifficult to reduce to sub-classes or species. If the attempt made in\nthe preceding books to define the principles of well-grounded\ngeneralization has been successful, all generalizations not conformable\nto those principles might, in a certain sense, be brought under the\npresent class: when however the rules are known and kept in view, but a\ncasual lapse committed in the application of them, this is a blunder,\nnot a fallacy. To entitle an error of generalization to the latter\nepithet, it must be committed on principle; there must lie in it some\nerroneous general conception of the inductive process; the legitimate\nmode of drawing conclusions from observation and experiment must be\nfundamentally misconceived.\n\nWithout attempting anything so chimerical as an exhaustive\nclassification of all the misconceptions which can exist on the subject,\nlet us content ourselves with noting, among the cautions which might be\nsuggested, a few of the most useful and needful.\n\n\n\u00a7 2. In the first place, there are certain kinds of generalization\nwhich, if the principles already laid down be correct, _must_ be\ngroundless: experience cannot afford the necessary conditions for\nestablishing them by a correct induction. Such, for instance, are all\ninferences from the order of nature existing on the earth, or in the\nsolar system, to that which may exist in remote parts of the universe;\nwhere the phenomena, for aught we know, may be entirely different, or\nmay succeed one another according to different laws, or even according\nto no fixed law at all. Such, again, in matters dependent on causation,\nare all universal negatives, all propositions that assert impossibility.\nThe non-existence of any given phenomenon, however uniformly experience\nmay as yet have testified to the fact, proves at most that no cause,\nadequate to its production, has yet manifested itself; but that no such\ncauses exist in nature can only be inferred if we are so foolish as to\nsuppose that we know all the forces in nature. The supposition would at\nleast be premature while our acquaintance with some even of those which\nwe do know is so extremely recent. And however much our knowledge of\nnature may hereafter be extended, it is not easy to see how that\nknowledge could ever be complete, or how, if it were, we could ever be\nassured of its being so.\n\nThe only laws of nature which afford sufficient warrant for attributing\nimpossibility (even with reference to the existing order of nature, and\nto our own region of the universe), are first, those of number and\nextension, which are paramount to the laws of the succession of\nphenomena, and not exposed to the agency of counteracting causes; and\nsecondly, the universal law of causality itself. That no variation in\nany effect or consequent will take place while the whole of the\nantecedents remain the same, may be affirmed with full assurance. But,\nthat the addition of some new antecedent might not entirely alter and\nsubvert the accustomed consequent, or that antecedents competent to do\nthis do not exist in nature, we are in no case empowered positively to\nconclude.\n\n\n\u00a7 3. It is next to be remarked that all generalizations which profess,\nlike the theories of Thales, Democritus, and others of the early Greek\nspeculators, to resolve all things into some one element, or like many\nmodern theories, to resolve phenomena radically different into the same,\nare necessarily false. By radically different phenomena I mean\nimpressions on our senses which differ in quality, and not merely in\ndegree. On this subject what appeared necessary was said in the chapter\non the Limits to the Explanation of Laws of Nature; but as the fallacy\nis even in our own times a common one, I shall touch on it somewhat\nfurther in this place.\n\nWhen we say that the force which retains the planets in their orbits is\nresolved into gravity, or that the force which makes substances combine\nchemically is resolved into electricity, we assert in the one case what\nis, and in the other case what might, and probably will ultimately, be a\nlegitimate result of induction. In both these cases, motion is resolved\ninto motion. The assertion is, that a case of motion, which was supposed\nto be special, and to follow a distinct law of its own, conforms to and\nis included in the general law which regulates another class of motions.\nBut, from these and similar generalizations, countenance and currency\nhave been given to attempts to resolve, not motion into motion, but heat\ninto motion, light into motion, sensation itself into motion; states of\nconsciousness into states of the nervous system, as in the ruder forms\nof the materialist philosophy; vital phenomena into mechanical or\nchemical processes, as in some schools of physiology.\n\nNow I am far from pretending that it may not be capable of proof, or\nthat it will not be an important addition to our knowledge if proved,\nthat certain motions in the particles of bodies are among the\n_conditions_ of the production of heat or light; that certain assignable\nphysical modifications of the nerves may be the _conditions_ not only of\nour sensations or emotions, but even of our thoughts; that certain\nmechanical and chemical conditions may, in the order of nature, be\nsufficient to determine to action the physiological laws of life. All I\ninsist upon, in common with every thinker who entertains any clear idea\nof the logic of science, is, that it shall not be supposed that by\nproving these things one step would be made towards a real explanation\nof heat, light, or sensation; or that the generic peculiarity of those\nphenomena can be in the least degree evaded by any such discoveries,\nhowever well established. Let it be shown, for instance, that the most\ncomplex series of physical causes and effects succeed one another in the\neye and in the brain to produce a sensation of colour; rays falling on\nthe eye, refracted, converging, crossing one another, making an inverted\nimage on the retina, and after this a motion--let it be a vibration, or\na rush of nervous fluid, or whatever else you are pleased to suppose,\nalong the optic nerve--a propagation of this motion to the brain itself,\nand as many more different motions as you choose; still, at the end of\nthese motions, there is something which is not motion, there is a\nfeeling or sensation of colour. Whatever number of motions we may be\nable to interpolate, and whether they be real or imaginary, we shall\nstill find, at the end of the series, a motion antecedent and a colour\nconsequent. The mode in which any one of the motions produces the next,\nmight possibly be susceptible of explanation by some general law of\nmotion; but the mode in which the last motion produces the sensation of\ncolour, cannot be explained by any law of motion; it is the law of\ncolour: which is, and must always remain, a peculiar thing. Where our\nconsciousness recognises between two phenomena an inherent distinction;\nwhere we are sensible of a difference which is not merely of degree, and\nfeel that no adding one of the phenomena to itself would produce the\nother; any theory which attempts to bring either under the laws of the\nother must be false; though a theory which merely treats the one as a\ncause or condition of the other, may possibly be true.\n\n\n\u00a7 4. Among the remaining forms of erroneous generalization, several of\nthose most worthy of and most requiring notice have fallen under our\nexamination in former places, where, in investigating the rules of\ncorrect induction, we have had occasion to advert to the distinction\nbetween it and some common mode of the incorrect. In this number is what\nI have formerly called the natural Induction of uninquiring minds, the\nInduction of the ancients, which proceeds _per enumerationem\nsimplicem_: \"This, that, and the other A are B, I cannot think of any A\nwhich is not B, therefore every A is B.\" As a final condemnation of this\nrude and slovenly mode of generalization, I will quote Bacon's emphatic\ndenunciation of it; the most important part, as I have more than once\nventured to assert, of the permanent service rendered by him to\nphilosophy. \"Inductio qu\u00e6 procedit per enumerationem simplicem, res\npuerilis est, et precario concludit\" (concludes only _by your leave_, or\nprovisionally,) \"et periculo exponitur ab instanti\u00e2 contradictori\u00e2, et\nplerumque secundum pauciora quam par est, et _ex his tantummodo qu\u00e6\npr\u00e6sto sunt pronunciat_. At Inductio qu\u00e6 ad inventionem et\ndemonstrationem Scientiarum et Artium erit utilis, Naturam separare\ndebet, per rejectiones et exclusiones debitas; ac deinde post negativas\ntot quot sufficiunt, super affirmativas concludere.\"\n\nI have already said that the mode of Simple Enumeration is still the\ncommon and received method of Induction in whatever relates to man and\nsociety. Of this a very few instances, more by way of memento than of\ninstruction, may suffice. What, for example, is to be thought of all the\n\"common-sense\" maxims for which the following may serve as the universal\nformula, \"Whatsoever has never been, will never be.\" As for example:\nnegroes have never been as civilized as whites sometimes are, therefore\nit is impossible they should be so. Women, as a class, are supposed not\nto have hitherto been equal in intellect to men, therefore they are\nnecessarily inferior. Society cannot prosper without this or the other\ninstitution; _e.g._ in Aristotle's time, without slavery; in later\ntimes, without an established priesthood, without artificial\ndistinctions of rank, &c. One poor person in a thousand, educated, while\nthe nine hundred and ninety-nine remain uneducated, has usually aimed at\nraising himself out of his class, therefore education makes people\ndissatisfied with the condition of a labourer. Bookish men, taken from\nspeculative pursuits and set to work on something they know nothing\nabout, have generally been found or thought to do it ill; therefore\nphilosophers are unfit for business, &c. &c. All these are inductions by\nsimple enumeration. Reasons having some reference to the canons of\nscientific investigation have been attempted to be given, however\nunsuccessfully, for some of these propositions; but to the multitude of\nthose who parrot them, the _enumeratio simplex, ex his tantummodo qu\u00e6\npr\u00e6sto sunt pronuncians_, is the sole evidence. Their fallacy consists\nin this, that they are inductions without elimination: there has been no\nreal comparison of instances, nor even ascertainment of the material\nfacts in any given instance. There is also the further error, of\nforgetting that such generalizations, even if well established, could\nnot be ultimate truths, but must be results of laws much more\nelementary; and therefore, until deduced from such, could at most be\nadmitted as empirical laws, holding good within the limits of space and\ntime by which the particular observations that suggested the\ngeneralization were bounded.\n\nThis error, of placing more empirical laws, and laws in which there is\nno direct evidence of causation, on the same footing of certainty as\nlaws of cause and effect, an error which is at the root of perhaps the\ngreater number of bad inductions, is exemplified only in its grossest\nform in the kind of generalizations to which we have now referred.\nThese, indeed, do not possess even the degree of evidence which pertains\nto a well-ascertained empirical law; but admit of refutation on the\nempirical ground itself, without ascending to causal laws. A little\nreflection, indeed, will show that mere negations can only form the\nground of the lowest and least valuable kind of empirical law. A\nphenomenon has never been noticed; this only proves that the conditions\nof that phenomenon have not yet occurred in experience, but does not\nprove that they may not occur hereafter. There is a better kind of\nempirical law than this, namely, when a phenomenon which is observed\npresents within the limits of observation a series of gradations, in\nwhich a regularity, or something like a mathematical law, is\nperceptible: from which, therefore, something may be rationally presumed\nas to those terms of the series which are beyond the limits of\nobservation. But in negation there are no gradations, and no series: the\ngeneralizations, therefore, which deny the possibility of any given\ncondition of man and society merely because it has never yet been\nwitnessed, cannot possess this higher degree of validity even as\nempirical laws. What is more, the minuter examination which that higher\norder of empirical laws presupposes, being applied to the subject-matter\nof these, not only does not confirm but actually refutes them. For in\nreality the past history of Man and Society, instead of exhibiting them\nas immovable, unchangeable, incapable of ever presenting new phenomena,\nshows them on the contrary to be, in many most important particulars,\nnot only changeable, but actually undergoing a progressive change. The\nempirical law, therefore, best expressive, in most cases, of the genuine\nresult of observation, would be, not that such and such a phenomenon\nwill continue unchanged, but that it will continue to change in some\nparticular manner.\n\nAccordingly, while almost all generalizations relating to Man and\nSociety, antecedent to the last fifty years, have erred in the gross way\nwhich we have attempted to characterize, namely, by implicitly assuming\nthat human nature and society will for ever revolve in the same orbit,\nand exhibit essentially the same phenomena; which is also the vulgar\nerror of the ostentatiously practical, the votaries of so-called common\nsense, in our day, especially in Great Britain; the more thinking minds\nof the present age, having applied a more minute analysis to the past\nrecords of our race, have for the most part adopted a contrary opinion,\nthat the human species is in a state of necessary progression, and that\nfrom the terms of the series which are past we may infer positively\nthose which are yet to come. Of this doctrine, considered as a\nphilosophical tenet, we shall have occasion to speak more fully in the\nconcluding Book. If not, in all its forms, free from error, it is at\nleast free from the gross and stupid error which we previously\nexemplified. But, in all except the most eminently philosophical minds,\nit is infected with precisely the same _kind_ of fallacy as that is. For\nwe must remember that even this other and better generalization, the\nprogressive change in the condition of the human species, is, after all,\nbut an empirical law: to which, too, it is not difficult to point out\nexceedingly large exceptions; and even if these could be got rid of,\neither by disputing the facts or by explaining and limiting the theory,\nthe general objection remains valid against the supposed law, as\napplicable to any other than what, in our third book, were termed\nAdjacent Cases. For not only is it no ultimate, but not even a causal\nlaw. Changes do indeed take place in human affairs, but every one of\nthose changes depends on determinate causes; the \"progressiveness of the\nspecies\" is not a cause, but a summary expression for the general result\nof all the causes. So soon as, by a quite different sort of induction,\nit shall be ascertained what causes have produced these successive\nchanges, from the beginning of history, in so far as they have really\ntaken place, and by what causes of a contrary tendency they have been\noccasionally checked or entirely counteracted, we may then be prepared\nto predict the future with reasonable foresight; we may be in possession\nof the real _law_ of the future; and may be able to declare on what\ncircumstances the continuance of the same onward movement will\neventually depend. But this it is the error of many of the more advanced\nthinkers, in the present age, to overlook; and to imagine that the\nempirical law collected from a mere comparison of the condition of our\nspecies at different past times, is a real law, is _the_ law of its\nchanges, not only past but also to come. The truth is, that the causes\non which the phenomena of the moral world depend, are in every age, and\nalmost in every country, combined in some different proportion; so that\nit is scarcely to be expected that the general result of them all should\nconform very closely, in its details at least, to any uniformly\nprogressive series. And all generalizations which affirm that mankind\nhave a tendency to grow better or worse, richer or poorer, more\ncultivated or more barbarous, that population increases faster than\nsubsistence, or subsistence than population, that inequality of fortune\nhas a tendency to increase or to break down, and the like, propositions\nof considerable value as empirical laws within certain (but generally\nrather narrow) limits, are in reality true or false according to times\nand circumstances.\n\nWhat we have said of empirical generalizations from times past to times\nstill to come, holds equally true of similar generalizations from\npresent times to times past; when persons whose acquaintance with moral\nand social facts is confined to their own age, take the men and the\nthings of that age for the type of men and things in general, and apply\nwithout scruple to the interpretation of the events of history, the\nempirical laws which represent sufficiently for daily guidance the\ncommon phenomena of human nature at that time and in that particular\nstate of society. If examples are wanted, almost every historical work,\nuntil a very recent period, abounded in them. The same may be said of\nthose who generalize empirically from the people of their own country to\nthe people of other countries, as if human beings felt, judged, and\nacted, everywhere in the same manner.\n\n\n\u00a7 5. In the foregoing instances, the distinction is confounded between\nempirical laws, which express merely the customary order of the\nsuccession of effects, and the laws of causation on which the effects\ndepend. There may, however, be incorrect generalization when this\nmistake is not committed; when the investigation takes its proper\ndirection, that of causes, and the result erroneously obtained purports\nto be a really causal law.\n\nThe most vulgar form of this fallacy is that which is commonly called\n_post hoc, ergo propter hoc_, or, _cum hoc, ergo propter hoc_. As when\nit was inferred that England owed her industrial pre-eminence to her\nrestrictions on commerce: as when the old school of financiers, and some\nspeculative writers, maintained that the national debt was one of the\ncauses of national prosperity: as when the excellence of the Church, of\nthe Houses of Lords and Commons, of the procedure of the law courts,\n&c., were inferred from the mere fact that the country had prospered\nunder them. In such cases as these, if it can be rendered probable by\nother evidence that the supposed causes have some tendency to produce\nthe effect ascribed to them, the fact of its having been produced,\nthough only in one instance, is of some value as a verification by\nspecific experience: but in itself it goes scarcely any way at all\ntowards establishing such a tendency, since, admitting the effect, a\nhundred other antecedents could show an equally strong title of _that_\nkind to be considered as the cause.\n\nIn these examples we see bad generalization _\u00e0 posteriori_, or\nempiricism properly so called: causation inferred from casual\nconjunction, without either due elimination, or any presumption arising\nfrom known properties of the supposed agent. But bad generalization _\u00e0\npriori_ is fully as common: which is properly called false theory;\nconclusions drawn, by way of deduction, from properties of some one\nagent which is known or supposed to be present, all other coexisting\nagents being overlooked. As the former is the error of sheer ignorance,\nso the latter is especially that of semi-instructed minds; and is mainly\ncommitted in attempting to explain complicated phenomena by a simpler\ntheory than their nature admits of. As when one school of physicians\nsought for the universal principle of all disease in \"lentor and morbid\nviscidity of the blood,\" and imputing most bodily derangements to\nmechanical obstructions, thought to cure them by mechanical\nremedies;[28] while another, the chemical school, \"acknowledged no\nsource of disease but the presence of some hostile acid or alkali, or\nsome deranged condition in the chemical composition of the fluid or\nsolid parts,\" and conceived, therefore, that \"all remedies must act by\nproducing chemical changes in the body. We find Tournefort busily\nengaged in testing every vegetable juice, in order to discover in it\nsome traces of an acid or alkaline ingredient, which might confer upon\nit medicinal activity. The fatal errors into which such an hypothesis\nwas liable to betray the practitioner, received an awful illustration in\nthe history of the memorable fever that raged at Leyden in the year\n1699, and which consigned two-thirds of the population of that city to\nan untimely grave; an event which in a great measure depended upon the\nProfessor Sylvius de la Boe, who having just embraced the chemical\ndoctrines of Van Helmont, assigned the origin of the distemper to a\nprevailing acid, and declared that its cure could alone [only] be\neffected by the copious administration of absorbent and testaceous\nmedicines.\"[29]\n\nThese aberrations in medical theory have their exact parallels in\npolitics. All the doctrines which ascribe absolute goodness to\nparticular forms of government, particular social arrangements, and even\nto particular modes of education, without reference to the state of\ncivilization and the various distinguishing characters of the society\nfor which they are intended, are open to the same objection--that of\nassuming one class of influencing circumstances to be the paramount\nrulers of phenomena which depend in an equal or greater degree on many\nothers. But on these considerations it is the less necessary that we\nshould now dwell, as they will occupy our attention more largely in the\nconcluding Book.\n\n\n\u00a7 6. The last of the modes of erroneous generalization to which I shall\nadvert, is that to which we may give the name of False Analogies. This\nFallacy stands distinguished from those already treated of by the\npeculiarity, that it does not even simulate a complete and conclusive\ninduction, but consists in the misapplication of an argument which is at\nbest only admissible as an inconclusive presumption, where real proof is\nunattainable.\n\nAn argument from analogy, is an inference that what is true in a certain\ncase, is true in a case known to be somewhat similar, but not known to\nbe exactly parallel, that is, to be similar in all the material\ncircumstances. An object has the property B: another object is not known\nto have that property, but resembles the first in a property A, not\nknown to be connected with B; and the conclusion to which the analogy\npoints, is that this object has the property B also. As, for example,\nthat the planets are inhabited, because the earth is so. The planets\nresemble the earth in describing elliptical orbits round the sun, in\nbeing attracted by it and by one another, in being nearly spherical,\nrevolving on their axes, &c.; but it is not known that any of these\nproperties, or all of them together, are the conditions on which the\npossession of inhabitants is dependent, or are marks of those\nconditions. Nevertheless, so long as we do not know what the conditions\nare, they _may_ be connected by some law of nature with those common\nproperties; and to the extent of that possibility the planets are more\nlikely to be inhabited, than if they did not resemble the earth at all.\nThis non-assignable and generally small increase of probability, beyond\nwhat would otherwise exist, is all the evidence which a conclusion can\nderive from analogy. For if we have the slightest reason to suppose any\nreal connexion between the two properties A and B, the argument is no\nlonger one of analogy. If it had been ascertained (I purposely put an\nabsurd supposition) that there was a connexion by causation between the\nfact of revolving on an axis and the existence of animated beings, or if\nthere were any reasonable ground for even suspecting such a connexion, a\nprobability would arise of the existence of inhabitants in the planets,\nwhich might be of any degree of strength, up to a complete induction;\nbut we should then infer the fact from the ascertained or presumed law\nof causation, and not from the analogy of the earth.\n\nThe name analogy, however, is sometimes employed by extension to denote\nthose arguments of an inductive character but not amounting to a real\ninduction, which are employed to strengthen the argument drawn from a\nsimple resemblance. Though A, the property common to the two cases,\ncannot be shown to be the cause or effect of B, the analogical reasoner\nwill endeavour to show that there is some less close degree of connexion\nbetween them; that A is one of a set of conditions from which, when all\nunited, B would result; or is an occasional effect of some cause which\nhas been known also to produce B; and the like. Any of which things, if\nshown, would render the existence of B by so much more probable, than if\nthere had not been even that amount of known connexion between B and A.\n\nNow an error or fallacy of analogy may occur in two ways. Sometimes it\nconsists in employing an argument of either of the above kinds with\ncorrectness indeed, but overrating its probative force. This very common\naberration is sometimes supposed to be particularly incident to persons\ndistinguished for their imagination; but in reality it is the\ncharacteristic intellectual vice of those whose imaginations are barren,\neither from want of exercise, natural defect, or the narrowness of their\nrange of ideas. To such minds objects present themselves clothed in but\nfew properties; and as, therefore, few analogies between one object and\nanother occur to them, they almost invariably overrate the degree of\nimportance of those few: while one whose fancy takes a wider range,\nperceives and remembers so many analogies tending to conflicting\nconclusions, that he is much less likely to lay undue stress on any of\nthem. We always find that those are the greatest slaves to metaphorical\nlanguage, who have but one set of metaphors.\n\nBut this is only one of the modes of error in the employment of\narguments of analogy. There is another, more properly deserving the name\nof fallacy; namely, when resemblance in one point is inferred from\nresemblance in another point, though there is not only no evidence to\nconnect the two circumstances by way of causation, but the evidence\ntends positively to disconnect them. This is properly the Fallacy of\nFalse Analogies.\n\nAs a first instance, we may cite that favourite argument in defence of\nabsolute power, drawn from the analogy of paternal government in a\nfamily, which government, however much in need of control, is not and\ncannot be controlled by the children themselves, while they remain\nchildren. Paternal government, says the argument, works well; therefore,\ndespotic government in a state will work well. I wave, as not pertinent\nin this place, all that could be said in qualification of the alleged\nexcellence of paternal government. However this might be, the argument\nfrom the family to the state would not the less proceed on a false\nanalogy; implying that the beneficial working of parental government\ndepends, in the family, on the only point which it has in common with\npolitical despotism, namely, irresponsibility. Whereas it depends, when\nreal, not on that but on two other circumstances of the case, the\naffection of the parent for the children, and the superiority of the\nparent in wisdom and experience; neither of which properties can be\nreckoned on, or are at all likely to exist, between a political despot\nand his subjects; and when either of these circumstances fails even in\nthe family, and the influence of the irresponsibility is allowed to work\nuncorrected, the result is anything but good government. This,\ntherefore, is a false analogy.\n\nAnother example is the not uncommon _dictum_, that bodies politic have\nyouth, maturity, old age, and death, like bodies natural: that after a\ncertain duration of prosperity, they tend spontaneously to decay. This\nalso is a false analogy, because the decay of the vital powers in an\nanimated body can be distinctly traced to the natural progress of those\nvery changes of structure which, in their earlier stages, constitute its\ngrowth to maturity: while in the body politic the progress of those\nchanges cannot, generally speaking, have any effect but the still\nfurther continuance of growth: it is the stoppage of that progress, and\nthe commencement of retrogression, that alone would constitute decay.\nBodies politic die, but it is of disease, or violent death: they have no\nold age.\n\nThe following sentence from Hooker's _Ecclesiastical Polity_ is an\ninstance of a false analogy from physical bodies to what are called\nbodies politic. \"As there could be in natural bodies no motion of\nanything unless there were some which moveth all things, and continueth\nimmovable: even so in politic societies there must be some unpunishable,\nor else no man shall suffer punishment.\" There is a double fallacy here,\nfor not only the analogy, but the premise from which it is drawn, is\nuntenable. The notion that there must be something immovable which\nmoves all other things, is the old scholastic error of a _primum\nmobile_.\n\nThe following instance I quote from Archbishop Whately's _Rhetoric_: \"It\nwould be admitted that a great and permanent diminution in the quantity\nof some useful commodity, such as corn, or coal, or iron, throughout the\nworld, would be a serious and lasting loss; and again, that if the\nfields and coal mines yielded regularly double quantities, with the same\nlabour, we should be so much the richer; hence it might be inferred,\nthat if the quantity of gold and silver in the world were diminished\none-half, or were doubled, like results would follow; the utility of\nthese metals, for the purposes of coin, being very great. Now there are\nmany points of resemblance and many of difference, between the precious\nmetals on the one hand, and corn, coal, &c., on the other; but the\nimportant circumstance to the supposed argument is, that the _utility_\nof gold and silver (as coin, which is far the chief) _depends on their\nvalue_, which is regulated by their scarcity; or rather, to speak\nstrictly, by the difficulty of obtaining them; whereas, if corn and coal\nwere ten times as abundant (_i.e._ more easily obtained), a bushel of\neither would still be as useful as now. But if it were twice as easy to\nprocure gold as it is, a sovereign would be twice as large; if only half\nas easy it would be of the size of a half-sovereign, and this (besides\nthe trifling circumstance of the cheapness or dearness of gold\nornaments) would be all the difference. The analogy, therefore, fails in\nthe point essential to the argument.\"\n\nThe same author notices, after Bishop Copleston, the case of False\nAnalogy which consists in inferring from the similarity in many respects\nbetween the metropolis of a country and the heart of the animal body,\nthat the increased size of the metropolis is a disease.\n\nSome of the false analogies on which systems of physics were confidently\ngrounded in the time of the Greek philosophers, are such as we now call\nfanciful, not that the resemblances are not often real, but that it is\nlong since any one has been inclined to draw from them the inferences\nwhich were then drawn. Such, for instance, are the curious speculations\nof the Pythagoreans on the subject of numbers. Finding that the\ndistances of the planets bore or seemed to bear to one another a\nproportion not varying much from that of the divisions of the monochord,\nthey inferred from it the existence of an inaudible music, that of the\nspheres: as if the music of a harp had depended solely on the numerical\nproportions, and not on the material, nor even on the existence of any\nmaterial, any strings at all. It has been similarly imagined that\ncertain combinations of numbers, which were found to prevail in some\nnatural phenomena, must run through the whole of nature: as that there\nmust be four elements, because there are four possible combinations of\nhot and cold, wet and dry; that there must be seven planets, because\nthere were seven metals, and even because there were seven days of the\nweek. Kepler himself thought that there could be only six planets\nbecause there were only five regular solids. With these we may class the\nreasonings, so common in the speculations of the ancients, founded on a\nsupposed _perfection_ in nature: meaning by nature the customary order\nof events as they take place of themselves without human interference.\nThis also is a rude guess at an analogy supposed to pervade all\nphenomena, however dissimilar. Since what was thought to be perfection\nappeared to obtain in some phenomena, it was inferred (in opposition to\nthe plainest evidence) to obtain in all. \"We always suppose that which\nis better to take place in nature, if it be possible,\" says Aristotle:\nand the vaguest and most heterogeneous qualities being confounded\ntogether under the notion of being _better_, there was no limit to the\nwildness of the inferences. Thus, because the heavenly bodies were\n\"perfect,\" they must move in circles and uniformly. For \"they\" (the\nPythagoreans) \"would not allow,\" says Geminus,[30] \"of any such disorder\namong divine and eternal things, as that they should sometimes move\nquicker and sometimes slower, and sometimes stand still; for no one\nwould tolerate such anomaly in the movements even of a man, who was\ndecent and orderly. The occasions of life, however, are often reasons\nfor men going quicker or slower; but in the incorruptible nature of the\nstars, it is not possible that any cause can be alleged of quickness or\nslowness.\" It is seeking an argument of analogy very far, to suppose\nthat the stars must observe the rules of decorum in gait and carriage,\nprescribed for themselves by the long-bearded philosophers satirized by\nLucian.\n\nAs late as the Copernican controversy it was urged as an argument in\nfavour of the true theory of the solar system, that it placed the fire,\nthe noblest element, in the centre of the universe. This was a remnant\nof the notion that the order of nature must be perfect, and that\nperfection consisted in conformity to rules of precedency in dignity,\neither real or conventional. Again, reverting to numbers: certain\nnumbers were _perfect_, therefore those numbers must obtain in the great\nphenomena of nature. Six was a perfect number, that is, equal to the sum\nof all its factors; an additional reason why there must be exactly six\nplanets. The Pythagoreans, on the other hand, attributed perfection to\nthe number ten; but agreed in thinking that the perfect number must be\nsomehow realized in the heavens; and knowing only of nine heavenly\nbodies, to make up the enumeration, they asserted \"that there was an\n_antichthon_ or counter-earth, on the other side of the sun, invisible\nto us.\"[31] Even Huygens was persuaded that when the number of the\nheavenly bodies had reached twelve, it could not admit of any further\nincrease. Creative power could not go beyond that sacred number.\n\nSome curious instances of false analogy are to be found in the arguments\nof the Stoics to prove the equality of all crimes, and the equal\nwretchedness of all who had not realized their idea of perfect virtue.\nCicero, towards the end of his Fourth Book _De Finibus_, states some of\nthese as follows. \"Ut, inquit, in fidibus plurimis, si nulla earum ita\ncontenta numeris sit, ut concentum servare possit, omnes \u00e6que incontent\u00e6\nsunt; sic peccata, quia discrepant, \u00e6que discrepant; paria sunt igitur.\"\nTo which Cicero himself aptly answers, \"\u00e6que contingit omnibus fidibus,\nut incontent\u00e6 sint; illud non continuo, ut \u00e6que incontent\u00e6.\" The Stoic\nresumes: \"Ut enim, inquit, gubernator \u00e6que peccat, si palcarum navem\nevertit, et si auri; item \u00e6que peccat qui parentem, et qui servum,\ninjuri\u00e2 verberat;\" assuming, that because the magnitude of the interest\nat stake makes no difference in the mere defect of skill, it can make\nnone in the moral defect: a false analogy. Again, \"Quis ignorat, si\nplures ex alto emergere velint, propius fore eos quidem ad respirandum,\nqui ad summam jam aquam appropinquant, sed nihilo magis respirare posse,\nquam eos, qui sunt in profundo? Nihil ergo adjuvat procedere, et\nprogredi in virtute, quominus miserrimus sit, antequam ad eam\npervenerit, quoniam in aqu\u00e2 nihil adjuvat: et quoniam catuli, qui jam\ndespecturi sunt, c\u00e6ci \u00e6que, et ii qui modo nati; Platonem quoque necesse\nest, quoniam nondum videbat sapientiam, \u00e6que c\u00e6cum animo, ac Phalarim\nfuisse.\" Cicero, in his own person, combats these false analogies by\nother analogies tending to an opposite conclusion. \"Ista similia non\nsunt, Cato.... Illa sunt similia; hebes acies est cuipiam oculorum:\ncorpore alius languescit: hi curatione adhibit\u00e2 levantur in dies: alter\nvalet plus quotidie: alter videt. Hi similes sunt omnibus, qui virtuti\nstudent; levantur vitiis, levantur erroribus.\"\n\n\n\u00a7 7. In these and all other arguments drawn from remote analogies, and\nfrom metaphors, which are cases of analogy, it is apparent (especially\nwhen we consider the extreme facility of raising up contrary analogies\nand conflicting metaphors) that so far from the metaphor or analogy\nproving anything, the applicability of the metaphor is the very thing to\nbe made out. It has to be shown that in the two cases asserted to be\nanalogous, the same law is really operating; that between the known\nresemblance and the inferred one there is some connexion by means of\ncausation. Cicero and Cato might have bandied opposite analogies for\never; it rested with each of them to prove by just induction, or at\nleast to render probable, that the case resembled the one set of\nanalogous cases and not the other, in the circumstances on which the\ndisputed question really hinged. Metaphors, for the most part,\ntherefore, assume the proposition which they are brought to prove:\ntheir use is, to aid the apprehension of it; to make clearly and vividly\ncomprehended what it is that the person who employs the metaphor is\nproposing to make out; and sometimes also, by what media he proposes to\ndo so. For an apt metaphor, though it cannot prove, often suggests the\nproof.\n\nFor instance, when D'Alembert (I believe) remarked that in certain\ngovernments, only two creatures find their way to the highest places,\nthe eagle and the serpent; the metaphor not only conveys with great\nvividness the assertion intended, but contributes towards substantiating\nit, by suggesting, in a lively manner, the means by which the two\nopposite characters thus typified effect their rise. When it is said\nthat a certain person misunderstands another because the lesser of two\nobjects cannot comprehend the greater, the application of what is true\nin the literal sense of the word _comprehend_, to its metaphorical\nsense, points to the fact which is the ground and justification of the\nassertion, viz. that one mind cannot thoroughly understand another\nunless it can contain it in itself, that is, unless it possesses all\nthat is contained in the other. When it is urged as an argument for\neducation, that if the soil is left uncultivated, weeds will spring up,\nthe metaphor, though no proof, but a statement of the thing to be\nproved, states it in terms which, by suggesting a parallel case, put the\nmind upon the track of the real proof. For, the reason why weeds grow in\nan uncultivated soil, is that the seeds of worthless products exist\neverywhere, and can germinate and grow in almost all circumstances,\nwhile the reverse is the case with those which are valuable; and this\nbeing equally true of mental products, this mode of conveying an\nargument, independently of its rhetorical advantages, has a logical\nvalue; since it not only suggests the grounds of the conclusion, but\npoints to another case in which those grounds have been found, or at\nleast deemed to be, sufficient.\n\nOn the other hand, when Bacon, who is equally conspicuous in the use and\nabuse of figurative illustration, says that the stream of time has\nbrought down to us only the least valuable part of the writings of the\nancients, as a river carries froth and straws floating on its surface,\nwhile more weighty objects sink to the bottom; this, even if the\nassertion illustrated by it were true, would be no good illustration,\nthere being no parity of cause. The levity by which substances float on\na stream, and the levity which is synonymous with worthlessness, have\nnothing in common except the name; and (to show how little value there\nis in the metaphor) we need only change the word into _buoyancy_, to\nturn the semblance of argument involved in Bacon's illustration against\nhimself.\n\nA metaphor, then, is not to be considered as an argument, but as an\nassertion that an argument exists; that a parity subsists between the\ncase from which the metaphor is drawn and that to which it is applied.\nThis parity may exist though the two cases be apparently very remote\nfrom one another; the only resemblance existing between them may be a\nresemblance of relations, an analogy in Ferguson's and Archbishop\nWhately's sense: as in the preceding instance, in which an illustration\nfrom agriculture was applied to mental cultivation.\n\n\n\u00a7 8. To terminate the subject of Fallacies of Generalization, it remains\nto be said, that the most fertile source of them is bad classification:\nbringing together in one group, and under one name, things which have no\ncommon properties, or none but such as are too unimportant to allow\ngeneral propositions of any considerable value to be made respecting the\nclass. The misleading effect is greatest, when a word which in common\nuse expresses some definite fact, is extended by slight links of\nconnexion to cases in which that fact does not exist, but some other or\nothers, only slightly resembling it. Thus Bacon,[32] in speaking of the\n_Idola_ or Fallacies arising from notions _temere et in\u00e6qualiter \u00e0 rebus\nabstract\u00e6_, exemplifies them by the notion of Humidum or Wet, so\nfamiliar in the physics of antiquity and of the middle ages. \"Invenietur\nverbum istud, Humidum, nihil aliud quam nota confusa diversarum\nactionum, qu\u00e6 nullam constantiam aut reductionem patiuntur. Significat\nenim, et quod circa aliud corpus facile se circumfundit; et quod in se\nest indeterminabile, nec consistere potest; et quod facile cedit\nundique; et quod facile se dividit et dispergit; et quod facile se unit\net colligit; et quod facile fluit, et in motu ponitur; et quod alteri\ncorpori facile adh\u00e6ret, idque madefacit; et quod facile reducitur in\nliquidum, sive colliquatur, cum antea consisteret. Itaque quum ad hujus\nnominis pr\u00e6dicationem et impositionem ventum sit; si alia accipias,\nflamma humida est; si alia accipias, aer humidus non est; si alia,\npulvis minutus humidus est; si alia, vitrum humidum est: ut facile\nappareat, istam notionem ex aqu\u00e2 tantum, et communibus et vulgaribus\nliquoribus, absque ull\u00e2 debit\u00e2 verificatione, temere abstractam esse.\"\n\nBacon himself is not exempt from a similar accusation when inquiring\ninto the nature of heat: where he occasionally proceeds like one who\nseeking for the cause of hardness, after examining that quality in iron,\nflint, and diamond, should expect to find that it is something which can\nbe traced also in hard water, a hard knot, and a hard heart.\n\nThe word [Greek: kin\u00easis] in the Greek philosophy, and the words\nGeneration and Corruption both then and long afterwards, denoted such a\nmultitude of heterogeneous phenomena, that any attempt at philosophizing\nin which those words were used was almost as necessarily abortive as if\nthe word _hard_ had been taken to denote a class including all the\nthings mentioned above. [Greek: Kin\u00easis], for instance, which properly\nsignified motion, was taken to denote not only all motion but even all\nchange: [Greek: alloi\u00f4sis] being recognised as one of the modes of\n[Greek: kin\u00easis]. The effect was, to connect with every form of [Greek:\nalloi\u00f4sis] or change, ideas drawn from motion in the proper and literal\nsense, and which had no real connexion with any other kind of [Greek:\nkin\u00easis] than that. Aristotle and Plato laboured under a continual\nembarrassment from this misuse of terms. But if we proceed further in\nthis direction we shall encroach upon the Fallacy of Ambiguity, which\nbelongs to a different class, the last in order of our classification,\nFallacies of Confusion.\n\n\n\n\nCHAPTER VI.\n\nFALLACIES OF RATIOCINATION.\n\n\n\u00a7 1. We have now, in our progress through the classes of Fallacies,\narrived at those to which, in the common books of logic, the appellation\nis in general exclusively appropriated; those which have their seat in\nthe ratiocinative or deductive part of the investigation of truth. On\nthese fallacies it is the less necessary for us to insist at any length,\nas they have been most satisfactorily treated in a work familiar to\nalmost all, in this country at least, who feel any interest in these\nspeculations, Archbishop Whately's _Logic_. Against the more obvious\nforms of this class of fallacies, the rules of the syllogism are a\ncomplete protection. Not (as we have so often said) that the\nratiocination cannot be good unless it be in the form of a syllogism;\nbut that, by showing it in that form, we are sure to discover if it be\nbad, or at least if it contain any fallacy of this class.\n\n\n\u00a7 2. Among Fallacies of Ratiocination, we ought perhaps to include the\nerrors committed in processes which have the appearance only, not the\nreality, of an inference from premises; the fallacies connected with the\nconversion and \u00e6quipollency of propositions. I believe errors of this\ndescription to be far more frequently committed than is generally\nsupposed, or than their extreme obviousness might seem to admit of. For\nexample, the simple conversion of an universal affirmative proposition,\nAll A are B, therefore all B are A, I take to be a very common form of\nerror: though committed, like many other fallacies, oftener in the\nsilence of thought than in express words, for it can scarcely be clearly\nenunciated without being detected. And so with another form of fallacy,\nnot substantially different from the preceding: the erroneous\nconversion of an hypothetical proposition. The proper converse of an\nhypothetical proposition is this: If the consequent be false, the\nantecedent is false; but this, If the consequent be true, the antecedent\nis true, by no means holds good, but is an error corresponding to the\nsimple conversion of an universal affirmative. Yet hardly anything is\nmore common than for people, in their private thoughts, to draw this\ninference. As when the conclusion is accepted, which it so often is, for\nproof of the premises. That the premises cannot be true if the\nconclusion is false, is the unexceptionable foundation of the legitimate\nmode of reasoning called a _reductio ad absurdum_. But people\ncontinually think and express themselves, as if they also believed that\nthe premises cannot be false if the conclusion is true. The truth, or\nsupposed truth, of the inferences which follow from a doctrine, often\nenables it to find acceptance in spite of gross absurdities in it. How\nmany philosophical systems which had scarcely any intrinsic\nrecommendation, have been received by thoughtful men because they were\nsupposed to lend additional support to religion, morality, some\nfavourite view of politics, or some other cherished persuasion: not\nmerely because their wishes were thereby enlisted on its side, but\nbecause its leading to what they deemed sound conclusions appeared to\nthem a strong presumption in favour of its truth: though the\npresumption, when viewed in its true light, amounted only to the absence\nof that particular evidence of falsehood, which would have resulted from\nits leading by correct inference to something already known to be false.\n\nAgain, the very frequent error in conduct, of mistaking reverse of wrong\nfor right, is the practical form of a logical error with respect to the\nOpposition of Propositions. It is committed for want of the habit of\ndistinguishing the _contrary_ of a proposition from the _contradictory_\nof it, and of attending to the logical canon, that contrary\npropositions, though they cannot both be true, may both be false. If the\nerror were to express itself in words, it would run distinctly counter\nto this canon. It generally, however, does not so express itself, and\nto compel it to do so is the most effectual method of detecting and\nexposing it.\n\n\n\u00a7 3. Among Fallacies of Ratiocination are to be ranked in the first\nplace, all the cases of vicious syllogism laid down in the books. These\ngenerally resolve themselves into having more than three terms to the\nsyllogism, either avowedly, or in the covert mode of an undistributed\nmiddleterm, or an _illicit process_ of one of the two extremes. It is\nnot, indeed, very easy fully to convict an argument of falling under any\none of these vicious cases in particular; for the reason already more\nthan once referred to, that the premises are seldom formally set out: if\nthey were, the fallacy would impose upon nobody; and while they are not,\nit is almost always to a certain degree optional in what manner the\nsuppressed link shall be filled up. The rules of the syllogism are rules\nfor compelling a person to be aware of the whole of what he must\nundertake to defend if he persists in maintaining his conclusion. He has\nit almost always in his power to make his syllogism good by introducing\na false premise; and hence it is scarcely ever possible decidedly to\naffirm that any argument involves a bad syllogism: but this detracts\nnothing from the value of the syllogistic rules, since it is by them\nthat a reasoner is compelled distinctly to make his election what\npremises he is prepared to maintain. The election made, there is\ngenerally so little difficulty in seeing whether the conclusion follows\nfrom the premises set out, that we might without much logical\nimpropriety have merged this fourth class of fallacies in the fifth, or\nFallacies of Confusion.\n\n\n\u00a7 4. Perhaps, however, the commonest, and certainly the most dangerous\nfallacies of this class, are those which do not lie in a single\nsyllogism, but slip in between one syllogism and another in a chain of\nargument, and are committed by _changing the premises_. A proposition is\nproved, or an acknowledged truth laid down, in the first part of an\nargumentation, and in the second a further argument is founded not on\nthe same proposition, but on some other, resembling it sufficiently to\nbe mistaken for it. Instances of this fallacy will be found in almost\nall the argumentative discourses of unprecise thinkers; and we need only\nhere advert to one of the obscurer forms of it, recognised by the\nschoolmen as the fallacy _\u00e0 dicto secundum quid ad dictum simpliciter_.\nThis is committed when, in the premises, a proposition is asserted with\na qualification, and the qualification lost sight of in the conclusion;\nor oftener, when a limitation or condition, though not asserted, is\nnecessary to the truth of the proposition, but is forgotten when that\nproposition comes to be employed as a premise. Many of the bad arguments\nin vogue belong to this class of error. The premise is some admitted\ntruth, some common maxim, the reasons or evidence for which have been\nforgotten, or are not thought of at the time, but if they had been\nthought of would have shown the necessity of so limiting the premise\nthat it would no longer have supported the conclusion drawn from it.\n\nOf this nature is the fallacy in what is called, by Adam Smith and\nothers, the Mercantile Theory in Political Economy. That theory sets out\nfrom the common maxim, that whatever brings in money enriches; or that\nevery one is rich in proportion to the quantity of money he obtains.\nFrom this it is concluded that the value of any branch of trade, or of\nthe trade of the country altogether, consists in the balance of money it\nbrings in; that any trade which carries more money out of the country\nthan it draws into it is a losing trade; that therefore money should be\nattracted into the country and kept there, by prohibitions and bounties:\nand a train of similar corollaries. All for want of reflecting that if\nthe riches of an individual are in proportion to the quantity of money\nhe can command, it is because that is the measure of his power of\npurchasing money's worth; and is therefore subject to the proviso that\nhe is not debarred from employing his money in such purchases. The\npremise, therefore, is only true _secundum quid_; but the theory assumes\nit to be true absolutely, and infers that increase of money is increase\nof riches, even when produced by means subversive of the condition under\nwhich alone money can be riches.\n\nA second instance is, the argument by which it used to be contended,\nbefore the commutation of tithe, that tithes fell on the landlord, and\nwere a deduction from rent; because the rent of tithe-free land was\nalways higher than that of land of the same quality, and the same\nadvantages of situation, subject to tithe. Whether it be true or not\nthat a tithe falls on rent, a treatise on Logic is not the place to\nexamine; but it is certain that this is no proof of it. Whether the\nproposition be true or false, tithe-free land must, by the necessity of\nthe case, pay a higher rent. For if tithes do not fall on rent, it must\nbe because they fall on the consumer; because they raise the price of\nagricultural produce. But if the produce be raised in price, the farmer\nof tithe-free as well as the farmer of tithed land gets the benefit. To\nthe latter the rise is but a compensation for the tithe he pays; to the\nfirst, who pays none, it is clear gain, and therefore enables him, and\nif there be freedom of competition forces him, to pay so much more rent\nto his landlord. The question remains, to what class of fallacies this\nbelongs. The premise is, that the owner of tithed land receives less\nrent than the owner of tithe-free land; the conclusion is, that\ntherefore he receives less than he himself would receive if tithe were\nabolished. But the premise is only true conditionally; the owner of\ntithed land receives less than what the owner of tithe-free land is\nenabled to receive _when other lands are tithed_; while the conclusion\nis applied to a state of circumstances in which that condition fails,\nand in which, by consequence, the premise would not be true. The\nfallacy, therefore, is _\u00e0 dicto secundum quid ad dictum simpliciter_.\n\nA third example is the opposition sometimes made to legitimate\ninterferences of government in the economical affairs of society,\ngrounded on a misapplication of the maxim, that an individual is a\nbetter judge than the government, of what is for his own pecuniary\ninterest. This objection was urged to Mr. Wakefield's principle of\ncolonization; the concentration of the settlers, by fixing such a price\non unoccupied land as may preserve the most desirable proportion between\nthe quantity of land in culture, and the labouring population. Against\nthis it was argued, that if individuals found it for their advantage to\noccupy extensive tracts of land, they, being better judges of their own\ninterest than the legislature (which can only proceed on general rules)\nought not to be restrained from doing so. But in this argument it was\nforgotten that the fact of a person's taking a large tract of land is\nevidence only that it is his interest to take as much as other people,\nbut not that it might not be for his interest to content himself with\nless, if he could be assured that other people would do so too; an\nassurance which nothing but a government regulation can give. If all\nother people took much, and he only a little, he would reap none of the\nadvantages derived from the concentration of the population and the\nconsequent possibility of procuring labour for hire, but would have\nplaced himself, without equivalent, in a situation of voluntary\ninferiority. The proposition, therefore, that the quantity of land which\npeople will take when left to themselves is that which is most for their\ninterest to take, is true only _secundum quid_: it is only their\ninterest while they have no guarantee for the conduct of one another.\nBut the arrangement disregards the limitation, and takes the proposition\nfor true _simpliciter_.\n\nOne of the conditions oftenest dropped, when what would otherwise be a\ntrue proposition is employed as a premise for proving others, is the\ncondition of _time_. It is a principle of political economy that prices,\nprofits, wages, &c. \"always find their level;\" but this is often\ninterpreted as if it meant that they are always, or generally, _at_\ntheir level; while the truth is, as Coleridge epigrammatically expresses\nit, that they are always _finding_ their level, \"which might be taken as\na paraphrase or ironical definition of a storm.\"\n\nUnder the same head of fallacy (_\u00e0 dicto secundum quid ad dictum\nsimpliciter_) might be placed all the errors which are vulgarly called\nmisapplications of abstract truths: that is, where a principle, true (as\nthe common expression is) _in the abstract_, that is, all modifying\ncauses being supposed absent, is reasoned on as if it were true\nabsolutely, and no modifying circumstance could ever by possibility\nexist. This very common form of error it is not requisite that we\nshould exemplify here, as it will be particularly treated of hereafter\nin its application to the subjects on which it is most frequent and most\nfatal, those of politics and society.[33]\n\n\n\n\nCHAPTER VII.\n\nFALLACIES OF CONFUSION.\n\n\n\u00a7 1. Under this fifth and last class it is convenient to arrange all\nthose fallacies, in which the source of error is not so much a false\nestimate of the probative force of known evidence, as an indistinct,\nindefinite, and fluctuating conception of what the evidence is.\n\nAt the head of these stands that multitudinous body of fallacious\nreasonings, in which the source of error is the ambiguity of terms: when\nsomething which is true if a word be used in a particular sense, is\nreasoned on as if it were true in another sense. In such a case there is\nnot a mal-estimation of evidence, because there is not properly any\nevidence to the point at all; there is evidence, but to a different\npoint, which from a confused apprehension of the meaning of the terms\nused, is supposed to be the same. This error will naturally be oftener\ncommitted in our ratiocinations than in our direct inductions, because\nin the former we are deciphering our own or other people's notes, while\nin the latter we have the things themselves present, either to the\nsenses or to the memory. Except, indeed, when the induction is not from\nindividual cases to a generality, but from generalities to a still\nhigher generalization; in that case the fallacy of ambiguity may affect\nthe inductive process as well as the ratiocinative. It occurs in\nratiocination in two ways: when the middleterm is ambiguous, or when one\nof the terms of the syllogism is taken in one sense in the premises, and\nin another sense in the conclusion.\n\nSome good exemplifications of this fallacy are given by Archbishop\nWhately. \"One case,\" says he, \"which may be regarded as coming under the\nhead of Ambiguous Middle, is (what I believe logical writers mean by\n'_Fallacia Figur\u00e6 Dictionis_,') the fallacy built on the grammatical\nstructure of language, from men's usually taking for granted that\n_paronymous_ (or _conjugate_) words, _i.e._ those belonging to each\nother, as the substantive, adjective, verb, &c. of the same root, have a\nprecisely corresponding meaning; which is by no means universally the\ncase. Such a fallacy could not indeed be even exhibited in strict\nlogical form, which would preclude even the attempt at it, since it has\ntwo middleterms in sound as well as sense. But nothing is more common in\npractice than to vary continually the terms employed, with a view to\ngrammatical convenience; nor is there anything unfair in such a\npractice, as long as the _meaning_ is preserved unaltered; _e.g._\n'murder should be punished with death; this man is a murderer, therefore\nhe deserves to die,' &c. Here we proceed on the assumption (in this case\njust) that to commit murder, and to be a murderer,--to deserve death,\nand to be one who ought to die, are, respectively, equivalent\nexpressions; and it would frequently prove a heavy inconvenience to be\ndebarred this kind of liberty; but the abuse of it gives rise to the\nFallacy in question: _e.g._ _projectors_ are unfit to be trusted; this\nman has formed a _project_, therefore he is unfit to be trusted: here\nthe sophist proceeds on the hypothesis that he who forms a _project_\nmust be a _projector_: whereas the bad sense that commonly attaches to\nthe latter word, is not at all implied in the former. This fallacy may\noften be considered as lying not in the Middle, but in one of the terms\nof the Conclusion; so that the conclusion drawn shall not be, in\nreality, at all warranted by the premises, though it will appear to be\nso, by means of the grammatical affinity of the words: _e.g._ to be\nacquainted with the guilty is a _presumption_ of guilt; this man is so\nacquainted, therefore we may _presume_ that he is guilty: this argument\nproceeds on the supposition of an exact correspondence between _presume_\nand _presumption_, which, however, does not really exist; for\n'presumption' is commonly used to express a kind of _slight suspicion_;\nwhereas, 'to presume' amounts to actual belief. There are innumerable\ninstances of a non-correspondence in paronymous words, similar to that\nabove instanced; as between _art_ and _artful_, _design_ and\n_designing_, _faith_ and _faithful_, &c.; and the more slight the\nvariation of the meaning, the more likely is the fallacy to be\nsuccessful; for when the words have become so widely removed in sense as\n'pity' and 'pitiful,' every one would perceive such a fallacy, nor could\nit be employed but in jest.[34]\n\n\"The present Fallacy is nearly allied to, or rather, perhaps, may be\nregarded as a branch of, that founded on _etymology_; viz. when a term\nis used, at one time in its customary, and at another in its\netymological sense. Perhaps no example of this can be found that is more\nextensively and mischievously employed than in the case of the word\n_representative_: assuming that its right meaning must correspond\nexactly with the strict and original sense of the verb 'represent,' the\nsophist persuades the multitude, that a member of the House of Commons\nis bound to be guided in all points by the opinion of his constituents;\nand, in short, to be merely their _spokesman_; whereas law and custom,\nwhich in this case may be considered as fixing the meaning of the term,\nrequire no such thing, but enjoin the representative to act according to\nthe best of his _own_ judgment, and on his own responsibility.\"\n\nThe following are instances of great practical importance, in which\narguments are habitually founded on a verbal ambiguity.\n\nThe mercantile public are frequently led into this fallacy by the\nphrase, \"scarcity of money.\" In the language of commerce \"money\" has two\nmeanings: _currency_, or the circulating medium; and _capital seeking\ninvestment_, especially investment on loan. In this last sense the word\nis used when the \"money market\" is spoken of, and when the \"value of\nmoney\" is said to be high or low, the rate of interest being meant. The\nconsequence of this ambiguity is, that as soon as scarcity of money in\nthe latter of these senses begins to be felt,--as soon as there is\ndifficulty of obtaining loans, and the rate of interest is high,--it is\nconcluded that this must arise from causes acting upon the quantity of\nmoney in the other and more popular sense; that the circulating medium\nmust have diminished in quantity, or ought to be increased. I am aware\nthat, independently of the double meaning of the term, there are in\nfacts themselves some peculiarities, giving an apparent support to this\nerror; but the ambiguity of the language stands on the very threshold of\nthe subject, and intercepts all attempts to throw light upon it.\n\nAnother ambiguous expression which continually meets us in the political\ncontroversies of the present time, especially in those which relate to\norganic changes, is the phrase \"influence of property:\" which is\nsometimes used for the influence of respect for superior intelligence,\nor gratitude for the kind offices which persons of large property have\nit so much in their power to bestow; at other times for the influence of\nfear; fear of the worst sort of power, which large property also gives\nto its possessor, the power of doing mischief to dependents. To confound\nthese two, is the standing fallacy of ambiguity brought against those\nwho seek to purify the electoral system from corruption and\nintimidation. Persuasive influence, acting through the conscience of the\nvoter, and carrying his heart and mind with it, is beneficial--therefore\n(it is pretended) coercive influence, which compels him to forget that\nhe is a moral agent, or to act in opposition to his moral convictions,\nought not to be placed under restraint.\n\nAnother word which is often turned into an instrument of the fallacy of\nambiguity, is Theory. In its most proper acceptation, theory means the\ncompleted result of philosophical induction from experience. In that\nsense, there are erroneous as well as true theories, for induction may\nbe incorrectly performed, but theory of some sort is the necessary\nresult of knowing anything of a subject, and having put one's knowledge\ninto the form of general propositions for the guidance of practice. In\nthis, the proper sense of the word, Theory is the explanation of\npractice. In another and a more vulgar sense, theory means any mere\nfiction of the imagination, endeavouring to conceive how a thing may\npossibly have been produced, instead of examining how it was produced.\nIn this sense only are theory, and theorists, unsafe guides; but because\nof this, ridicule or discredit is attempted to be attached to theory in\nits proper sense, that is, to legitimate generalization, the end and aim\nof all philosophy; and a conclusion is represented as worthless, just\nbecause that has been done, which if done correctly, constitutes the\nhighest worth that a principle for the guidance of practice can possess,\nnamely, to comprehend in a few words the real law on which a phenomenon\ndepends, or some property or relation which is universally true of it.\n\n\"The Church\" is sometimes understood to mean the clergy alone, sometimes\nthe whole body of believers, or at least of communicants. The\ndeclamations respecting the inviolability of church property are\nindebted for the greater part of their apparent force to this ambiguity.\nThe clergy, being called the church, are supposed to be the real owners\nof what is called church property; whereas they are in truth only the\nmanaging members of a much larger body of proprietors, and enjoy on\ntheir own part a mere usufruct, not extending beyond a life interest.\n\nThe following is a Stoical argument taken from Cicero _De Finibus_, book\nthe third: \"Quod est bonum, omne laudabile est. Quod autem laudabile\nest, omne honestum est. Bonum igitur quod est, honestum est.\" Here the\nambiguous word is _laudabile_, which in the minor premise means anything\nwhich mankind are accustomed, on good grounds, to admire or value; as\nbeauty, for instance, or good fortune: but in the major, it denotes\nexclusively moral qualities. In much the same manner the Stoics\nendeavoured logically to justify as philosophical truths, their\nfigurative and rhetorical expressions of ethical sentiment: as that the\nvirtuous man is alone free, alone beautiful, alone a king, &c. Whoever\nhas virtue has Good (because it has been previously determined not to\ncall anything else good); but, again, Good necessarily includes\nfreedom, beauty, and even kingship, all these being good things;\ntherefore whoever has virtue has all these.\n\nThe following is an argument of Descartes to prove, in his _\u00e0 priori_\nmanner, the being of a God. The conception, says he, of an infinite\nBeing proves the real existence of such a being. For if there is not\nreally any such being, _I_ must have made the conception; but if I could\nmake it, I can also unmake it; which evidently is not true; therefore\nthere must be, externally to myself, an archetype, from which the\nconception was derived. In this argument (which, it may be observed,\nwould equally prove the real existence of ghosts and of witches) the\nambiguity is in the pronoun _I_, by which, in one place, is to be\nunderstood my _will_, in another the _laws of my nature_. If the\nconception, existing as it does in my mind, had no original without, the\nconclusion would unquestionably follow that _I_ made it; that is, the\nlaws of my nature must have somehow evolved it: but that my _will_ made\nit, would not follow. Now when Descartes afterwards adds that I cannot\nunmake the conception, he means that I cannot get rid of it by an act of\nmy will: which is true, but is not the proposition required. I can as\nmuch unmake this conception as I can any other: no conception which I\nhave once had, can I ever dismiss by mere volition: but what some of the\nlaws of my nature have produced, other laws, or those same laws in other\ncircumstances, may, and often do, subsequently efface.\n\nAnalogous to this are some of the ambiguities in the free-will\ncontroversy; which, as they will come under special consideration in the\nconcluding Book, I only mention _memori\u00e6 caus\u00e2_. In that discussion,\ntoo, the word _I_ is often shifted from one meaning to another, at one\ntime standing for my volitions, at another time for the actions which\nare the consequences of them, or the mental dispositions from which they\nproceed. The latter ambiguity is exemplified in an argument of Coleridge\n(in his _Aids to Reflection_), in support of the freedom of the will. It\nis not true, he says, that a man is governed by motives; \"the man makes\nthe motive, not the motive the man;\" the proof being that \"what is a\nstrong motive to one man is no motive at all to another.\" The premise is\ntrue, but only amounts to this, that different persons have different\ndegrees of susceptibility to the same motive; as they have also to the\nsame intoxicating liquid, which however does not prove that they are\nfree to be drunk or not drunk, whatever quantity of the fluid they may\ndrink. What is proved is, that certain mental conditions in the person\nhimself, must co-operate, in the production of the act, with the\nexternal inducement: but those mental conditions also are the effect of\ncauses; and there is nothing in the argument to prove that they can\narise without a cause--that a spontaneous determination of the will,\nwithout any cause at all, ever takes place, as the free-will doctrine\nsupposes.\n\nThe double use, in the free-will controversy, of the word Necessity,\nwhich sometimes stands only for Certainty, at other times for\nCompulsion; sometimes for what _cannot_ be prevented, at other times\nonly for what we have reason to be assured _will_ not; we shall have\noccasion hereafter to pursue to some of its ulterior consequences.\n\nA most important ambiguity, both in common and in metaphysical language,\nis thus pointed out by Archbishop Whately in the Appendix to his Logic:\n\"_Same_ (as well as _One_, _Identical_, and other words derived from\nthem,) is used frequently in a sense very different from its primary\none, as applicable to a _single_ object; being employed to denote great\n_similarity_. When several objects are undistinguishably alike, _one\nsingle description_ will apply equally to any of them; and thence they\nare said to be all of _one and the same_ nature, appearance, &c. As,\n_e.g._ when we say 'this house is built of the _same_ stone with such\nanother,' we only mean that the stones are undistinguishable in their\nqualities; not that the one building was pulled down, and the other\nconstructed with the materials. Whereas _sameness_, in the primary\nsense, does not even necessarily imply similarity; for if we say of any\nman that he is greatly altered since such a time, we understand, and\nindeed imply by the very expression, that he is _one person_, though\ndifferent in several qualities. It is worth observing also, that Same,\nin the secondary sense, admits, according to popular usage, of degrees:\nwe speak of two things being _nearly_ the same, but not entirely:\npersonal identity does not admit of degrees. Nothing, perhaps, has\ncontributed more to the error of Realism than inattention to this\nambiguity. When several persons are said to have _one and the same_\nopinion, thought, or idea, many men, overlooking the true simple\nstatement of the case, which is, that they are _all thinking alike_,\nlook for something more abstruse and mystical, and imagine there must be\nsome _One Thing_, in the primary sense, though not an individual, which\nis present at once in the mind of each of these persons; and thence\nreadily sprung Plato's theory of Ideas, each of which was, according to\nhim, one real, eternal object, existing entire and complete in each of\nthe individual objects that are known by one name.\"\n\nIt is, indeed, not a matter of inference but of authentic history, that\nPlato's doctrine of Ideas, and the Aristotelian doctrine (in this\nrespect similar to the Platonic) of substantial forms and second\nsubstances, grew up in the precise way here pointed out; from the\nsupposed necessity of finding, in things which were said to have the\n_same_ nature, or the _same_ qualities, something which was the _same_\nin the very sense in which a man is the same as himself. All the idle\nspeculations respecting [Greek: to on, to hen, to homoion], and similar\nabstractions, so common in the ancient and in some modern schools of\nthought, sprang from the same source. The Aristotelian logicians saw,\nhowever, one case of the ambiguity, and provided against it with their\npeculiar felicity in the invention of technical language, when they\ndistinguished things which differed both _specie_ and _numero_, from\nthose which differed _numero tantum_, that is, which were exactly alike\n(in some particular respect at least) but were distinct individuals. An\nextension of this distinction to the two meanings of the word Same,\nnamely, things which are the same _specie tantum_, and a thing which is\nthe same _numero_ as well as _specie_, would have prevented the\nconfusion which has been a source of so much darkness and such an\nabundance of positive error in metaphysical philosophy.\n\nOne of the most singular examples of the length to which a thinker of\neminence may be led away by an ambiguity of language, is afforded by\nthis very case. I refer to the famous argument by which Bishop Berkeley\nflattered himself that he had for ever put an end to \"scepticism,\natheism, and irreligion.\" It is briefly as follows. I thought of a thing\nyesterday; I ceased to think of it; I think of it again to-day. I had,\ntherefore, in my mind yesterday an _idea_ of the object; I have also an\nidea of it to-day; this idea is evidently not another, but the very same\nidea. Yet an intervening time elapsed in which I had it not. Where was\nthe idea during this interval? It must have been somewhere; it did not\ncease to exist; otherwise the idea I had yesterday could not be the\n_same_ idea; no more than the man I see alive to-day can be the same\nwhom I saw yesterday, if the man has died in the meanwhile. Now an idea\ncannot be conceived to exist anywhere except in a mind; and hence there\nmust exist an Universal Mind, in which all ideas have their permanent\nresidence, during the intervals of their conscious presence in our own\nminds.\n\nIt is evident that Berkeley here confounded sameness _numero_ with\nsameness _specie_, that is, with exact resemblance, and assumed the\nformer where there was only the latter; not perceiving that when we say\nwe have the same thought to-day which we had yesterday, we do not mean\nthe same individual thought, but a thought exactly similar: as we say\nthat we have the same illness which we had last year, meaning only the\nsame sort of illness.\n\nIn one remarkable instance the scientific world was divided into two\nfuriously hostile parties by an ambiguity of language affecting a branch\nof science which, more completely than most others, enjoys the advantage\nof a precise and well-defined terminology. I refer to the famous dispute\nrespecting the _vis viva_, the history of which is given at large in\nProfessor Playfair's Dissertation. The question was, whether the _force_\nof a moving body was proportional (its mass being given) to its velocity\nsimply, or to the square of its velocity: and the ambiguity was in the\nword Force. \"One of the effects,\" says Playfair, \"produced by a moving\nbody is proportional to the square of the velocity, while another is\nproportional to the velocity simply:\" from whence clearer thinkers were\nsubsequently led to establish a double measure of the efficiency of a\nmoving power, one being called _vis viva_, and the other _momentum_.\nAbout the facts, both parties were from the first agreed: the only\nquestion was, with which of the two effects the term _force_ should be,\nor could most conveniently be, associated. But the disputants were by no\nmeans aware that this was all; they thought that force was one thing,\nthe production of effects another; and the question, by which set of\neffects the force which produced both the one and the other should be\nmeasured, was supposed to be a question not of terminology but of fact.\n\nThe ambiguity of the word Infinite is the real fallacy in the amusing\nlogical puzzle of Achilles and the Tortoise, a puzzle which has been too\nhard for the ingenuity or patience of many philosophers, and which no\nless a thinker than Sir William Hamilton considered as insoluble; as a\nsound argument, though leading to a palpable falsehood. The fallacy, as\nHobbes hinted, lies in the tacit assumption that whatever is infinitely\ndivisible is infinite; but the following solution, (to the invention of\nwhich I have no claim,) is more precise and satisfactory.\n\nThe argument is, let Achilles run ten times as fast as the tortoise, yet\nif the tortoise has the start, Achilles will never overtake him. For\nsuppose them to be at first separated by an interval of a thousand feet:\nwhen Achilles has run these thousand feet, the tortoise will have got on\na hundred; when Achilles has run those hundred, the tortoise will have\nrun ten, and so on for ever: therefore Achilles may run for ever without\novertaking the tortoise.\n\nNow, the \"for ever,\" in the conclusion, means, for any length of time\nthat can be supposed; but in the premises \"ever\" does not mean any\n_length_ of time: it means any _number of subdivisions_ of time. It\nmeans that we may divide a thousand feet by ten, and that quotient again\nby ten, and so on as often as we please; that there never needs be an\nend to the subdivisions of the distance, nor consequently to those of\nthe time in which it is performed. But an unlimited number of\nsubdivisions may be made of that which is itself limited. The argument\nproves no other infinity of duration than may be embraced within five\nminutes. As long as the five minutes are not expired, what remains of\nthem may be divided by ten, and again by ten, as often as we like, which\nis perfectly compatible with their being only five minutes altogether.\nIt proves, in short, that to pass through this finite space requires a\ntime which is infinitely divisible, but not an infinite time: the\nconfounding of which distinction Hobbes had already seen to be the gist\nof the fallacy.\n\nThe following ambiguities of the word _right_ (in addition to the\nobvious and familiar one of _a_ right and the _adjective_ right) are\nextracted from a forgotten paper of my own, in a periodical:--\n\n\"Speaking morally, you are said to have a right to do a thing, if all\npersons are morally bound not to hinder you from doing it. But, in\nanother sense, to have a right to do a thing is the opposite of having\n_no_ right to do it, _i.e._ of being under a moral obligation to forbear\ndoing it. In this sense, to say that you have a right to do a thing,\nmeans that you may do it without any breach of duty on your part; that\nother persons not only ought not to hinder you, but have no cause to\nthink worse of you for doing it. This is a perfectly distinct\nproposition from the preceding. The right which you have by virtue of a\nduty incumbent upon other persons, is obviously quite a different thing\nfrom a right consisting in the absence of any duty incumbent upon\nyourself. Yet the two things are perpetually confounded. Thus a man will\nsay he has a right to publish his opinions; which may be true in this\nsense, that it would be a breach of duty in any other person to\ninterfere and prevent the publication: but he assumes thereupon, that in\npublishing his opinions, he himself violates no duty; which may either\nbe true or false, depending, as it does, on his having taken due pains\nto satisfy himself, first, that the opinions are true, and next, that\ntheir publication in this manner, and at this particular juncture, will\nprobably be beneficial to the interests of truth on the whole.\n\n\"The second ambiguity is that of confounding a right of any kind, with a\nright to enforce that right by resisting or punishing a violation of it.\nPeople will say, for example, that they have a right to good government,\nwhich is undeniably true, it being the moral duty of their governors to\ngovern them well. But in granting this, you are supposed to have\nadmitted their right or liberty to turn out their governors, and perhaps\nto punish them, for having failed in the performance of this duty;\nwhich, far from being the same thing, is by no means universally true,\nbut depends on an immense number of varying circumstances,\" requiring to\nbe conscientiously weighed before adopting or acting on such a\nresolution. This last example is (like others which have been cited) a\ncase of fallacy within fallacy; it involves not only the second of the\ntwo ambiguities pointed out, but the first likewise.\n\nOne not unusual form of the Fallacy of Ambiguous Terms, is known\ntechnically as the Fallacy of Composition and Division: when the same\nterm is collective in the premises, distributive in the conclusion, or\n_vice vers\u00e2_: or when the middle term is collective in one premise,\ndistributive in the other. As if one were to say (I quote from\nArchbishop Whately) \"All the angles of a triangle are equal to two right\nangles: ABC is an angle of a triangle; therefore ABC is equal to two\nright angles.... There is no fallacy more common, or more likely to\ndeceive, than the one now before us. The form in which it is most\nusually employed is to establish some truth, separately, concerning\n_each single_ member of a certain class, and thence to infer the same of\nthe _whole collectively_.\" As in the argument one sometimes hears, to\nprove that the world could do without great men. If Columbus (it is\nsaid) had never lived, America would still have been discovered, at most\nonly a few years later; if Newton had never lived, some other person\nwould have discovered the law of gravitation; and so forth. Most true:\nthese things would have been done, but in all probability not until\nsome one had again been found with the qualities of Columbus or Newton.\nBecause any one great man might have had his place supplied by other\ngreat men, the argument concludes that all great men could have been\ndispensed with. The term \"great men\" is distributive in the premises and\ncollective in the conclusion.\n\n\"Such also is the fallacy which probably operates on most adventurers in\nlotteries; _e.g._ 'the gaining of a high prize is no uncommon\noccurrence; and what is no uncommon occurrence may reasonably be\nexpected; therefore the gaining of a high prize may reasonably be\nexpected:' the conclusion when applied to the individual (as in practice\nit is) must be understood in the sense of 'reasonably expected _by a\ncertain individual_;' therefore for the major premise to be true, the\nmiddle term must be understood to mean, 'no uncommon occurrence to some\none _particular_ person;' whereas for the minor (which has been placed\nfirst) to be true, you must understand it of 'no uncommon occurrence to\n_some one or other_;' and thus you will have the Fallacy of Composition.\n\n\"This is a Fallacy with which men are extremely apt to deceive\n_themselves_; for when a multitude of particulars are presented to the\nmind, many are too weak or too indolent to take a comprehensive view of\nthem, but confine their attention to each single point, by turns; and\nthen decide, infer, and act, accordingly: _e.g._ the imprudent\nspendthrift, finding that he is able to afford this, _or_ that, _or_ the\nother expense, forgets that _all of them together_ will ruin him.\" The\ndebauchee destroys his health by successive acts of intemperance,\nbecause no _one_ of those acts would be of itself sufficient to do him\nany serious harm. A sick person reasons with himself, \"one, and another,\nand another, of my symptoms, do not prove that I have a fatal disease;\"\nand practically concludes that all taken together do not prove it.\n\n\n\u00a7 2. We have now sufficiently exemplified one of the principal Genera in\nthis Order of Fallacies; where, the source of error being the ambiguity\nof terms, the premises are verbally what is required to support the\nconclusion, but not really so. In the second great Fallacy of Confusion\nthey are neither verbally nor really sufficient, though, from their\nmultiplicity and confused arrangement, and still oftener from defect of\nmemory, they are not seen to be what they are. The fallacy I mean is\nthat of Petitio Principii, or begging the question; including the more\ncomplex and not uncommon variety of it, which is termed Reasoning in a\nCircle.\n\n_Petitio Principii_, as defined by Archbishop Whately, is the fallacy\n\"in which the premise either appears manifestly to be the same as the\nconclusion, or is actually proved from the conclusion, or is such as\nwould naturally and properly so be proved.\" By the last clause I presume\nis meant, that it is not susceptible of any other proof; for otherwise,\nthere would be no fallacy. To deduce from a proposition, propositions\nfrom which it would itself more naturally be deduced, is often an\nallowable deviation from the usual didactic order; or at most, what, by\nan adaptation of a phrase familiar to mathematicians, may be called a\nlogical _inelegance_.[35]\n\nThe employment of a proposition to prove that on which it is itself\ndependent for proof, by no means implies the degree of mental imbecility\nwhich might at first be supposed. The difficulty of comprehending how\nthis fallacy could possibly be committed, disappears when we reflect\nthat all persons, even the instructed, hold a great number of opinions\nwithout exactly recollecting how they came by them. Believing that they\nhave at some former time verified them by sufficient evidence, but\nhaving forgotten what the evidence was, they may easily be betrayed into\ndeducing from them the very propositions which are alone capable of\nserving as premises for their establishment. \"As if,\" says Archbishop\nWhately, \"one should attempt to prove the being of a God from the\nauthority of Holy Writ;\" which might easily happen to one with whom both\ndoctrines, as fundamental tenets of his religious creed, stand on the\nsame ground of familiar and traditional belief.\n\nArguing in a circle, however, is a stronger case of the fallacy, and\nimplies more than the mere passive reception of a premise by one who\ndoes not remember how it is to be proved. It implies an actual attempt\nto prove two propositions reciprocally from one another; and is seldom\nresorted to, at least in express terms, by any person in his own\nspeculations, but is committed by those who, being hard pressed by an\nadversary, are forced into giving reasons for an opinion of which, when\nthey began to argue, they had not sufficiently considered the grounds.\nAs in the following example from Archbishop Whately: \"Some mechanicians\nattempt to prove (what they ought to lay down as a probable but doubtful\nhypothesis[36]) that every particle of matter gravitates equally: 'why?'\n'because those bodies which contain more particles ever gravitate more\nstrongly, _i.e._ are heavier:' 'but, (it may be urged,) those which are\nheaviest are not always more bulky;' 'no, but they contain more\nparticles, though more closely condensed:' 'how do you know that?'\n'because they are heavier:' 'how does that prove it?' 'because all\nparticles of matter gravitating equally, that mass which is specifically\nthe heavier must needs have the more of them in the same space.'\" It\nappears to me that the fallacious reasoner, in his private thoughts,\nwould not be likely to proceed beyond the first step. He would acquiesce\nin the sufficiency of the reason first given, \"bodies which contain more\nparticles are heavier.\" It is when he finds this questioned, and is\ncalled upon to prove it, without knowing how, that he tries to\nestablish his premise by supposing proved what he is attempting to prove\nby it. The most effectual way, in fact, of exposing a Petitio Principii,\nwhen circumstances allow of it, is by challenging the reasoner to prove\nhis premises; which if he attempts to do, he is necessarily driven into\narguing in a circle.\n\nIt is not uncommon, however, for thinkers, and those not of the lowest\ndescription, to be led, even in their own thoughts, not indeed into\nformally proving each of two propositions from the other, but into\nadmitting propositions which can only be so proved. In the preceding\nexample the two together form a complete and consistent, though\nhypothetical, explanation of the facts concerned. And the tendency to\nmistake mutual coherency for truth; to trust one's safety to a strong\nchain though it has no point of support; is at the bottom of much which,\nwhen reduced to the strict forms of argumentation, can exhibit itself no\notherwise than as reasoning in a circle. All experience bears testimony\nto the enthralling effect of neat concatenation in a system of\ndoctrines, and the difficulty with which people admit the persuasion\nthat anything which holds so well together can possibly fall.\n\nSince every case where a conclusion which can only be proved from\ncertain premises is used for the proof of those premises, is a case of\n_petitio principii_, that fallacy includes a very great proportion of\nall incorrect reasoning. It is necessary, for completing our view of the\nfallacy, to exemplify some of the disguises under which it is accustomed\nto mask itself, and to escape exposure.\n\nA proposition would not be admitted by any person in his senses as a\ncorollary from itself, unless it were expressed in language which made\nit seem different. One of the commonest modes of so expressing it, is to\npresent the proposition itself in abstract terms, as a proof of the same\nproposition expressed in concrete language. This is a very frequent\nmode, not only of pretended proof, but of pretended explanation; and is\nparodied when Moli\u00e8re makes one of his absurd physicians say, \"l'opium\nendormit parcequ'il a une vertu soporifique,\" or, in the equivalent\ndoggrel,\n\n Mihi \u00e0 docto doctore,\n Domandatur causam et rationem quare\n Opium facit dormire.\n A quoi respondeo,\n Quia est in eo\n Virtus dormitiva,\n Cujus est natura\n Sensus assoupire.\n\nThe words Nature and Essence are grand instruments of this mode of\nbegging the question. As in the well-known argument of the scholastic\ntheologians, that the mind thinks always, because the _essence_ of the\nmind is to think. Locke had to point out, that if by essence is here\nmeant some property which must manifest itself by actual exercise at all\ntimes, the premise is a direct assumption of the conclusion; while if it\nonly means that to think is the distinctive property of a mind, there is\nno connexion between the premise and the conclusion, since it is not\nnecessary that a distinctive property should be perpetually in action.\n\nThe following is one of the modes in which these abstract terms, Nature\nand Essence, are used as instruments of this fallacy. Some particular\nproperties of a thing are selected, more or less arbitrarily, to be\ntermed its nature or essence; and when this has been done, these\nproperties are supposed to be invested with a kind of indefeasibleness;\nto have become paramount to all the other properties of the thing, and\nincapable of being prevailed over or counteracted by them. As when\nAristotle, in a passage already cited, \"decides that there is no void on\nsuch arguments as this: in a void there could be no difference of up and\ndown; for as in nothing there are no differences, so there are none in a\nprivation or negation; but a void is merely a privation or negation of\nmatter; therefore, in a void, bodies could not move up and down, which\nit is in their _nature_ to do.\"[37] In other words; it is in the\n_nature_ of bodies to move up and down, _ergo_ any physical fact which\nsupposes them not so to move, cannot be authentic. This mode of\nreasoning, by which a bad generalization is made to overrule all facts\nwhich contradict it, is _petitio principii_ in one of its most palpable\nforms.\n\nNone of the modes of assuming what should be proved are in more frequent\nuse than what are termed by Bentham \"question-begging appellatives;\"\nnames which beg the question under the disguise of stating it. The most\npotent of these are such as have a laudatory or vituperative character.\nFor instance, in politics, the word Innovation. The dictionary meaning\nof this term being merely \"a change to something new,\" it is difficult\nfor the defenders even of the most salutary improvement to deny that it\nis an innovation; yet the word having acquired in common usage a\nvituperative connotation in addition to its dictionary meaning, the\nadmission is always construed as a large concession to the disadvantage\nof the thing proposed.\n\nThe following passage from the argument in refutation of the Epicureans,\nin the second book of Cicero _de Finibus_, affords a fine example of\nthis sort of fallacy. \"Et quidem illud ipsum non nimium probo (et tantum\npatior) philosophum loqui de cupiditatibus finiendis. An potest\ncupiditas finiri? tollenda est, atque extrahenda radicitus. Quis est\nenim, in quo sit cupiditas, quin recte cupidus dici possit? Ergo et\navarus erit, sed finite: adulter, verum habebit modum: et luxuriosus\neodem modo. Qualis ista philosophia est, qu\u00e6 non interitum afferat\npravitatis, sed sit contenta mediocritate vitiorum?\" The question was,\nwhether certain desires, when kept within bounds, are vices or not; and\nthe argument decides the point by applying to them a word (_cupiditas_)\nwhich _implies_ vice. It is shown, however, in the remarks which follow,\nthat Cicero did not intend this as a serious argument, but as a\ncriticism on what he deemed an inappropriate expression. \"Rem ipsam\nprorsus probo: elegantiam desidero. Appellet h\u00e6c _desideria natur\u00e6_;\ncupiditatis nomen servet alio,\" &c. But many persons, both ancient and\nmodern, have employed this, or something equivalent to it, as a real and\nconclusive argument. We may remark that the passage respecting\n_cupiditas_ and _cupidus_ is also an example of another fallacy already\nnoticed, that of Paronymous Terms.\n\nMany more of the arguments of the ancient moralists, and especially of\nthe Stoics, fall within the definition of Petitio Principii. In the _De\nFinibus_, for example, which I continue to quote as being probably the\nbest extant exemplification at once of the doctrines and the methods of\nthe schools of philosophy existing at that time; of what value as\narguments are such pleas as those of Cato in the third book: That if\nvirtue were not happiness, it could not be a thing to _boast_ of: That\nif death or pain were evils, it would be impossible not to fear them,\nand it could not, therefore, be laudable to despise them, &c. In one way\nof viewing these arguments, they may be regarded as appeals to the\nauthority of the general sentiment of mankind, which had stamped its\napproval upon certain actions and characters by the phrases referred to;\nbut that such could have been the meaning intended is very unlikely,\nconsidering the contempt of the ancient philosophers for vulgar opinion.\nIn any other sense they are clear cases of Petitio Principii, since the\nword laudable, and the idea of boasting, imply principles of conduct;\nand practical maxims can only be proved from speculative truths, namely\nfrom the properties of the subject matter, and cannot, therefore, be\nemployed to prove those properties. As well might it be argued that a\ngovernment is good because we ought to support it, or that there is a\nGod because it is our duty to pray to him.\n\nIt is assumed by all the disputants in the _De Finibus_ as the\nfoundation of the inquiry into the _summum bonum_, that \"sapiens semper\nbeatus est.\" Not simply that wisdom gives the best chance of happiness,\nor that wisdom consists in knowing what happiness is, and by what things\nit is promoted; these propositions would not have been enough for\nthem:--but that the sage always is, and must of necessity be, happy. The\nidea that wisdom could be consistent with unhappiness, was always\nrejected as inadmissible: the reason assigned by one of the\ninterlocutors, near the beginning of the third book, being, that if the\nwise could be unhappy, there was little use in pursuing wisdom. But by\nunhappiness they did not mean pain or suffering; to that, it was granted\nthat the wisest person was liable in common with others: he was happy,\nbecause in possessing wisdom he had the most valuable of all\npossessions, the most to be sought and prized of all things, and to\npossess the most valuable thing was to be the most happy. By laying it\ndown, therefore, at the commencement of the inquiry, that the sage must\nbe happy, the disputed question respecting the _summum bonum_ was in\nfact begged; with the further assumption, that pain and suffering, so\nfar as they can coexist with wisdom, are not unhappiness, and are no\nevil.\n\nThe following are additional instances of Petitio Principii, under more\nor less of disguise.\n\nPlato, in the _Sophistes_, attempts to prove that things may exist which\nare incorporeal, by the argument that justice and wisdom are\nincorporeal, and justice and wisdom must be something. Here, if by\n_something_ be meant, as Plato did in fact mean, a thing capable of\nexisting in and by itself, and not as a quality of some other thing, he\nbegs the question in asserting that justice and wisdom must be\nsomething: if he means anything else, his conclusion is not proved. This\nfallacy might also be classed under ambiguous middleterm: _something_,\nin the one premise, meaning some substance, in the other merely some\nobject of thought, whether substance or attribute.\n\nIt was formerly an argument employed in proof of what is now no longer a\npopular doctrine, the infinite divisibility of matter, that every\nportion of matter, however small, must at least have an upper and an\nunder surface. Those who used this argument did not see that it assumed\nthe very point in dispute, the impossibility of arriving at a minimum of\nthickness; for if there be a minimum, its upper and under surface will\nof course be one: it will be itself a surface, and no more. The argument\nowes its very considerable plausibility to this, that the premise does\nactually seem more obvious than the conclusion, though really identical\nwith it. As expressed in the premise, the proposition appeals directly\nand in concrete language to the incapacity of the human imagination for\nconceiving a minimum. Viewed in this light, it becomes a case of the _\u00e0\npriori_ fallacy or natural prejudice, that whatever cannot be conceived\ncannot exist. Every fallacy of Confusion (it is almost unnecessary to\nrepeat) will, if cleared up, become a fallacy of some other sort; and it\nwill be found of deductive or ratiocinative fallacies generally, that\nwhen they mislead, there is mostly, as in this case, a fallacy of some\nother description lurking under them, by virtue of which chiefly it is\nthat the verbal juggle, which is the outside or body of this kind of\nfallacy, passes undetected.\n\nEuler's Algebra, a book otherwise of great merit, but full, to\noverflowing, of logical errors in respect to the foundation of the\nscience, contains the following argument to prove that _minus_\nmultiplied by _minus_ gives _plus_, a doctrine the opprobrium of all\nmere mathematicians, and which Euler had not a glimpse of the true\nmethod of proving. He says, _minus_ multiplied by _minus_ cannot give\n_minus_; for _minus_ multiplied by _plus_ gives _minus_, and _minus_\nmultiplied by _minus_ cannot give the same product as _minus_ multiplied\nby _plus_. Now one is obliged to ask, why minus multiplied by minus must\ngive any product at all? and if it does, why its product cannot be the\nsame as that of minus multiplied by plus? for this would seem, at the\nfirst glance, not more absurd than that minus by minus should give the\nsame as plus by plus, the proposition which Euler prefers to it. The\npremise requires proof, as much as the conclusion: nor can it be proved,\nexcept by that more comprehensive view of the nature of multiplication,\nand of algebraic processes in general, which would also supply a far\nbetter proof of the mysterious doctrine which Euler is here endeavouring\nto demonstrate.\n\nA striking instance of reasoning in a circle is that of some ethical\nwriters, who first take for their standard of moral truth what, being\nthe general, they deem to be the natural or instinctive sentiments and\nperceptions of mankind, and then explain away the numerous instances of\ndivergence from their assumed standard, by representing them as cases in\nwhich the perceptions are unhealthy. Some particular mode of conduct or\nfeeling is affirmed to be _unnatural_; why? because it is abhorrent to\nthe universal and natural sentiments of mankind. Finding no such\nsentiment in yourself, you question the fact; and the answer is (if your\nantagonist is polite), that you are an exception, a peculiar case. But\nneither (say you) do I find in the people of some other country, or of\nsome former age, any such feeling of abhorrence; \"ay, but their feelings\nwere sophisticated and unhealthy.\"\n\nOne of the most notable specimens of reasoning in a circle is the\ndoctrine of Hobbes, Rousseau, and others, which rests the obligations by\nwhich human beings are bound as members of society, on a supposed social\ncompact. I wave the consideration of the fictitious nature of the\ncompact itself; but when Hobbes, through the whole Leviathan,\nelaborately deduces the obligation of obeying the sovereign, not from\nthe necessity or utility of doing so, but from a promise supposed to\nhave been made by our ancestors, on renouncing savage life and agreeing\nto establish political society, it is impossible not to retort by the\nquestion, why are we bound to keep a promise made for us by others? or\nwhy bound to keep a promise at all? No satisfactory ground can be\nassigned for the obligation, except the mischievous consequences of the\nabsence of faith and mutual confidence among mankind. We are, therefore,\nbrought round to the interests of society, as the ultimate ground of the\nobligation of a promise; and yet those interests are not admitted to be\na sufficient justification for the existence of government and law.\nWithout a promise it is thought that we should not be bound to that\nwhich is implied in all modes of living in society, namely, to yield a\ngeneral obedience to the laws therein established; and so necessary is\nthe promise deemed, that if none has actually been made, some additional\nsafety is supposed to be given to the foundations of society by feigning\none.\n\n\n\u00a7 3. Two principal subdivisions of the class of Fallacies of Confusion\nhaving been disposed of; there remains a third, in which the confusion\nis not, as in the Fallacy of Ambiguity, in misconceiving the import of\nthe premises, nor, as in _Petitio Principii_, in forgetting what the\npremises are, but in mistaking the conclusion which is to be proved.\nThis is the fallacy of _Ignoratio Elenchi_, in the widest sense of the\nphrase; also called by Archbishop Whately the Fallacy of Irrelevant\nConclusion. His examples and remarks are highly worthy of citation.\n\n\"Various kinds of propositions are, according to the occasion,\nsubstituted for the one of which proof is required: sometimes the\nparticular for the universal; sometimes a proposition with different\nterms; and various are the contrivances employed to effect and to\nconceal this substitution, and to make the conclusion which the sophist\nhas drawn, answer practically the same purpose as the one he ought to\nhave established. We say, 'practically the same purpose,' because it\nwill very often happen that some _emotion_ will be excited, some\nsentiment impressed on the mind, (by a dexterous employment of this\nfallacy), such as shall bring men into the _disposition_ requisite for\nyour purpose; though they may not have assented to, or even stated\ndistinctly in their own minds, the _proposition_ which it was your\nbusiness to establish. Thus if a sophist has to defend one who has been\nguilty of some _serious_ offence, which he wishes to extenuate, though\nhe is unable distinctly to prove that it is not such, yet if he can\nsucceed in _making the audience laugh_ at some casual matter, he has\ngained practically the same point. So also if any one has pointed out\nthe extenuating circumstances in some particular case of offence, so as\nto show that it differs widely from the generality of the same class,\nthe sophist if he find himself unable to disprove these circumstances,\nmay do away the force of them, by simply _referring the action to that\nvery class_, which no one can deny that it belongs to, and the very name\nof which will excite a feeling of disgust sufficient to counteract the\nextenuation; _e.g._ let it be a case of peculation, and that many\n_mitigating_ circumstances have been brought forward which cannot be\ndenied; the sophistical opponent will reply, 'Well, but after all, the\nman is a _rogue_, and there is an end of it;' now in reality this was\n(by hypothesis) never the question; and the mere assertion of what was\nnever denied, _ought_ not, in fairness, to be regarded as decisive: but,\npractically, the odiousness of the word, arising in great measure from\nthe association of those very circumstances which belong to most of the\nclass, but which we have supposed to be _absent_ in _this particular_\ninstance, excites precisely that feeling of disgust, which in effect\ndestroys the force of the defence. In like manner we may refer to this\nhead all cases of improper appeal to the passions, and everything else\nwhich is mentioned by Aristotle as extraneous to the matter in hand\n([Greek: ex\u00f4 tou pragmatos]).\"\n\nAgain, \"instead of proving that 'this prisoner has committed an\natrocious fraud,' you prove that the fraud he is accused of is\natrocious: instead of proving (as in the well-known tale of Cyrus and\nthe two coats) that the taller boy had a right to force the other boy to\nexchange coats with him, you prove that the exchange would have been\nadvantageous to both: instead of proving that the poor ought to be\nrelieved in this way rather than in that, you prove that the poor ought\nto be relieved: instead of proving that the irrational agent--whether a\nbrute or a madman--can never be deterred from any act by apprehension of\npunishment (as for instance a dog from sheep-biting, by fear of being\nbeaten), you prove that the beating of one dog does not operate as an\n_example_ to _other_ dogs, &c.\n\n\"It is evident that _ignoratio elenchi_ may be employed as well for the\napparent refutation of your opponent's proposition, as for the apparent\nestablishment of your own; for it is substantially the same thing, to\nprove what was not denied or to disprove what was not asserted. The\nlatter practice is not less common, and it is more offensive, because it\nfrequently amounts to a personal affront, in attributing to a person,\nopinions, &c., which he perhaps holds in abhorrence. Thus, when in a\ndiscussion one party vindicates, on the ground of general expediency, a\nparticular instance of resistance to government in a case of intolerable\noppression, the opponent may gravely maintain, 'that we ought not to do\nevil that good may come;' a proposition which of course had never been\ndenied, the point in dispute being, 'whether resistance in this\nparticular case _were_ doing evil or not.' Or again, by way of\ndisproving the assertion of the right of private judgment in religion,\none may hear a grave argument to prove that 'it is impossible every one\ncan be _right in his judgment_.'\"\n\nThe works of controversial writers are seldom free from this fallacy.\nThe attempts, for instance, to disprove the population doctrines of\nMalthus, have been mostly cases of _ignoratio elenchi_. Malthus has been\nsupposed to be refuted if it could be shown that in some countries or\nages population has been nearly stationary; as if he had asserted that\npopulation always increases in a given ratio, or had not expressly\ndeclared that it increases only in so far as it is not restrained by\nprudence, or kept down by poverty and disease. Or, perhaps, a collection\nof facts is produced to prove that in some one country the people are\nbetter off with a dense population than they are in another country with\na thin one; or that the people have become more numerous and better off\nat the same time. As if the assertion were that a dense population could\nnot possibly be well off: as if it were not part of the very doctrine,\nand essential to it, that where there is a more abundant capital there\nmay be a greater population without any increase of poverty, or even\nwith a diminution of it.\n\nThe favourite argument against Berkeley's theory of the non-existence of\nmatter, and the most popularly effective, next to a \"grin\"[38]--an\nargument, moreover, which is not confined to \"coxcombs,\" nor to men like\nSamuel Johnson, whose greatly overrated ability certainly did not lie in\nthe direction of metaphysical speculation, but is the stock argument of\nthe Scotch school of metaphysicians--is a palpable _ignoratio elenchi_.\nThe argument is perhaps as frequently expressed by gesture as by words,\nand one of its commonest forms consists in knocking a stick against the\nground. This short and easy confutation overlooks the fact, that in\ndenying matter, Berkeley did not deny anything to which our senses bear\nwitness, and therefore cannot be answered by any appeal to them. His\nscepticism related to the supposed substratum, or hidden cause of the\nappearances perceived by our senses: the evidence of which, whatever may\nbe thought of its conclusiveness, is certainly not the evidence of\nsense. And it will always remain a signal proof of the want of\nmetaphysical profundity of Reid, Stewart, and, I am sorry to add, of\nBrown, that they should have persisted in asserting that Berkeley, if he\nbelieved his own doctrine, was bound to walk into the kennel, or run his\nhead against a post. As if persons who do not recognise an occult cause\nof their sensations, could not possibly believe that a fixed order\nsubsists among the sensations themselves. Such a want of comprehension\nof the distinction between a thing and its sensible manifestation, or,\nin metaphysical language, between the noumenon and the phenomenon, would\nbe impossible to even the dullest disciple of Kant or Coleridge.\n\nIt would be easy to add a greater number of examples of this fallacy, as\nwell as of the others which I have attempted to characterize. But a more\ncopious exemplification does not seem to be necessary; and the\nintelligent reader will have little difficulty in adding to the\ncatalogue from his own reading and experience. We shall therefore here\nclose our exposition of the general principles of logic, and proceed to\nthe supplementary inquiry which is necessary to complete our design.\n\nFOOTNOTES:\n\n[1] Supra, p. 204.\n\n[2] _Vulgar Errors_, book v. chap. 21.\n\n[3] _Pharmacologia_, Historical Introduction, p. 16.\n\n[4] The author of one of the Bridgewater Treatises has fallen, as it\nseems to me, into a similar fallacy when, after arguing in rather a\ncurious way to prove that matter may exist without any of the known\nproperties of matter, and may therefore be changeable, he concludes that\nit cannot be eternal, because \"eternal (passive) existence necessarily\ninvolves incapability of change.\" I believe it would be difficult to\npoint out any other connexion between the facts of eternity and\nunchangeableness, than a strong association between the two ideas. Most\nof the _\u00e0 priori_ arguments, both religious and anti-religious, on the\norigin of things, are fallacies drawn from the same source.\n\n[5] Supra, book ii. chap. v. \u00a7 6, and ch. vii. \u00a7 1, 2, 3. See also\n_Examination of Sir William Hamilton's Philosophy_, chap. vi. and\nelsewhere.\n\n[6] I quote this passage from Playfair's celebrated _Dissertations on\nthe Progress of Mathematical and Physical Science_.\n\n[7] This statement I must now correct, as too unqualified. The maxim in\nquestion was maintained with full conviction by no less an authority\nthan Sir William Hamilton. See my _Examination_, chap. xxiv.\n\n[8] _Nouveaux Essais sur l'Entendement Humain--Avant-propos_.\n([OE]uvres, Paris ed. 1842, vol. i. p. 19.)\n\n[9] This doctrine also was accepted as true, and conclusions were\ngrounded on it, by Sir William Hamilton. See _Examination_, chap. xxiv.\n\n[10] Not that of Leibnitz, but the principle commonly appealed to under\nthat name by mathematicians.\n\n[11] _Dissertation_, ut supra, p. 27.\n\n[12] _Hist. Ind. Sc._ Book i. chap. i.\n\n[13] _Novum Organum_, Aph. 75.\n\n[14] Supra, book iii. ch. vii. \u00a7 4.\n\n[15] It is hardly needful to remark that nothing is here intended to be\nsaid against the possibility at some future period of making gold; by\nfirst discovering it to be a compound, and putting together its\ndifferent elements or ingredients. But this is a totally different idea\nfrom that of the seekers of the grand arcanum.\n\n[16] _Pharmacologia_, pp. 43-5.\n\n[17] Vol. i. chap. 8.\n\n[18] _Nov. Org._, Aph. 46.\n\n[19] Playfair's _Dissertation_, sect. 4.\n\n[20] _Nov. Org. Renov._, p. 61.\n\n[21] _Pharmacologia_, p. 21.\n\n[22] _Pharmacologia_, pp. 23-4.\n\n[23] Ibid. p. 28.\n\n[24] Ibid. p. 62.\n\n[25] _Pharmacologia_, pp. 61-2.\n\n[26] Supra, p. 182.\n\n[27] _Elements of the Philosophy of the Mind_, vol. ii. ch. 4, sect. 5.\n\n[28] \"Thus Fourcroy,\" says Dr. Paris, \"explained the operation of\nmercury by its specific gravity, and the advocates of this doctrine\nfavoured the general introduction of the preparations of iron,\nespecially in scirrhus of the spleen or liver, upon the same\nhypothetical principle; for, say they, whatever is most forcible in\nremoving the obstruction must be the most proper instrument of cure;\nsuch is steel, which, besides the attenuating power with which it is\nfurnished, has still a greater force in this case from the gravity of\nits particles, which, being seven times specifically heavier than any\nvegetable, acts in proportion with a stronger impulse, and therefore is\na more powerful deobstruent. This may be taken as a specimen of the\nstyle in which these mechanical physicians reasoned and\npractised.\"--_Pharmacologia_, pp. 38-9.\n\n[29] _Pharmacologia_, pp. 39, 40.\n\n[30] I quote from Dr. Whewell's _Hist. Ind. Sc._ 3rd ed. i. 129.\n\n[31] _Hist. Ind. Sc._ i. 52.\n\n[32] _Nov. Org._ Aph. 60.\n\n[33] \"An advocate,\" says Mr. De Morgan (_Formal Logic_, p. 270), \"is\nsometimes guilty of the argument _\u00e0 dicto secundum quid ad dictum\nsimpliciter_: it is his business to do for his client all that his\nclient might _honestly_ do for himself. Is not the word in italics\nfrequently omitted? _Might_ any man honestly try to do for himself all\nthat counsel frequently try to do for him? We are often reminded of the\ntwo men who stole the leg of mutton; one could swear he had not got it,\nthe other that he had not taken it. The counsel is doing his duty by his\nclient, the client has left the matter to his counsel. Between the\nunexecuted intention of the client, and the unintended execution of the\ncounsel, there may be a wrong done, and, if we are to believe the usual\nmaxims, no wrong-doer.\"\n\nThe same writer justly remarks (p. 251) that there is a converse\nfallacy, _\u00e0 dicto simpliciter ad dictum secundum quid_, called by the\nscholastic logicians, _fallacia accidentis_; and another which may be\ncalled _\u00e0 dicto secundum quid ad dictum secundum alterum quid_ (p. 265).\nFor apt instances of both, I must refer the reader to Mr. De Morgan's\nable chapter on Fallacies.\n\n[34] An example of this fallacy is the popular error that _strong_ drink\nmust be a cause of _strength_. There is here fallacy within fallacy; for\ngranting that the words \"strong\" and \"strength\" were not (as they are)\napplied in a totally different sense to fermented liquors and to the\nhuman body, there would still be involved the error of supposing that an\neffect must be like its cause; that the conditions of a phenomenon are\nlikely to resemble the phenomenon itself; which we have already treated\nof as an _\u00e0 priori_ fallacy of the first rank. As well might it be\nsupposed that a strong poison will make the person who takes it, strong.\n\n[35] In his later editions, Archbishop Whately confines the name of\nPetitio Principii \"to those cases in which one of the premises either is\nmanifestly the same in sense with the conclusion, or is actually proved\nfrom it, or is such as the persons you are addressing are not likely to\nknow, or to admit, except as an inference from the conclusion: as,\n_e.g._ if any one should infer the authenticity of a certain history,\nfrom its recording such and such facts, the reality of which rests on\nthe evidence of that history.\"\n\n[36] No longer even a probable hypothesis, since the establishment of\nthe atomic theory; it being now certain that the integral particles of\ndifferent substances gravitate unequally. It is true that these\nparticles, though real _minima_ for the purposes of chemical\ncombination, may not be the ultimate particles of the substance; and\nthis doubt alone renders the hypothesis admissible, even as an\nhypothesis.\n\n[37] _Hist. Ind. Sc._ i. 34.\n\n[38] \"And coxcombs vanquish Berkeley with a grin.\"\n\n\n\n\nBOOK VI.\n\nON THE LOGIC OF THE MORAL SCIENCES.\n\n\n\"Si l'homme peut pr\u00e9dire, avec une assurance presque enti\u00e8re, les\nph\u00e9nom\u00e8nes dont il conna\u00eet les lois; si lors m\u00eame qu'elles lui sont\ninconnues, il peut, d'apr\u00e8s l'exp\u00e9rience, pr\u00e9voir avec une grande\nprobabilit\u00e9 les \u00e9v\u00e9nemens de l'avenir; pourquoi regarderait-on comme une\nentreprise chim\u00e9rique, celle de tracer avec quelque vraisemblance le\ntableau des destin\u00e9es futures de l'esp\u00e8ce humaine, d'apr\u00e8s les r\u00e9sultats\nde son histoire? Le seul fondement de croyance dans les sciences\nnaturelles, est cette id\u00e9e, que les lois g\u00e9n\u00e9rales, connues ou ignor\u00e9es,\nqui r\u00e8glent les ph\u00e9nom\u00e8nes de l'univers, sont n\u00e9cessaires et constantes;\net par quelle raison ce principe serait-il moins vrai pour le\nd\u00e9veloppement des facult\u00e9s intellectuelles et morales de l'homme, que\npour les autres op\u00e9rations de la nature? Enfin, puisque des opinions\nform\u00e9es d'apr\u00e8s l'exp\u00e9rience ... sont la seule r\u00e8gle de la conduite des\nhommes les plus sages, pourquoi interdirait-on au philosophe d'appuyer\nses conjectures sur cette m\u00eame base, pourvu qu'il ne leur attribue pas\nune certitude sup\u00e9rieure \u00e0 celle qui peut na\u00eetre du nombre, de la\nconstance, de l'exactitude des observations?\"--CONDORCET, _Esquisse d'un\nTableau Historique des Progr\u00e8s de l'Esprit Humain_.\n\n\n\n\nCHAPTER I.\n\nINTRODUCTORY REMARKS.\n\n\n\u00a7 1. Principles of Evidence and Theories of Method are not to be\nconstructed _\u00e0 priori_. The laws of our rational faculty, like those of\nevery other natural agency, are only learnt by seeing the agent at work.\nThe earlier achievements of science were made without the conscious\nobservance of any Scientific Method; and we should never have known by\nwhat process truth is to be ascertained, if we had not previously\nascertained many truths. But it was only the easier problems which could\nbe thus resolved: natural sagacity, when it tried its strength against\nthe more difficult ones, either failed altogether, or if it succeeded\nhere and there in obtaining a solution, had no sure means of convincing\nothers that its solution was correct. In scientific investigation, as in\nall other works of human skill, the way of obtaining the end is seen as\nit were instinctively by superior minds in some comparatively simple\ncase, and is then, by judicious generalization, adapted to the variety\nof complex cases. We learn to do a thing in difficult circumstances, by\nattending to the manner in which we have spontaneously done the same\nthing in easier ones.\n\nThis truth is exemplified by the history of the various branches of\nknowledge which have successively, in the ascending order of their\ncomplication, assumed the character of sciences; and will doubtless\nreceive fresh confirmation from those, of which the final scientific\nconstitution is yet to come, and which are still abandoned to the\nuncertainties of vague and popular discussion. Although several other\nsciences have emerged from this state at a comparatively recent date,\nnone now remain in it except those which relate to man himself, the\nmost complex and most difficult subject of study on which the human mind\ncan be engaged.\n\nConcerning the physical nature of man, as an organized being,--though\nthere is still much uncertainty and much controversy, which can only be\nterminated by the general acknowledgment and employment of stricter\nrules of induction than are commonly recognised,--there is, however, a\nconsiderable body of truths which all who have attended to the subject\nconsider to be fully established; nor is there now any radical\nimperfection in the method observed in this department of science by its\nmost distinguished modern teachers. But the laws of Mind, and, in even a\ngreater degree, those of Society, are so far from having attained a\nsimilar state of even partial recognition, that it is still a\ncontroversy whether they are capable of becoming subjects of science in\nthe strict sense of the term: and among those who are agreed on this\npoint, there reigns the most irreconcileable diversity on almost every\nother. Here, therefore, if anywhere, the principles laid down in the\npreceding Books may be expected to be useful.\n\nIf, on matters so much the most important with which human intellect can\noccupy itself, a more general agreement is ever to exist among thinkers;\nif what has been pronounced \"the proper study of mankind\" is not\ndestined to remain the only subject which Philosophy cannot succeed in\nrescuing from Empiricism; the same process through which the laws of\nmany simpler phenomena have by general acknowledgment been placed beyond\ndispute, must be consciously and deliberately applied to those more\ndifficult inquiries. If there are some subjects on which the results\nobtained have finally received the unanimous assent of all who have\nattended to the proof, and others on which mankind have not yet been\nequally successful; on which the most sagacious minds have occupied\nthemselves from the earliest date, and have never succeeded in\nestablishing any considerable body of truths, so as to be beyond denial\nor doubt; it is by generalizing the methods successfully followed in the\nformer inquiries, and adapting them to the latter, that we may hope to\nremove this blot on the face of science. The remaining chapters are an\nendeavour to facilitate this most desirable object.\n\n\n\u00a7 2. In attempting this, I am not unmindful how little can be done\ntowards it in a mere treatise on Logic, or how vague and unsatisfactory\nall precepts of Method must necessarily appear, when not practically\nexemplified in the establishment of a body of doctrine. Doubtless, the\nmost effectual mode of showing how the sciences of Ethics and Politics\nmay be constructed, would be to construct them: a task which, it needs\nscarcely be said, I am not about to undertake. But even if there were no\nother examples, the memorable one of Bacon would be sufficient to\ndemonstrate, that it is sometimes both possible and useful to point out\nthe way, though without being oneself prepared to adventure far into it.\nAnd if more were to be attempted, this at least is not a proper place\nfor the attempt.\n\nIn substance, whatever can be done in a work like this for the Logic of\nthe Moral Sciences, has been or ought to have been accomplished in the\nfive preceding Books; to which the present can be only a kind of\nsupplement or appendix, since the methods of investigation applicable to\nmoral and social science must have been already described, if I have\nsucceeded in enumerating and characterizing those of science in general.\nIt remains, however, to examine which of those methods are more\nespecially suited to the various branches of moral inquiry; under what\npeculiar facilities or difficulties they are there employed; how far the\nunsatisfactory state of those inquiries is owing to a wrong choice of\nmethods, how far to want of skill in the application of right ones; and\nwhat degree of ultimate success may be attained or hoped for, by a\nbetter choice or more careful employment of logical processes\nappropriate to the case. In other words, whether moral sciences exist,\nor can exist; to what degree of perfection they are susceptible of being\ncarried; and by what selection or adaptation of the methods brought to\nview in the previous part of this work, that degree of perfection is\nattainable.\n\nAt the threshold of this inquiry we are met by an objection, which, if\nnot removed, would be fatal to the attempt to treat human conduct as a\nsubject of science. Are the actions of human beings, like all other\nnatural events, subject to invariable laws? Does that constancy of\ncausation, which is the foundation of every scientific theory of\nsuccessive phenomena, really obtain among them? This is often denied;\nand for the sake of systematic completeness, if not from any very urgent\npractical necessity, the question should receive a deliberate answer in\nthis place. We shall devote to the subject a chapter apart.\n\n\n\n\nCHAPTER II.\n\nOF LIBERTY AND NECESSITY.\n\n\n\u00a7 1. The question, whether the law of causality applies in the same\nstrict sense to human actions as to other phenomena, is the celebrated\ncontroversy concerning the freedom of the will: which, from at least as\nfar back as the time of Pelagius, has divided both the philosophical and\nthe religious world. The affirmative opinion is commonly called the\ndoctrine of Necessity, as asserting human volitions and actions to be\nnecessary and inevitable. The negative maintains that the will is not\ndetermined, like other phenomena, by antecedents, but determines itself;\nthat our volitions are not, properly speaking, the effects of causes, or\nat least have no causes which they uniformly and implicitly obey.\n\nI have already made it sufficiently apparent that the former of these\nopinions is that which I consider the true one; but the misleading terms\nin which it is often expressed, and the indistinct manner in which it is\nusually apprehended, have both obstructed its reception, and perverted\nits influence when received. The metaphysical theory of free will, as\nheld by philosophers, (for the practical feeling of it, common in a\ngreater or less degree to all mankind, is in no way inconsistent with\nthe contrary theory,) was invented because the supposed alternative of\nadmitting human actions to be _necessary_, was deemed inconsistent with\nevery one's instinctive consciousness, as well as humiliating to the\npride and even degrading to the moral nature of man. Nor do I deny that\nthe doctrine, as sometimes held, is open to these imputations; for the\nmisapprehension in which I shall be able to show that they originate,\nunfortunately is not confined to the opponents of the doctrine, but\nparticipated in by many, perhaps we might say by most, of its\nsupporters.\n\n\n\u00a7 2. Correctly conceived, the doctrine called Philosophical Necessity\nis simply this: that, given the motives which are present to an\nindividual's mind, and given likewise the character and disposition of\nthe individual, the manner in which he will act might be unerringly\ninferred: that if we knew the person thoroughly, and knew all the\ninducements which are acting upon him, we could foretell his conduct\nwith as much certainty as we can predict any physical event. This\nproposition I take to be a mere interpretation of universal experience,\na statement in words of what every one is internally convinced of. No\none who believed that he knew thoroughly the circumstances of any case,\nand the characters of the different persons concerned, would hesitate to\nforetell how all of them would act. Whatever degree of doubt he may in\nfact feel, arises from the uncertainty whether he really knows the\ncircumstances, or the character of some one or other of the persons,\nwith the degree of accuracy required: but by no means from thinking that\nif he did know these things, there could be any uncertainty what the\nconduct would be. Nor does this full assurance conflict in the smallest\ndegree with what is called our feeling of freedom. We do not feel\nourselves the less free, because those to whom we are intimately known\nare well assured how we shall will to act in a particular case. We\noften, on the contrary, regard the doubt what our conduct will be, as a\nmark of ignorance of our character, and sometimes even resent it as an\nimputation. The religious metaphysicians who have asserted the freedom\nof the will, have always maintained it to be consistent with divine\nforeknowledge of our actions: and if with divine, then with any other\nforeknowledge. We may be free, and yet another may have reason to be\nperfectly certain what use we shall make of our freedom. It is not,\ntherefore, the doctrine that our volitions and actions are invariable\nconsequents of our antecedent states of mind, that is either\ncontradicted by our consciousness, or felt to be degrading.\n\nBut the doctrine of causation, when considered as obtaining between our\nvolitions and their antecedents, is almost universally conceived as\ninvolving more than this. Many do not believe, and very few practically\nfeel, that there is nothing in causation but invariable, certain, and\nunconditional sequence. There are few to whom mere constancy of\nsuccession appears a sufficiently stringent bond of union for so\npeculiar a relation as that of cause and effect. Even if the reason\nrepudiates, the imagination retains, the feeling of some more intimate\nconnexion, of some peculiar tie, or mysterious constraint exercised by\nthe antecedent over the consequent. Now this it is which, considered as\napplying to the human will, conflicts with our consciousness, and\nrevolts our feelings. We are certain that, in the case of our volitions,\nthere is not this mysterious constraint. We know that we are not\ncompelled, as by a magical spell, to obey any particular motive. We\nfeel, that if we wished to prove that we have the power of resisting the\nmotive, we could do so, (that wish being, it needs scarcely be observed,\na _new antecedent_;) and it would be humiliating to our pride, and (what\nis of more importance) paralysing to our desire of excellence if we\nthought otherwise. But neither is any such mysterious compulsion now\nsupposed, by the best philosophical authorities, to be exercised by any\nother cause over its effect. Those who think that causes draw their\neffects after them by a mystical tie, are right in believing that the\nrelation between volitions and their antecedents is of another nature.\nBut they should go farther, and admit that this is also true of all\nother effects and their antecedents. If such a tie is considered to be\ninvolved in the word necessity, the doctrine is not true of human\nactions; but neither is it then true of inanimate objects. It would be\nmore correct to say that matter is not bound by necessity than that mind\nis so.\n\nThat the free-will metaphysicians, being mostly of the school which\nrejects Hume's and Brown's analysis of Cause and Effect, should miss\ntheir way for want of the light which that analysis affords, cannot\nsurprise us. The wonder is, that the necessarians, who usually admit\nthat philosophical theory, should in practice equally lose sight of it.\nThe very same misconception of the doctrine called Philosophical\nNecessity, which prevents the opposite party from recognising its truth,\nI believe to exist more or less obscurely in the minds of most\nnecessarians, however they may in words disavow it. I am much mistaken\nif they habitually feel that the necessity which they recognise in\nactions is but uniformity of order, and capability of being predicted.\nThey have a feeling as if there were at bottom a stronger tie between\nthe volitions and their causes: as if, when they asserted that the will\nis governed by the balance of motives, they meant something more cogent\nthan if they had only said, that whoever knew the motives, and our\nhabitual susceptibilities to them, could predict how we should will to\nact. They commit, in opposition to their own scientific system, the very\nsame mistake which their adversaries commit in obedience to theirs; and\nin consequence do really in some instances suffer those depressing\nconsequences, which their opponents erroneously impute to the doctrine\nitself.\n\n\n\u00a7 3. I am inclined to think that this error is almost wholly an effect\nof the associations with a word; and that it would be prevented, by\nforbearing to employ, for the expression of the simple fact of\ncausation, so extremely inappropriate a term as Necessity. That word, in\nits other acceptations, involves much more than mere uniformity of\nsequence: it implies irresistibleness. Applied to the will, it only\nmeans that the given cause will be followed by the effect, subject to\nall possibilities of counteraction by other causes: but in common use it\nstands for the operation of those causes exclusively, which are supposed\ntoo powerful to be counteracted at all. When we say that all human\nactions take place of necessity, we only mean that they will certainly\nhappen if nothing prevents:--when we say that dying of want, to those\nwho cannot get food, is a necessity, we mean that it will certainly\nhappen whatever may be done to prevent it. The application of the same\nterm to the agencies on which human actions depend, as is used to\nexpress those agencies of nature which are really uncontrollable, cannot\nfail, when habitual, to create a feeling of uncontrollableness in the\nformer also. This however is a mere illusion. There are physical\nsequences which we call necessary, as death for want of food or air;\nthere are others which, though as much cases of causation as the\nformer, are not said to be necessary, as death from poison, which an\nantidote, or the use of the stomach-pump, will sometimes avert. It is\napt to be forgotten by people's feelings, even if remembered by their\nunderstandings, that human actions are in this last predicament: they\nare never (except in some cases of mania) ruled by any one motive with\nsuch absolute sway, that there is no room for the influence of any\nother. The causes, therefore, on which action depends, are never\nuncontrollable; and any given effect is only necessary provided that the\ncauses tending to produce it are not controlled. That whatever happens,\ncould not have happened otherwise unless something had taken place which\nwas capable of preventing it, no one surely needs hesitate to admit. But\nto call this by the name necessity is to use the term in a sense so\ndifferent from its primitive and familiar meaning, from that which it\nbears in the common occasions of life, as to amount almost to a play\nupon words. The associations derived from the ordinary sense of the term\nwill adhere to it in spite of all we can do: and though the doctrine of\nNecessity, as stated by most who hold it, is very remote from fatalism,\nit is probable that most necessarians are fatalists, more or less, in\ntheir feelings.\n\nA fatalist believes, or half believes (for nobody is a consistent\nfatalist), not only that whatever is about to happen, will be the\ninfallible result of the causes which produce it, (which is the true\nnecessarian doctrine,) but moreover that there is no use in struggling\nagainst it; that it will happen however we may strive to prevent it.\nNow, a necessarian, believing that our actions follow from our\ncharacters, and that our characters follow from our organization, our\neducation, and our circumstances, is apt to be, with more or less of\nconsciousness on his part, a fatalist as to his own actions, and to\nbelieve that his nature is such, or that his education and circumstances\nhave so moulded his character, that nothing can now prevent him from\nfeeling and acting in a particular way, or at least that no effort of\nhis own can hinder it. In the words of the sect which in our own day has\nmost perseveringly inculcated and most perversely misunderstood this\ngreat doctrine, his character is formed _for_ him, and not _by_ him;\ntherefore his wishing that it had been formed differently is of no use;\nhe has no power to alter it. But this is a grand error. He has, to a\ncertain extent, a power to alter his character. Its being, in the\nultimate resort, formed for him, is not inconsistent with its being, in\npart, formed _by_ him as one of the intermediate agents. His character\nis formed by his circumstances (including among these his particular\norganization); but his own desire to mould it in a particular way, is\none of those circumstances, and by no means one of the least\ninfluential. We cannot, indeed, directly will to be different from what\nwe are. But neither did those who are supposed to have formed our\ncharacters, directly will that we should be what we are. Their will had\nno direct power except over their own actions. They made us what they\ndid make us, by willing, not the end, but the requisite means; and we,\nwhen our habits are not too inveterate, can, by similarly willing the\nrequisite means, make ourselves different. If they could place us under\nthe influence of certain circumstances, we, in like manner, can place\nourselves under the influence of other circumstances. We are exactly as\ncapable of making our own character, _if we will_, as others are of\nmaking it for us.\n\nYes (answers the Owenite), but these words, \"if we will,\" surrender the\nwhole point: since the will to alter our own character is given us, not\nby any efforts of ours, but by circumstances which we cannot help; it\ncomes to us either from external causes, or not at all. Most true: if\nthe Owenite stops here, he is in a position from which nothing can expel\nhim. Our character is formed by us as well as for us; but the wish which\ninduces us to attempt to form it is formed for us; and how? Not, in\ngeneral, by our organization, nor wholly by our education, but by our\nexperience; experience of the painful consequences of the character we\npreviously had: or by some strong feeling of admiration or aspiration,\naccidentally aroused. But to think that we have no power of altering our\ncharacter, and to think that we shall not use our power unless we desire\nto use it, are very different things, and have a very different effect\non the mind. A person who does not wish to alter his character, cannot\nbe the person who is supposed to feel discouraged or paralysed by\nthinking himself unable to do it. The depressing effect of the fatalist\ndoctrine can only be felt where there _is_ a wish to do what that\ndoctrine represents as impossible. It is of no consequence what we think\nforms our character, when we have no desire of our own about forming it;\nbut it is of great consequence that we should not be prevented from\nforming such a desire by thinking the attainment impracticable, and that\nif we have the desire, we should know that the work is not so\nirrevocably done as to be incapable of being altered.\n\nAnd indeed, if we examine closely, we shall find that this feeling, of\nour being able to modify our own character _if we wish_, is itself the\nfeeling of moral freedom which we are conscious of. A person feels\nmorally free who feels that his habits or his temptations are not his\nmasters, but he theirs: who even in yielding to them knows that he could\nresist; that were he desirous of altogether throwing them off, there\nwould not be required for that purpose a stronger desire than he knows\nhimself to be capable of feeling. It is of course necessary, to render\nour consciousness of freedom complete, that we should have succeeded in\nmaking our character all we have hitherto attempted to make it; for if\nwe have wished and not attained, we have, to that extent, not power over\nour own character, we are not free. Or at least, we must feel that our\nwish, if not strong enough to alter our character, is strong enough to\nconquer our character when the two are brought into conflict in any\nparticular case of conduct. And hence it is said with truth, that none\nbut a person of confirmed virtue is completely free.\n\nThe application of so improper a term as Necessity to the doctrine of\ncause and effect in the matter of human character, seems to me one of\nthe most signal instances in philosophy of the abuse of terms, and its\npractical consequences one of the most striking examples of the power of\nlanguage over our associations. The subject will never be generally\nunderstood, until that objectionable term is dropped. The free-will\ndoctrine, by keeping in view precisely that portion of the truth which\nthe word Necessity puts out of sight, namely the power of the mind to\nco-operate in the formation of its own character, has given to its\nadherents a practical feeling much nearer to the truth than has\ngenerally (I believe) existed in the minds of necessarians. The latter\nmay have had a stronger sense of the importance of what human beings can\ndo to shape the characters of one another; but the free-will doctrine\nhas, I believe, fostered in its supporters a much stronger spirit of\nself-culture.\n\n\n\u00a7 4. There is still one fact which requires to be noticed (in addition\nto the existence of a power of self-formation) before the doctrine of\nthe causation of human actions can be freed from the confusion and\nmisapprehensions which surround it in many minds. When the will is said\nto be determined by motives, a motive does not mean always, or solely,\nthe anticipation of a pleasure or of a pain. I shall not here inquire\nwhether it be true that, in the commencement, all our voluntary actions\nare mere means consciously employed to obtain some pleasure, or avoid\nsome pain. It is at least certain that we gradually, through the\ninfluence of association, come to desire the means without thinking of\nthe end: the action itself becomes an object of desire, and is performed\nwithout reference to any motive beyond itself. Thus far, it may still be\nobjected, that, the action having through association become\npleasurable, we are, as much as before, moved to act by the anticipation\nof a pleasure, namely the pleasure of the action itself. But granting\nthis, the matter does not end here. As we proceed in the formation of\nhabits, and become accustomed to will a particular act or a particular\ncourse of conduct because it is pleasurable, we at last continue to will\nit without any reference to its being pleasurable. Although, from some\nchange in us or in our circumstances, we have ceased to find any\npleasure in the action, or perhaps to anticipate any pleasure as the\nconsequence of it, we still continue to desire the action, and\nconsequently to do it. In this manner it is that habits of hurtful\nexcess continue to be practised although they have ceased to be\npleasurable; and in this manner also it is that the habit of willing to\npersevere in the course which he has chosen, does not desert the moral\nhero, even when the reward, however real, which he doubtless receives\nfrom the consciousness of well-doing, is anything but an equivalent for\nthe sufferings he undergoes, or the wishes which he may have to\nrenounce.\n\nA habit of willing is commonly called a purpose; and among the causes of\nour volitions, and of the actions which flow from them, must be reckoned\nnot only likings and aversions, but also purposes. It is only when our\npurposes have become independent of the feelings of pain or pleasure\nfrom which they originally took their rise, that we are said to have a\nconfirmed character. \"A character,\" says Novalis, \"is a completely\nfashioned will:\" and the will, once so fashioned, may be steady and\nconstant, when the passive susceptibilities of pleasure and pain are\ngreatly weakened, or materially changed.\n\nWith the corrections and explanations now given, the doctrine of the\ncausation of our volitions by motives, and of motives by the desirable\nobjects offered to us, combined with our particular susceptibilities of\ndesire, may be considered, I hope, as sufficiently established for the\npurposes of this treatise.[1]\n\n\n\n\nCHAPTER III.\n\nTHAT THERE IS, OR MAY BE, A SCIENCE OF HUMAN NATURE.\n\n\n\u00a7 1. It is a common notion, or at least it is implied in many common\nmodes of speech, that the thoughts, feelings, and actions of sentient\nbeings are not a subject of science, in the same strict sense in which\nthis is true of the objects of outward nature. This notion seems to\ninvolve some confusion of ideas, which it is necessary to begin by\nclearing up.\n\nAny facts are fitted, in themselves, to be a subject of science, which\nfollow one another according to constant laws; although those laws may\nnot have been discovered, nor even be discoverable by our existing\nresources. Take, for instance, the most familiar class of meteorological\nphenomena, those of rain and sunshine. Scientific inquiry has not yet\nsucceeded in ascertaining the order of antecedence and consequence among\nthese phenomena, so as to be able, at least in our regions of the earth,\nto predict them with certainty, or even with any high degree of\nprobability. Yet no one doubts that the phenomena depend on laws, and\nthat these must be derivative laws resulting from known ultimate laws,\nthose of heat, electricity, vaporization, and elastic fluids. Nor can it\nbe doubted that if we were acquainted with all the antecedent\ncircumstances, we could, even from those more general laws, predict\n(saving difficulties of calculation) the state of the weather at any\nfuture time. Meteorology, therefore, not only has in itself every\nnatural requisite for being, but actually is, a science; though, from\nthe difficulty of observing the facts on which the phenomena depend (a\ndifficulty inherent in the peculiar nature of those phenomena) the\nscience is extremely imperfect; and were it perfect, might probably be\nof little avail in practice, since the data requisite for applying its\nprinciples to particular instances would rarely be procurable.\n\nA case may be conceived, of an intermediate character between the\nperfection of science, and this its extreme imperfection. It may happen\nthat the greater causes, those on which the principal part of the\nphenomena depends, are within the reach of observation and measurement;\nso that if no other causes intervened, a complete explanation could be\ngiven not only of the phenomenon in general, but of all the variations\nand modifications which it admits of. But inasmuch as other, perhaps\nmany other causes, separately insignificant in their effects, co-operate\nor conflict in many or in all cases with those greater causes; the\neffect, accordingly, presents more or less of aberration from what would\nbe produced by the greater causes alone. Now if these minor causes are\nnot so constantly accessible, or not accessible at all, to accurate\nobservation; the principal mass of the effect may still, as before, be\naccounted for, and even predicted; but there will be variations and\nmodifications which we shall not be competent to explain thoroughly, and\nour predictions will not be fulfilled accurately, but only\napproximately.\n\nIt is thus, for example, with the theory of the tides. No one doubts\nthat Tidology (as Dr. Whewell proposes to call it) is really a science.\nAs much of the phenomena as depends on the attraction of the sun and\nmoon is completely understood, and may in any, even unknown, part of the\nearth's surface, be foretold with certainty; and the far greater part of\nthe phenomena depends on those causes. But circumstances of a local or\ncasual nature, such as the configuration of the bottom of the ocean, the\ndegree of confinement from shores, the direction of the wind, &c.,\ninfluence, in many or in all places, the height and time of the tide;\nand a portion of these circumstances being either not accurately\nknowable, not precisely measurable, or not capable of being certainly\nforeseen, the tide in known places commonly varies from the calculated\nresult of general principles by some difference that we cannot explain,\nand in unknown ones may vary from it by a difference that we are not\nable to foresee or conjecture. Nevertheless, not only is it certain\nthat these variations depend on causes, and follow their causes by laws\nof unerring uniformity; not only, therefore, is tidology a science, like\nmeteorology, but it is, what hitherto at least meteorology is not, a\nscience largely available in practice. General laws may be laid down\nrespecting the tides, predictions may be founded on those laws, and the\nresult will in the main, though often not with complete accuracy,\ncorrespond to the predictions.\n\nAnd this is what is or ought to be meant by those who speak of sciences\nwhich are not _exact_ sciences. Astronomy was once a science, without\nbeing an exact science. It could not become exact until not only the\ngeneral course of the planetary motions, but the perturbations also,\nwere accounted for, and referred to their causes. It has become an exact\nscience, because its phenomena have been brought under laws\ncomprehending the whole of the causes by which the phenomena are\ninfluenced, whether in a great or only in a trifling degree, whether in\nall or only in some cases, and assigning to each of those causes the\nshare of effect which really belongs to it. But in the theory of the\ntides the only laws as yet accurately ascertained, are those of the\ncauses which affect the phenomenon in all cases, and in a considerable\ndegree; while others which affect it in some cases only, or, if in all,\nonly in a slight degree, have not been sufficiently ascertained and\nstudied to enable us to lay down their laws; still less to deduce the\ncompleted law of the phenomenon, by compounding the effects of the\ngreater with those of the minor causes. Tidology, therefore, is not yet\nan exact science; not from any inherent incapacity of being so, but from\nthe difficulty of ascertaining with complete precision the real\nderivative uniformities. By combining, however, the exact laws of the\ngreater causes, and of such of the minor ones as are sufficiently known,\nwith such empirical laws or such approximate generalizations respecting\nthe miscellaneous variations as can be obtained by specific observation,\nwe can lay down general propositions which will be true in the main, and\non which, with allowance for the degree of their probable inaccuracy, we\nmay safely ground our expectations and our conduct.\n\n\n\u00a7 2. The science of human nature is of this description. It falls far\nshort of the standard of exactness now realized in Astronomy; but there\nis no reason that it should not be as much a science as Tidology is, or\nas Astronomy was when its calculations had only mastered the main\nphenomena, but not the perturbations.\n\nThe phenomena with which this science is conversant being the thoughts,\nfeelings, and actions of human beings, it would have attained the ideal\nperfection of a science if it enabled us to foretell how an individual\nwould think, feel, or act, throughout life, with the same certainty with\nwhich astronomy enables us to predict the places and the occultations of\nthe heavenly bodies. It needs scarcely be stated that nothing\napproaching to this can be done. The actions of individuals could not be\npredicted with scientific accuracy, were it only because we cannot\nforesee the whole of the circumstances in which those individuals will\nbe placed. But further, even in any given combination of (present)\ncircumstances, no assertion, which is both precise and universally true,\ncan be made respecting the manner in which human beings will think,\nfeel, or act. This is not, however, because every person's modes of\nthinking, feeling, and acting, do not depend on causes; nor can we doubt\nthat if, in the case of any individual, our data could be complete, we\neven now know enough of the ultimate laws by which mental phenomena are\ndetermined, to enable us in many cases to predict, with tolerable\ncertainty, what, in the greater number of supposable combinations of\ncircumstances, his conduct or sentiments would be. But the impressions\nand actions of human beings are not solely the result of their present\ncircumstances, but the joint result of those circumstances and of the\ncharacters of the individuals: and the agencies which determine human\ncharacter are so numerous and diversified, (nothing which has happened\nto the person throughout life being without its portion of influence,)\nthat in the aggregate they are never in any two cases exactly similar.\nHence, even if our science of human nature were theoretically perfect,\nthat is, if we could calculate any character as we can calculate the\norbit of any planet, _from given data_; still, as the data are never\nall given, nor ever precisely alike in different cases, we could neither\nmake positive predictions, nor lay down universal propositions.\n\nInasmuch, however, as many of those effects which it is of most\nimportance to render amenable to human foresight and control are\ndetermined, like the tides, in an incomparably greater degree by general\ncauses, than by all partial causes taken together; depending in the main\non those circumstances and qualities which are common to all mankind, or\nat least to large bodies of them, and only in a small degree on the\nidiosyncrasies of organization or the peculiar history of individuals;\nit is evidently possible with regard to all such effects, to make\npredictions which will _almost_ always be verified, and general\npropositions which are almost always true. And whenever it is sufficient\nto know how the great majority of the human race, or of some nation or\nclass of persons, will think, feel, and act, these propositions are\nequivalent to universal ones. For the purposes of political and social\nscience this _is_ sufficient. As we formerly remarked,[2] an approximate\ngeneralization is, in social inquiries, for most practical purposes\nequivalent to an exact one; that which is only probable when asserted of\nindividual human beings indiscriminately selected, being certain when\naffirmed of the character and collective conduct of masses.\n\nIt is no disparagement, therefore, to the science of Human Nature, that\nthose of its general propositions which descend sufficiently into detail\nto serve as a foundation for predicting phenomena in the concrete, are\nfor the most part only approximately true. But in order to give a\ngenuinely scientific character to the study, it is indispensable that\nthese approximate generalizations, which in themselves would amount only\nto the lowest kind of empirical laws, should be connected deductively\nwith the laws of nature from which they result; should be resolved into\nthe properties of the causes on which the phenomena depend. In other\nwords, the science of Human Nature may be said to exist, in proportion\nas the approximate truths, which compose a practical knowledge of\nmankind, can be exhibited as corollaries from the universal laws of\nhuman nature on which they rest; whereby the proper limits of those\napproximate truths would be shown, and we should be enabled to deduce\nothers for any new state of circumstances, in anticipation of specific\nexperience.\n\nThe proposition now stated is the text on which the two succeeding\nchapters will furnish the comment.\n\n\n\n\nCHAPTER IV.\n\nOF THE LAWS OF MIND.\n\n\n\u00a7 1. What the Mind is, as well as what Matter is, or any other question\nrespecting Things in themselves, as distinguished from their sensible\nmanifestations, it would be foreign to the purposes of this treatise to\nconsider. Here, as throughout our inquiry, we shall keep clear of all\nspeculations respecting the mind's own nature, and shall understand by\nthe laws of mind, those of mental Phenomena; of the various feelings or\nstates of consciousness of sentient beings. These, according to the\nclassification we have uniformly followed, consist of Thoughts,\nEmotions, Volitions, and Sensations; the last being as truly states of\nMind as the three former. It is usual indeed to speak of sensations as\nstates of body, not of mind. But this is the common confusion, of giving\none and the same name to a phenomenon and to the proximate cause or\nconditions of the phenomenon. The immediate antecedent of a sensation is\na state of body, but the sensation itself is a state of mind. If the\nword mind means anything, it means that which feels. Whatever opinion we\nhold respecting the fundamental identity or diversity of matter and\nmind, in any case the distinction between mental and physical facts,\nbetween the internal and the external world, will always remain, as a\nmatter of classification: and in that classification, sensations, like\nall other feelings, must be ranked as mental phenomena. The mechanism of\ntheir production, both in the body itself and in what is called outward\nnature, is all that can with any propriety be classed as physical.\n\nThe phenomena of mind, then, are the various feelings of our nature,\nboth those improperly called physical, and those peculiarly designated\nas mental: and by the laws of mind, I mean the laws according to which\nthose feelings generate one another.\n\n\n\u00a7 2. All states of mind are immediately caused either by other states of\nmind, or by states of body. When a state of mind is produced by a state\nof mind, I call the law concerned in the case, a law of Mind. When a\nstate of mind is produced directly by a state of body, the law is a law\nof Body, and belongs to physical science.\n\nWith regard to those states of mind which are called sensations, all are\nagreed that these have for their immediate antecedents, states of body.\nEvery sensation has for its proximate cause some affection of the\nportion of our frame called the nervous system; whether this affection\noriginate in the action of some external object, or in some pathological\ncondition of the nervous organization itself. The laws of this portion\nof our nature--the varieties of our sensations, and the physical\nconditions on which they proximately depend--manifestly belong to the\nprovince of Physiology.\n\nWhether the remainder of our mental states are similarly dependent on\nphysical conditions, is one of the _vexat\u00e6 questiones_ in the science of\nhuman nature. It is still disputed whether our thoughts, emotions, and\nvolitions are generated through the intervention of material mechanism;\nwhether we have organs of thought and of emotion, in the same sense in\nwhich we have organs of sensation. Many eminent physiologists hold the\naffirmative. These contend, that a thought (for example) is as much the\nresult of nervous agency, as a sensation: that some particular state of\nour nervous system, in particular of that central portion of it called\nthe brain, invariably precedes, and is presupposed by, every state of\nour consciousness. According to this theory, one state of mind is never\nreally produced by another: all are produced by states of body. When one\nthought seems to call up another by association, it is not really a\nthought which recals a thought; the association did not exist between\nthe two thoughts, but between the two states of the brain or nerves\nwhich preceded the thoughts: one of those states recals the other, each\nbeing attended, in its passage, by the particular state of consciousness\nwhich is consequent on it. On this theory the uniformities of succession\namong states of mind would be mere derivative uniformities, resulting\nfrom the laws of succession of the bodily states which cause them. There\nwould be no original mental laws, no Laws of Mind in the sense in which\nI use the term, at all: and mental science would be a mere branch,\nthough the highest and most recondite branch, of the science of\nphysiology. M. Comte, accordingly, claims the scientific cognizance of\nmoral and intellectual phenomena exclusively for physiologists; and not\nonly denies to Psychology, or Mental Philosophy properly so called, the\ncharacter of a science, but places it, in the chimerical nature of its\nobjects and pretensions, almost on a par with astrology.\n\nBut, after all has been said which can be said, it remains incontestible\nthat there exist uniformities of succession among states of mind, and\nthat these can be ascertained by observation and experiment. Further,\nthat every mental state has a nervous state for its immediate antecedent\nand proximate cause, though extremely probable, cannot hitherto be said\nto be proved, in the conclusive manner in which this can be proved of\nsensations; and even were it certain, yet every one must admit that we\nare wholly ignorant of the characteristics of these nervous states; we\nknow not, and at present have no means of knowing, in what respect one\nof them differs from another; and our only mode of studying their\nsuccessions or coexistences must be by observing the successions and\ncoexistences of the mental states, of which they are supposed to be the\ngenerators or causes. The successions, therefore, which obtain among\nmental phenomena, do not admit of being deduced from the physiological\nlaws of our nervous organization: and all real knowledge of them must\ncontinue, for a long time at least, if not always, to be sought in the\ndirect study, by observation and experiment, of the mental successions\nthemselves. Since therefore the order of our mental phenomena must be\nstudied in those phenomena, and not inferred from the laws of any\nphenomena more general, there is a distinct and separate Science of\nMind.\n\nThe relations, indeed, of that science to the science of physiology must\nnever be overlooked or undervalued. It must by no means be forgotten\nthat the laws of mind may be derivative laws resulting from laws of\nanimal life, and that their truth therefore may ultimately depend on\nphysical conditions; and the influence of physiological states or\nphysiological changes in altering or counteracting the mental\nsuccessions, is one of the most important departments of psychological\nstudy. But, on the other hand, to reject the resource of psychological\nanalysis, and construct the theory of the mind solely on such data as\nphysiology at present affords, seems to me as great an error in\nprinciple, and an even more serious one in practice. Imperfect as is the\nscience of mind, I do not scruple to affirm, that it is in a\nconsiderably more advanced state than the portion of physiology which\ncorresponds to it; and to discard the former for the latter appears to\nme an infringement of the true canons of inductive philosophy, which\nmust produce, and which does produce, erroneous conclusions in some very\nimportant departments of the science of human nature.\n\n\n\u00a7 3. The subject, then, of Psychology, is the uniformities of\nsuccession, the laws, whether ultimate or derivative, according to which\none mental state succeeds another; is caused by, or at least, is caused\nto follow, another. Of these laws, some are general, others more\nspecial. The following are examples of the most general laws.\n\nFirst: Whenever any state of consciousness has once been excited in us,\nno matter by what cause; an inferior degree of the same state of\nconsciousness, a state of consciousness resembling the former, but\ninferior in intensity, is capable of being reproduced in us, without the\npresence of any such cause as excited it at first. Thus, if we have once\nseen or touched an object, we can afterwards think of the object though\nit be absent from our sight or from our touch. If we have been joyful or\ngrieved at some event, we can think of, or remember our past joy or\ngrief, though no new event of a happy or painful nature has taken place.\nWhen a poet has put together a mental picture of an imaginary object, a\nCastle of Indolence, a Una, or a Hamlet, he can afterwards think of the\nideal object he has created, without any fresh act of intellectual\ncombination. This law is expressed by saying, in the language of Hume,\nthat every mental _impression_ has its _idea_.\n\nSecondly: These ideas, or secondary mental states, are excited by our\nimpressions, or by other ideas, according to certain laws which are\ncalled Laws of Association. Of these laws the first is, that similar\nideas tend to excite one another. The second is, that when two\nimpressions have been frequently experienced (or even thought of) either\nsimultaneously or in immediate succession, then whenever one of these\nimpressions, or the idea of it, recurs, it tends to excite the idea of\nthe other. The third law is, that greater intensity in either or both of\nthe impressions, is equivalent, in rendering them excitable by one\nanother, to a greater frequency of conjunction. These are the laws of\nideas: on which I shall not enlarge in this place, but refer the reader\nto works professedly psychological, in particular to Mr. James Mill's\n_Analysis of the Phenomena of the Human Mind_, where the principal laws\nof association, along with many of their applications, are copiously\nexemplified, and with a masterly hand.[3]\n\nThese simple or elementary Laws of Mind have been ascertained by the\nordinary methods of experimental inquiry; nor could they have been\nascertained in any other manner. But a certain number of elementary\nlaws having thus been obtained, it is a fair subject of scientific\ninquiry how far those laws can be made to go in explaining the actual\nphenomena. It is obvious that complex laws of thought and feeling not\nonly may, but must, be generated from these simple laws. And it is to be\nremarked, that the case is not always one of Composition of Causes: the\neffect of concurring causes is not always precisely the sum of the\neffects of those causes when separate, nor even always an effect of the\nsame kind with them. Reverting to the distinction which occupies so\nprominent a place in the theory of induction; the laws of the phenomena\nof mind are sometimes analogous to mechanical, but sometimes also to\nchemical laws. When many impressions or ideas are operating in the mind\ntogether, there sometimes takes place a process, of a similar kind to\nchemical combination. When impressions have been so often experienced in\nconjunction, that each of them calls up readily and instantaneously the\nideas of the whole group, those ideas sometimes melt and coalesce into\none another, and appear not several ideas, but one; in the same manner\nas, when the seven prismatic colours are presented to the eye in rapid\nsuccession, the sensation produced is that of white. But as in this last\ncase it is correct to say that the seven colours when they rapidly\nfollow one another _generate_ white, but not that they actually _are_\nwhite; so it appears to me that the Complex Idea, formed by the blending\ntogether of several simpler ones, should, when it really appears simple,\n(that is, when the separate elements are not consciously distinguishable\nin it,) be said to _result from_, or _be generated by_, the simple\nideas, not to _consist_ of them. Our idea of an orange really _consists_\nof the simple ideas of a certain colour, a certain form, a certain taste\nand smell, &c., because we can, by interrogating our consciousness,\nperceive all these elements in the idea. But we cannot perceive, in so\napparently simple a feeling as our perception of the shape of an object\nby the eye, all that multitude of ideas derived from other senses,\nwithout which it is well ascertained that no such visual perception\nwould ever have had existence; nor, in our idea of Extension, can we\ndiscover those elementary ideas of resistance, derived from our\nmuscular frame, in which it has been conclusively shown that the idea\noriginates. These therefore are cases of mental chemistry: in which it\nis proper to say that the simple ideas generate, rather than that they\ncompose, the complex ones.\n\nWith respect to all the other constituents of the mind, its beliefs, its\nabstruser conceptions, its sentiments, emotions, and volitions; there\nare some (among whom are Hartley, and the author of the _Analysis_) who\nthink that the whole of these are generated from simple ideas of\nsensation, by a chemistry similar to that which we have just\nexemplified. These philosophers have made out a great part of their\ncase, but I am not satisfied that they have established the whole of it.\nThey have shown that there is such a thing as mental chemistry; that the\nheterogeneous nature of a feeling A, considered in relation to B and C,\nis no conclusive argument against its being generated from B and C.\nHaving proved this, they proceed to show, that where A is found, B and C\nwere or may have been present, and why therefore, they ask, should not A\nhave been generated from B and C? But even if this evidence were carried\nto the highest degree of completeness which it admits of; if it were\nshown (which hitherto it has not, in all cases, been) that certain\ngroups of associated ideas not only might have been, but actually were,\npresent whenever the more recondite mental feeling was experienced; this\nwould amount only to the Method of Agreement, and could not prove\ncausation until confirmed by the more conclusive evidence of the Method\nof Difference. If the question be whether Belief is a mere case of close\nassociation of ideas, it would be necessary to examine experimentally if\nit be true that any ideas whatever, provided they are associated with\nthe required degree of closeness, give rise to belief. If the inquiry be\ninto the origin of moral feelings, the feeling for example of moral\nreprobation, it is necessary to compare all the varieties of actions or\nstates of mind which are ever morally disapproved, and see whether in\nall these cases it can be shown, or reasonably surmised, that the action\nor state of mind had become connected by association, in the\ndisapproving mind, with some particular class of hateful or disgusting\nideas; and the method employed is, thus far, that of Agreement. But\nthis is not enough. Supposing this proved, we must try further by the\nMethod of Difference, whether this particular kind of hateful or\ndisgusting ideas, when it becomes associated with an action previously\nindifferent, will render that action a subject of moral disapproval. If\nthis question can be answered in the affirmative, it is shown to be a\nlaw of the human mind, that an association of that particular\ndescription is the generating cause of moral reprobation. That all this\nis the case has been rendered extremely probable, but the experiments\nhave not been tried with the degree of precision necessary for a\ncomplete and absolutely conclusive induction.[4]\n\nIt is further to be remembered, that even if all which this theory of\nmental phenomena contends for could be proved, we should not be the more\nenabled to resolve the laws of the more complex feelings into those of\nthe simpler ones. The generation of one class of mental phenomena from\nanother, whenever it can be made out, is a highly interesting fact in\npsychological chemistry; but it no more supersedes the necessity of an\nexperimental study of the generated phenomenon, than a knowledge of the\nproperties of oxygen and sulphur enables us to deduce those of sulphuric\nacid without specific observation and experiment. Whatever, therefore,\nmay be the final issue of the attempt to account for the origin of our\njudgments, our desires, or our volitions, from simpler mental phenomena,\nit is not the less imperative to ascertain the sequences of the complex\nphenomena themselves, by special study in conformity to the canons of\nInduction. Thus, in respect to Belief, psychologists will always have to\ninquire, what beliefs we have by direct consciousness, and according to\nwhat laws one belief produces another; what are the laws, in virtue of\nwhich one thing is recognised by the mind, either rightly or\nerroneously, as evidence of another thing. In regard to Desire, they\nwill have to examine what objects we desire naturally, and by what\ncauses we are made to desire things originally indifferent, or even\ndisagreeable to us; and so forth. It may be remarked, that the general\nlaws of association prevail among these more intricate states of mind,\nin the same manner as among the simpler ones. A desire, an emotion, an\nidea of the higher order of abstraction, even our judgments and\nvolitions when they have become habitual, are called up by association,\naccording to precisely the same laws as our simple ideas.\n\n\n\u00a7 4. In the course of these inquiries it will be natural and necessary\nto examine, how far the production of one state of mind by another is\ninfluenced by any assignable state of body. The commonest observation\nshows that different minds are susceptible in very different degrees, to\nthe action of the same psychological causes. The idea, for example, of a\ngiven desirable object, will excite in different minds very different\ndegrees of intensity of desire. The same subject of meditation,\npresented to different minds, will excite in them very unequal degrees\nof intellectual action. These differences of mental susceptibility in\ndifferent individuals may be, first, original and ultimate facts, or,\nsecondly, they may be consequences of the previous mental history of\nthose individuals, or thirdly and lastly, they may depend on varieties\nof physical organization. That the previous mental history of the\nindividuals must have some share in producing or in modifying the whole\nof their mental character, is an inevitable consequence of the laws of\nmind; but that differences of bodily structure also co-operate, is the\nopinion of all physiologists, confirmed by common experience. It is to\nbe regretted that hitherto this experience, being accepted in the gross,\nwithout due analysis, has been made the groundwork of empirical\ngeneralizations most detrimental to the progress of real knowledge.\n\nIt is certain that the natural differences which really exist in the\nmental predispositions or susceptibilities of different persons, are\noften not unconnected with diversities in their organic constitution.\nBut it does not therefore follow that these organic differences must in\nall cases influence the mental phenomena directly and immediately. They\noften affect them through the medium of their psychological causes. For\nexample, the idea of some particular pleasure may excite in different\npersons, even independently of habit or education, very different\nstrengths of desire, and this may be the effect of their different\ndegrees or kinds of nervous susceptibility; but these organic\ndifferences, we must remember, will render the pleasurable sensation\nitself more intense in one of these persons than in the other; so that\nthe idea of the pleasure will also be an intenser feeling, and will, by\nthe operation of mere mental laws, excite an intenser desire, without\nits being necessary to suppose that the desire itself is directly\ninfluenced by the physical peculiarity. As in this, so in many cases,\nsuch differences in the kind or in the intensity of the physical\nsensations as must necessarily result from differences of bodily\norganization, will of themselves account for many differences not only\nin the degree, but even in the kind, of the other mental phenomena. So\ntrue is this, that even different _qualities_ of mind, different types\nof mental character, will naturally be produced by mere differences of\nintensity in the sensations generally: as is well pointed out in an able\nessay on Dr. Priestley, mentioned in a former chapter:--\n\n\"The sensations which form the elements of all knowledge are received\neither simultaneously or successively; when several are received\nsimultaneously, as the smell, the taste, the colour, the form, &c. of a\nfruit, their association together constitutes our idea of an _object_;\nwhen received successively, their association makes up the idea of an\n_event_. Anything, then, which favours the associations of synchronous\nideas, will tend to produce a knowledge of objects, a perception of\nqualities; while anything which favours association in the successive\norder, will tend to produce a knowledge of events, of the order of\noccurrences, and of the connexion of cause and effect: in other words,\nin the one case a perceptive mind, with a discriminate feeling of the\npleasurable and painful properties of things, a sense of the grand and\nthe beautiful, will be the result: in the other, a mind attentive to the\nmovements and phenomena, a ratiocinative and philosophic intellect. Now\nit is an acknowledged principle, that all sensations experienced during\nthe presence of any vivid impression, become strongly associated with\nit, and with each other; and does it not follow, that the synchronous\nfeelings of a sensitive constitution, (_i.e._ the one which has vivid\nimpressions,) will be more intimately blended than in a differently\nformed mind? If this suggestion has any foundation in truth, it leads to\nan inference not unimportant; that where nature has endowed an\nindividual with great original susceptibility, he will probably be\ndistinguished by fondness for natural history, a relish for the\nbeautiful and great, and moral enthusiasm; where there is but a\nmediocrity of sensibility, a love of science, of abstract truth, with a\ndeficiency of taste and of fervour, is likely to be the result.\"\n\nWe see from this example, that when the general laws of mind are more\naccurately known, and above all, more skilfully applied to the detailed\nexplanation of mental peculiarities, they will account for many more of\nthose peculiarities than is ordinarily supposed. Unfortunately the\nreaction of the last and present generation against the philosophy of\nthe eighteenth century has produced a very general neglect of this great\ndepartment of analytical inquiry; of which, consequently, the recent\nprogress has been by no means proportional to its early promise. The\nmajority of those who speculate on human nature, prefer dogmatically to\nassume that the mental differences which they perceive, or think they\nperceive, among human beings, are ultimate facts, incapable of being\neither explained or altered, rather than take the trouble of fitting\nthemselves, by the requisite processes of thought, for referring those\nmental differences to the outward causes by which they are for the most\npart produced, and on the removal of which they would cease to exist.\nThe German school of metaphysical speculation, which has not yet lost\nits temporary predominance in European thought, has had this among many\nother injurious influences: and at the opposite extreme of the\npsychological scale, no writer, either of early or of recent date, is\nchargeable in a higher degree with this aberration from the true\nscientific spirit, than M. Comte.\n\nIt is certain that, in human beings at least, differences in education\nand in outward circumstances are capable of affording an adequate\nexplanation of by far the greatest portion of character; and that the\nremainder may be in great part accounted for by physical differences in\nthe sensations produced in different individuals by the same external or\ninternal cause. There are, however, some mental facts which do not seem\nto admit of these modes of explanation. Such, to take the strongest\ncase, are the various instincts of animals, and the portion of human\nnature which corresponds to those instincts. No mode has been suggested,\neven by way of hypothesis, in which these can receive any satisfactory,\nor even plausible, explanation from psychological causes alone; and\nthere is great reason to think that they have as positive, and even as\ndirect and immediate, a connexion with physical conditions of the brain\nand nerves, as any of our mere sensations have. A supposition which (it\nis perhaps not superfluous to add) in no way conflicts with the\nindisputable fact, that these instincts may be modified to any extent,\nor entirely conquered, in human beings at least, by other mental\ninfluences, and by education.\n\nWhether organic causes exercise a direct influence over any other\nclasses of mental phenomena, is hitherto as far from being ascertained,\nas is the precise nature of the organic conditions even in the case of\ninstincts. The physiology, however, of the brain and nervous system is\nin a state of such rapid advance, and is continually bringing forth such\nnew and interesting results, that if there be really a connexion between\nmental peculiarities and any varieties cognizable by our senses in the\nstructure of the cerebral and nervous apparatus, the nature of that\nconnexion is now in a fair way of being found out. The latest\ndiscoveries in cerebral physiology appear to have proved, that any such\nconnexion which may exist is of a radically different character from\nthat contended for by Gall and his followers, and that whatever may\nhereafter be found to be the true theory of the subject, phrenology at\nleast is untenable.\n\n\n\n\nCHAPTER V.\n\nOF ETHOLOGY, OR THE SCIENCE OF THE FORMATION OF CHARACTER.\n\n\n\u00a7 1. The laws of mind as characterized in the preceding chapter, compose\nthe universal or abstract portion of the philosophy of human nature; and\nall the truths of common experience, constituting a practical knowledge\nof mankind, must, to the extent to which they are truths, be results or\nconsequences of these. Such familiar maxims, when collected _\u00e0\nposteriori_ from observation of life, occupy among the truths of the\nscience the place of what, in our analysis of Induction, have so often\nbeen spoken of under the title of Empirical Laws.\n\nAn Empirical Law (it will be remembered) is an uniformity, whether of\nsuccession or of coexistence, which holds true in all instances within\nour limits of observation, but is not of a nature to afford any\nassurance that it would hold beyond those limits; either because the\nconsequent is not really the effect of the antecedent, but forms part\nalong with it of a chain of effects, flowing from prior causes not yet\nascertained; or because there is ground to believe that the sequence\n(though a case of causation) is resolvable into simpler sequences, and,\ndepending therefore on a concurrence of several natural agencies, is\nexposed to an unknown multitude of possibilities of counteraction. In\nother words, an empirical law is a generalization, of which, not content\nwith finding it true, we are obliged to ask, why is it true? knowing\nthat its truth is not absolute, but dependent on some more general\nconditions, and that it can only be relied on in so far as there is\nground of assurance that those conditions are realized.\n\nNow, the observations concerning human affairs collected from common\nexperience, are precisely of this nature. Even if they were universally\nand exactly true within the bounds of experience, which they never are,\nstill they are not the ultimate laws of human action; they are not the\nprinciples of human nature, but results of those principles under the\ncircumstances in which mankind have happened to be placed. When the\nPsalmist said in his haste that \"all men are liars,\" he enunciated what\nin some ages and countries is borne out by ample experience; but it is\nnot a law of man's nature to lie; though it is one of the consequences\nof the laws of human nature, that lying is nearly universal when certain\nexternal circumstances exist universally, especially circumstances\nproductive of habitual distrust and fear. When the character of the old\nis asserted to be cautious, and of the young impetuous, this, again, is\nbut an empirical law; for it is not because of their youth that the\nyoung are impetuous, nor because of their age that the old are cautious.\nIt is chiefly, if not wholly, because the old, during their many years\nof life, have generally had much experience of its various evils, and\nhaving suffered or seen others suffer much from incautious exposure to\nthem, have acquired associations favourable to circumspection: while the\nyoung, as well from the absence of similar experience as from the\ngreater strength of the inclinations which urge them to enterprise,\nengage themselves in it more readily. Here, then, is the _explanation_\nof the empirical law; here are the conditions which ultimately determine\nwhether the law holds good or not. If an old man has not been oftener\nthan most young men in contact with danger and difficulty, he will be\nequally incautious: if a youth has not stronger inclinations than an old\nman, he probably will be as little enterprising. The empirical law\nderives whatever truth it has, from the causal laws of which it is a\nconsequence. If we know those laws, we know what are the limits to the\nderivative law: while, if we have not yet accounted for the empirical\nlaw--if it rest only on observation--there is no safety in applying it\nfar beyond the limits of time, place, and circumstance, in which the\nobservations were made.\n\nThe really scientific truths, then, are not these empirical laws, but\nthe causal laws which explain them. The empirical laws of those\nphenomena which depend on known causes, and of which a general theory\ncan therefore be constructed, have, whatever may be their value in\npractice, no other function in science than that of verifying the\nconclusions of theory. Still more must this be the case when most of the\nempirical laws amount, even within the limits of observation, only to\napproximate generalizations.\n\n\n\u00a7 2. This however is not, so much as is sometimes supposed, a\npeculiarity of the sciences called moral. It is only in the simplest\nbranches of science that empirical laws are ever exactly true; and not\nalways in those. Astronomy, for example, is the simplest of all the\nsciences which explain, in the concrete, the actual course of natural\nevents. The causes or forces, on which astronomical phenomena depend,\nare fewer in number than those which determine any other of the great\nphenomena of nature. Accordingly, as each effect results from the\nconflict of but few causes, a great degree of regularity and uniformity\nmight be expected to exist among the effects; and such is really the\ncase: they have a fixed order, and return in cycles. But propositions\nwhich should express, with absolute correctness, all the successive\npositions of a planet until the cycle is completed, would be of almost\nunmanageable complexity, and could be obtained from theory alone. The\ngeneralizations which can be collected on the subject from direct\nobservation, even such as Kepler's law, are mere approximations: the\nplanets, owing to their perturbations by one another, do not move in\nexact ellipses. Thus even in astronomy, perfect exactness in the mere\nempirical laws is not to be looked for; much less, then, in more complex\nsubjects of inquiry.\n\nThe same example shows how little can be inferred against the\nuniversality or even the simplicity of the ultimate laws, from the\nimpossibility of establishing any but approximate empirical laws of the\neffects. The laws of causation according to which a class of phenomena\nare produced may be very few and simple, and yet the effects themselves\nmay be so various and complicated that it shall be impossible to trace\nany regularity whatever completely through them. For the phenomena in\nquestion may be of an eminently modifiable character; insomuch that\ninnumerable circumstances are capable of influencing the effect,\nalthough they may all do it according to a very small number of laws.\nSuppose that all which passes in the mind of man is determined by a few\nsimple laws: still, if those laws be such that there is not one of the\nfacts surrounding a human being, or of the events which happen to him,\nthat does not influence in some mode or degree his subsequent mental\nhistory, and if the circumstances of different human beings are\nextremely different, it will be no wonder if very few propositions can\nbe made respecting the details of their conduct or feelings, which will\nbe true of all mankind.\n\nNow, without deciding whether the ultimate laws of our mental nature are\nfew or many, it is at least certain that they are of the above\ndescription. It is certain that our mental states, and our mental\ncapacities and susceptibilities, are modified, either for a time or\npermanently, by everything which happens to us in life. Considering\ntherefore how much these modifying causes differ in the case of any two\nindividuals, it would be unreasonable to expect that the empirical laws\nof the human mind, the generalizations which can be made respecting the\nfeelings or actions of mankind without reference to the causes that\ndetermine them, should be anything but approximate generalizations. They\nare the common wisdom of common life, and as such are invaluable;\nespecially as they are mostly to be applied to cases not very dissimilar\nto those from which they were collected. But when maxims of this sort,\ncollected from Englishmen, come to be applied to Frenchmen, or when\nthose collected from the present day are applied to past or future\ngenerations, they are apt to be very much at fault. Unless we have\nresolved the empirical law into the laws of the causes on which it\ndepends, and ascertained that those causes extend to the case which we\nhave in view, there can be no reliance placed in our inferences. For\nevery individual is surrounded by circumstances different from those of\nevery other individual; every nation or generation of mankind from every\nother nation or generation: and none of these differences are without\ntheir influence in forming a different type of character. There is,\nindeed, also a certain general resemblance; but peculiarities of\ncircumstances are continually constituting exceptions even to the\npropositions which are true in the great majority of cases.\n\nAlthough, however, there is scarcely any mode of feeling or conduct\nwhich is, in the absolute sense, common to all mankind; and though the\ngeneralizations which assert that any given variety of conduct or\nfeeling will be found universally, (however nearly they may approximate\nto truth within given limits of observation,) will be considered as\nscientific propositions by no one who is at all familiar with scientific\ninvestigation; yet all modes of feeling and conduct met with among\nmankind have causes which produce them; and in the propositions which\nassign those causes, will be found the explanation of the empirical\nlaws, and the limiting principle of our reliance on them. Human beings\ndo not all feel and act alike in the same circumstances; but it is\npossible to determine what makes one person, in a given position, feel\nor act in one way, another in another; how any given mode of feeling and\nconduct, compatible with the general laws (physical and mental) of human\nnature, has been, or may be, formed. In other words, mankind have not\none universal character, but there exist universal laws of the Formation\nof Character. And since it is by these laws, combined with the facts of\neach particular case, that the whole of the phenomena of human action\nand feeling are produced, it is on these that every rational attempt to\nconstruct the science of human nature in the concrete, and for practical\npurposes, must proceed.\n\n\n\u00a7 3. The laws, then, of the formation of character being the principal\nobject of scientific inquiry into human nature; it remains to determine\nthe method of investigation best fitted for ascertaining them. And the\nlogical principles according to which this question is to be decided,\nmust be those which preside over every other attempt to investigate the\nlaws of very complex phenomena. For it is evident that both the\ncharacter of any human being, and the aggregate of the circumstances by\nwhich that character has been formed, are facts of a high order of\ncomplexity. Now to such cases we have seen that the Deductive Method,\nsetting out from general laws, and verifying their consequences by\nspecific experience, is alone applicable. The grounds of this great\nlogical doctrine have formerly been stated: and its truth will derive\nadditional support from a brief examination of the specialities of the\npresent case.\n\nThere are only two modes in which laws of nature can be ascertained:\ndeductively, and experimentally: including under the denomination of\nexperimental inquiry, observation as well as artificial experiment. Are\nthe laws of the formation of character susceptible of a satisfactory\ninvestigation by the method of experimentation? Evidently not; because,\neven if we suppose unlimited power of varying the experiment, (which is\nabstractedly possible, though no one but an oriental despot has that\npower, or if he had, would probably be disposed to exercise it,) a still\nmore essential condition is wanting; the power of performing any of the\nexperiments with scientific accuracy.\n\nThe instances requisite for the prosecution of a directly experimental\ninquiry into the formation of character, would be a number of human\nbeings to bring up and educate, from infancy to mature age. And to\nperform any one of these experiments with scientific propriety, it would\nbe necessary to know and record every sensation or impression received\nby the young pupil from a period long before it could speak; including\nits own notions respecting the sources of all those sensations and\nimpressions. It is not only impossible to do this completely, but even\nto do so much of it as should constitute a tolerable approximation. One\napparently trivial circumstance which eluded our vigilance, might let in\na train of impressions and associations sufficient to vitiate the\nexperiment as an authentic exhibition of the effects flowing from given\ncauses. No one who has sufficiently reflected on education is ignorant\nof this truth: and whoever has not, will find it most instructively\nillustrated in the writings of Rousseau and Helvetius on that great\nsubject.\n\nUnder this impossibility of studying the laws of the formation of\ncharacter by experiments purposely contrived to elucidate them, there\nremains the resource of simple observation. But if it be impossible to\nascertain the influencing circumstances with any approach to\ncompleteness even when we have the shaping of them ourselves, much more\nimpossible is it when the cases are further removed from our\nobservation, and altogether out of our control. Consider the difficulty\nof the very first step--of ascertaining what actually is the character\nof the individual, in each particular case that we examine. There is\nhardly any person living, concerning some essential part of whose\ncharacter there are not differences of opinion even among his intimate\nacquaintances: and a single action, or conduct continued only for a\nshort time, goes a very little way towards ascertaining it. We can only\nmake our observations in a rough way, and _en masse_; not attempting to\nascertain completely in any given instance, what character has been\nformed, and still less by what causes; but only observing in what state\nof previous circumstances it is found that certain marked mental\nqualities or deficiencies _oftenest_ exist. These conclusions, besides\nthat they are mere approximate generalizations, deserve no reliance even\nas such, unless the instances are sufficiently numerous to eliminate not\nonly chance, but every assignable circumstance in which a number of the\ncases examined may happen to have resembled one another. So numerous and\nvarious, too, are the circumstances which form individual character,\nthat the consequence of any particular combination is hardly ever some\ndefinite and strongly marked character, always found where that\ncombination exists, and not otherwise. What is obtained, even after the\nmost extensive and accurate observation, is merely a comparative result;\nas for example, that in a given number of Frenchmen, taken\nindiscriminately, there will be found more persons of a particular\nmental tendency, and fewer of the contrary tendency, than among an\nequal number of Italians or English, similarly taken; or thus: of a\nhundred Frenchmen and an equal number of Englishmen, fairly selected,\nand arranged according to the degree in which they possess a particular\nmental characteristic, each number, 1, 2, 3, &c., of the one series,\nwill be found to possess more of that characteristic than the\ncorresponding number of the other. Since, therefore, the comparison is\nnot one of kinds, but of ratios and degrees; and since in proportion as\nthe differences are slight, it requires a greater number of instances to\neliminate chance; it cannot often happen to any one to know a sufficient\nnumber of cases with the accuracy requisite for making the sort of\ncomparison last mentioned; less than which, however, would not\nconstitute a real induction. Accordingly there is hardly one current\nopinion respecting the characters of nations, classes, or descriptions\nof persons, which is universally acknowledged as indisputable.[5]\n\nAnd finally, if we could even obtain by way of experiment a much more\nsatisfactory assurance of these generalizations than is really possible,\nthey would still be only empirical laws. They would show, indeed, that\nthere was some connexion between the type of character formed, and the\ncircumstances existing in the case; but not what the precise connexion\nwas, nor to which of the peculiarities of those circumstances the effect\nwas really owing. They could only, therefore, be received as results of\ncausation, requiring to be resolved into the general laws of the causes:\nuntil the determination of which, we could not judge within what limits\nthe derivative laws might serve as presumptions in cases yet unknown, or\neven be depended on as permanent in the very cases from which they were\ncollected. The French people had, or were supposed to have, a certain\nnational character: but they drive out their royal family and\naristocracy, alter their institutions, pass through a series of\nextraordinary events for half a century, and at the end of that time are\nfound to be, in many respects, greatly altered. A long list of mental\nand moral differences are observed, or supposed, to exist between men\nand women: but at some future, and, it may be hoped, not distant period,\nequal freedom and an equally independent social position come to be\npossessed by both, and their differences of character are either removed\nor totally altered.\n\nBut if the differences which we think we observe between French and\nEnglish, or between men and women, can be connected with more general\nlaws; if they be such as might be expected to be produced by the\ndifferences of government, former customs, and physical peculiarities in\nthe two nations, and by the diversities of education, occupations,\npersonal independence, and social privileges, and whatever original\ndifferences there may be in bodily strength and nervous sensibility,\nbetween the two sexes; then, indeed, the coincidence of the two kinds of\nevidence justifies us in believing that we have both reasoned rightly\nand observed rightly. Our observation, though not sufficient as proof,\nis ample as verification. And having ascertained not only the empirical\nlaws, but the causes, of the peculiarities, we need be under no\ndifficulty in judging how far they may be expected to be permanent, or\nby what circumstances they would be modified or destroyed.\n\n\n\u00a7 4. Since, then, it is impossible to obtain really accurate\npropositions respecting the formation of character from observation and\nexperiment alone, we are driven perforce to that which, even if it had\nnot been the indispensable, would have been the most perfect, mode of\ninvestigation, and which it is one of the principal aims of philosophy\nto extend; namely, that which tries its experiments not on the complex\nfacts, but on the simple ones of which they are compounded; and after\nascertaining the laws of the causes, the composition of which gives rise\nto the complex phenomena, then considers whether these will not explain\nand account for the approximate generalizations which have been framed\nempirically respecting the sequences of those complex phenomena. The\nlaws of the formation of character are, in short, derivative laws,\nresulting from the general laws of mind; and are to be obtained by\ndeducing them from those general laws; by supposing any given set of\ncircumstances, and then considering what, according to the laws of mind,\nwill be the influence of those circumstances on the formation of\ncharacter.\n\nA science is thus formed, to which I would propose to give the name of\nEthology, or the Science of Character; from [Greek: \u00eathos], a word more\nnearly corresponding to the term \"character\" as I here use it, than any\nother word in the same language. The name is perhaps etymologically\napplicable to the entire science of our mental and moral nature; but if,\nas is usual and convenient, we employ the name Psychology for the\nscience of the elementary laws of mind, Ethology will serve for the\nulterior science which determines the kind of character produced, in\nconformity to those general laws, by any set of circumstances, physical\nand moral. According to this definition, Ethology is the science which\ncorresponds to the art of education; in the widest sense of the term,\nincluding the formation of national or collective character as well as\nindividual. It would indeed be vain to expect (however completely the\nlaws of the formation of character might be ascertained) that we could\nknow so accurately the circumstances of any given case as to be able\npositively to predict the character that would be produced in that\ncase. But we must remember that a degree of knowledge far short of the\npower of actual prediction, is often of much practical value. There may\nbe great power of influencing phenomena, with a very imperfect knowledge\nof the causes by which they are in any given instance determined. It is\nenough that we know that certain means have a _tendency_ to produce a\ngiven effect, and that others have a tendency to frustrate it. When the\ncircumstances of an individual or of a nation are in any considerable\ndegree under our control, we may, by our knowledge of tendencies, be\nenabled to shape those circumstances in a manner much more favourable to\nthe ends we desire, than the shape which they would of themselves\nassume. This is the limit of our power; but within this limit the power\nis a most important one.\n\nThis science of Ethology may be called the Exact Science of Human\nNature; for its truths are not, like the empirical laws which depend on\nthem, approximate generalizations, but real laws. It is, however, (as in\nall cases of complex phenomena) necessary to the exactness of the\npropositions, that they should be hypothetical only, and affirm\ntendencies, not facts. They must not assert that something will always,\nor certainly, happen; but only that such and such will be the effect of\na given cause, so far as it operates uncounteracted. It is a scientific\nproposition, that bodily strength tends to make men courageous; not that\nit always makes them so: that an interest on one side of a question\ntends to bias the judgment; not that it invariably does so: that\nexperience tends to give wisdom; not that such is always its effect.\nThese propositions, being assertive only of tendencies, are not the less\nuniversally true because the tendencies may be frustrated.\n\n\n\u00a7 5. While on the one hand Psychology is altogether, or principally, a\nscience of observation and experiment, Ethology, as I have conceived it,\nis, as I have already remarked, altogether deductive. The one ascertains\nthe simple laws of Mind in general, the other traces their operation in\ncomplex combinations of circumstances. Ethology stands to Psychology in\na relation very similar to that in which the various branches of natural\nphilosophy stand to mechanics. The principles of Ethology are properly\nthe middle principles, the _axiomata media_ (as Bacon would have said)\nof the science of mind: as distinguished, on the one hand from the\nempirical laws resulting from simple observation, and on the other from\nthe highest generalizations.\n\nAnd this seems a suitable place for a logical remark, which, though of\ngeneral application, is of peculiar importance in reference to the\npresent subject. Bacon has judiciously observed that the _axiomata\nmedia_ of every science principally constitute its value. The lowest\ngeneralizations, until explained by and resolved into the middle\nprinciples of which they are the consequences, have only the imperfect\naccuracy of empirical laws; while the most general laws are _too_\ngeneral, and include too few circumstances, to give sufficient\nindication of what happens in individual cases, where the circumstances\nare almost always immensely numerous. In the importance, therefore,\nwhich Bacon assigns, in every science, to the middle principles, it is\nimpossible not to agree with him. But I conceive him to have been\nradically wrong in his doctrine respecting the mode in which these\n_axiomata media_ should be arrived at; though there is no one\nproposition laid down in his works for which he has been more\nextravagantly eulogized. He enunciates as an universal rule, that\ninduction should proceed from the lowest to the middle principles, and\nfrom those to the highest, never reversing that order, and consequently\nleaving no room for the discovery of new principles by way of deduction\nat all. It is not to be conceived that a man of his sagacity could have\nfallen into this mistake, if there had existed in his time, among the\nsciences which treat of successive phenomena, one single instance of a\ndeductive science, such as mechanics, astronomy, optics, acoustics, &c.\nnow are. In those sciences it is evident that the higher and middle\nprinciples are by no means derived from the lowest, but the reverse. In\nsome of them the very highest generalizations were those earliest\nascertained with any scientific exactness; as, for example (in\nmechanics), the laws of motion. Those general laws had not indeed at\nfirst the acknowledged universality which they acquired after having\nbeen successfully employed to explain many classes of phenomena to which\nthey were not originally seen to be applicable; as when the laws of\nmotion were employed, in conjunction with other laws, to explain\ndeductively the celestial phenomena. Still, the fact remains, that the\npropositions which were afterwards recognised as the most general truths\nof the science, were, of all its accurate generalizations, those\nearliest arrived at. Bacon's greatest merit cannot therefore consist, as\nwe are so often told that it did, in exploding the vicious method\npursued by the ancients of flying to the highest generalizations first,\nand deducing the middle principles from them; since this is neither a\nvicious nor an exploded, but the universally accredited method of modern\nscience, and that to which it owes its greatest triumphs. The error of\nancient speculation did not consist in making the largest\ngeneralizations first, but in making them without the aid or warrant of\nrigorous inductive methods, and applying them deductively without the\nneedful use of that important part of the Deductive Method termed\nVerification.\n\nThe order in which truths of the various degrees of generality should be\nascertained, cannot, I apprehend, be prescribed by any unbending rule. I\nknow of no maxim which can be laid down on the subject, but to obtain\nthose first, in respect to which the conditions of a real induction can\nbe first and most completely realized. Now, wherever our means of\ninvestigation can reach causes, without stopping at the empirical laws\nof the effects, the simplest cases, being those in which fewest causes\nare simultaneously concerned, will be most amenable to the inductive\nprocess; and these are the cases which elicit laws of the greatest\ncomprehensiveness. In every science, therefore, which has reached the\nstage at which it becomes a science of causes, it will be usual as well\nas desirable first to obtain the highest generalizations, and then\ndeduce the more special ones from them. Nor can I discover any\nfoundation for the Baconian maxim, so much extolled by subsequent\nwriters, except this: That before we attempt to explain deductively\nfrom more general laws any new class of phenomena, it is desirable to\nhave gone as far as is practicable in ascertaining the empirical laws of\nthose phenomena; so as to compare the results of deduction, not with one\nindividual instance after another, but with general propositions\nexpressive of the points of agreement which have been found among many\ninstances. For if Newton had been obliged to verify the theory of\ngravitation, not by deducing from it Kepler's laws, but by deducing all\nthe observed planetary positions which had served Kepler to establish\nthose laws, the Newtonian theory would probably never have emerged from\nthe state of an hypothesis.[6]\n\nThe applicability of these remarks to the special case under\nconsideration, cannot admit of question. The science of the formation of\ncharacter is a science of causes. The subject is one to which those\namong the canons of induction, by which laws of causation are\nascertained, can be rigorously applied. It is, therefore, both natural\nand advisable to ascertain the simplest, which are necessarily the most\ngeneral, laws of causation first, and to deduce the middle principles\nfrom them. In other words, Ethology, the deductive science, is a system\nof corollaries from Psychology, the experimental science.\n\n\n\u00a7 6. Of these, the earlier alone has been, as yet, really conceived or\nstudied as a science; the other, Ethology, is still to be created. But\nits creation has at length become practicable. The empirical laws,\ndestined to verify its deductions, have been formed in abundance by\nevery successive age of humanity; and the premises for the deductions\nare now sufficiently complete. Excepting the degree of uncertainty which\nstill exists as to the extent of the natural differences of individual\nminds, and the physical circumstances on which these may be dependent,\n(considerations which are of secondary importance when we are\nconsidering mankind in the average, or _en masse_,) I believe most\ncompetent judges will agree that the general laws of the different\nconstituent elements of human nature are even now sufficiently\nunderstood, to render it possible for a competent thinker to deduce from\nthose laws with a considerable approach to certainty, the particular\ntype of character which would be formed, in mankind generally, by any\nassumed set of circumstances. A science of Ethology, founded on the laws\nof Psychology, is therefore possible; though little has yet been done,\nand that little not at all systematically, towards forming it. The\nprogress of this important but most imperfect science will depend on a\ndouble process: first, that of deducing theoretically the ethological\nconsequences of particular circumstances of position, and comparing them\nwith the recognised results of common experience; and secondly, the\nreverse operation; increased study of the various types of human nature\nthat are to be found in the world; conducted by persons not only capable\nof analysing and recording the circumstances in which these types\nseverally prevail, but also sufficiently acquainted with psychological\nlaws, to be able to explain and account for the characteristics of the\ntype, by the peculiarities of the circumstances: the residuum alone,\nwhen there proves to be any, being set down to the account of congenital\npredispositions.\n\nFor the experimental or _\u00e0 posteriori_ part of this process, the\nmaterials are continually accumulating by the observation of mankind. So\nfar as thought is concerned, the great problem of Ethology is to deduce\nthe requisite middle principles from the general laws of Psychology.\nThe subject to be studied is, the origin and sources of all those\nqualities in human beings which are interesting to us, either as facts\nto be produced, to be avoided, or merely to be understood: and the\nobject is, to determine, from the general laws of mind, combined with\nthe general position of our species in the universe, what actual or\npossible combinations of circumstances are capable of promoting or of\npreventing the production of those qualities. A science which possesses\nmiddle principles of this kind, arranged in the order, not of causes,\nbut of the effects which it is desirable to produce or to prevent, is\nduly prepared to be the foundation of the corresponding Art. And when\nEthology shall be thus prepared, practical education will be the mere\ntransformation of those principles into a parallel system of precepts,\nand the adaptation of these to the sum total of the individual\ncircumstances which exist in each particular case.\n\nIt is hardly necessary again to repeat, that, as in every other\ndeductive science, verification _\u00e0 posteriori_ must proceed _pari passu_\nwith deduction _\u00e0 priori_. The inference given by theory as to the type\nof character which would be formed by any given circumstances, must be\ntested by specific experience of those circumstances whenever\nobtainable; and the conclusions of the science as a whole, must undergo\na perpetual verification and correction from the general remarks\nafforded by common experience respecting human nature in our own age,\nand by history respecting times gone by. The conclusions of theory\ncannot be trusted, unless confirmed by observation; nor those of\nobservation, unless they can be affiliated to theory, by deducing them\nfrom the laws of human nature, and from a close analysis of the\ncircumstances of the particular situation. It is the accordance of these\ntwo kinds of evidence separately taken--the consilience of _\u00e0 priori_\nreasoning and specific experience--which forms the only sufficient\nground for the principles of any science so \"immersed in matter,\"\ndealing with such complex and concrete phenomena, as Ethology.\n\n\n\n\nCHAPTER VI.\n\nGENERAL CONSIDERATIONS ON THE SOCIAL SCIENCE.\n\n\n\u00a7 1. Next after the science of individual man, comes the science of man\nin society: of the actions of collective masses of mankind, and the\nvarious phenomena which constitute social life.\n\nIf the formation of individual character is already a complex subject of\nstudy, this subject must be, in appearance at least, still more complex;\nbecause the number of concurrent causes, all exercising more or less\ninfluence on the total effect, is greater, in the proportion in which a\nnation, or the species at large, exposes a larger surface to the\noperation of agents, psychological and physical, than any single\nindividual. If it was necessary to prove, in opposition to an existing\nprejudice, that the simpler of the two is capable of being a subject of\nscience; the prejudice is likely to be yet stronger against the\npossibility of giving a scientific character to the study of Politics,\nand of the phenomena of Society. It is, accordingly, but of yesterday\nthat the conception of a political or social science has existed,\nanywhere but in the mind of here and there an insulated thinker,\ngenerally very ill prepared for its realization: though the subject\nitself has of all others engaged the most general attention, and been a\ntheme of interested and earnest discussions, almost from the beginning\nof recorded time.\n\nThe condition indeed of politics, as a branch of knowledge, was until\nvery lately, and has scarcely even yet ceased to be, that which Bacon\nanimadverted on, as the natural state of the sciences while their\ncultivation is abandoned to practitioners; not being carried on as a\nbranch of speculative inquiry, but only with a view to the exigencies of\ndaily practice, and the _fructifera experimenta_, therefore, being\naimed at, almost to the exclusion of the _lucifera_. Such was medical\ninvestigation, before physiology and natural history began to be\ncultivated as branches of general knowledge. The only questions examined\nwere, what diet is wholesome, or what medicine will cure some given\ndisease; without any previous systematic inquiry into the laws of\nnutrition, and of the healthy and morbid action of the different organs,\non which laws the effect of any diet or medicine must evidently depend.\nAnd in politics, the questions which engaged general attention were\nsimilar:--Is such an enactment, or such a form of government, beneficial\nor the reverse--either universally, or to some particular community?\nwithout any previous inquiry into the general conditions by which the\noperation of legislative measures, or the effects produced by forms of\ngovernment, are determined. Students in politics thus attempted to study\nthe pathology and therapeutics of the social body, before they had laid\nthe necessary foundation in its physiology; to cure disease, without\nunderstanding the laws of health. And the result was such as it must\nalways be when persons, even of ability, attempt to deal with the\ncomplex questions of a science before its simpler and more elementary\ntruths have been established.\n\nNo wonder that when the phenomena of society have so rarely been\ncontemplated in the point of view characteristic of science, the\nphilosophy of society should have made little progress; should contain\nfew general propositions sufficiently precise and certain, for common\ninquirers to recognise in them a scientific character. The vulgar notion\naccordingly is, that all pretension to lay down general truths on\npolitics and society is quackery; that no universality and no certainty\nare attainable in such matters. What partly excuses this common notion\nis, that it is really not without foundation in one particular sense. A\nlarge proportion of those who have laid claim to the character of\nphilosophic politicians, have attempted, not to ascertain universal\nsequences, but to frame universal precepts. They have imagined some one\nform of government, or system of laws, to fit all cases; a pretension\nwell meriting the ridicule with which it is treated by practitioners,\nand wholly unsupported by the analogy of the art to which, from the\nnature of its subject, that of politics must be the most nearly allied.\nNo one now supposes it possible that one remedy can cure all diseases,\nor even the same disease in all constitutions and habits of body.\n\nIt is not necessary even to the perfection of a science, that the\ncorresponding art should possess universal, or even general, rules. The\nphenomena of society might not only be completely dependent on known\ncauses, but the mode of action of all those causes might be reducible to\nlaws of considerable simplicity, and yet no two cases might admit of\nbeing treated in precisely the same manner. So great might be the\nvariety of circumstances on which the results in different cases depend,\nthat the art might not have a single general precept to give, except\nthat of watching the circumstances of the particular case, and adapting\nour measures to the effects which, according to the principles of the\nscience, result from those circumstances. But although, in so\ncomplicated a class of subjects, it is impossible to lay down practical\nmaxims of universal application, it does not follow that the phenomena\ndo not conform to universal laws.\n\n\n\u00a7 2. All phenomena of society are phenomena of human nature, generated\nby the action of outward circumstances upon masses of human beings: and\nif, therefore, the phenomena of human thought, feeling, and action, are\nsubject to fixed laws, the phenomena of society cannot but conform to\nfixed laws, the consequence of the preceding. There is, indeed, no hope\nthat these laws, though our knowledge of them were as certain and as\ncomplete as it is in astronomy, would enable us to predict the history\nof society, like that of the celestial appearances, for thousands of\nyears to come. But the difference of certainty is not in the laws\nthemselves, it is in the data to which these laws are to be applied. In\nastronomy the causes influencing the result are few, and change little,\nand that little according to known laws; we can ascertain what they are\nnow, and thence determine what they will be at any epoch of a distant\nfuture. The data, therefore, in astronomy, are as certain as the laws\nthemselves. The circumstances, on the contrary, which influence the\ncondition and progress of society, are innumerable, and perpetually\nchanging; and though they all change in obedience to causes, and\ntherefore to laws, the multitude of the causes is so great as to defy\nour limited powers of calculation. Not to say that the impossibility of\napplying precise numbers to facts of such a description, would set an\nimpassable limit to the possibility of calculating them beforehand, even\nif the powers of the human intellect were otherwise adequate to the\ntask.\n\nBut, as before remarked, an amount of knowledge quite insufficient for\nprediction, may be most valuable for guidance. The science of society\nwould have attained a very high point of perfection, if it enabled us,\nin any given condition of social affairs, in the condition for instance\nof Europe or any European country at the present time, to understand by\nwhat causes it had, in any and every particular, been made what it was;\nwhether it was tending to any, and to what, changes; what effects each\nfeature of its existing state was likely to produce in the future; and\nby what means any of those effects might be prevented, modified, or\naccelerated, or a different class of effects superinduced. There is\nnothing chimerical in the hope that general laws, sufficient to enable\nus to answer these various questions for any country or time with the\nindividual circumstances of which we are well acquainted, do really\nadmit of being ascertained; and that the other branches of human\nknowledge, which this undertaking presupposes, are so far advanced that\nthe time is ripe for its commencement. Such is the object of the Social\nScience.\n\nThat the nature of what I consider the true method of the science may be\nmade more palpable, by first showing what that method is not; it will be\nexpedient to characterize briefly two radical misconceptions of the\nproper mode of philosophizing on society and government, one or other of\nwhich is, either explicitly or more often unconsciously, entertained by\nalmost all who have meditated or argued respecting the logic of\npolitics since the notion of treating it by strict rules, and on\nBaconian principles, has been current among the more advanced thinkers.\nThese erroneous methods, if the word method can be applied to erroneous\ntendencies arising from the absence of any sufficiently distinct\nconception of method, may be termed the Experimental, or Chemical, mode\nof investigation, and the Abstract, or Geometrical, mode. We shall begin\nwith the former.\n\n\n\n\nCHAPTER VII.\n\nOF THE CHEMICAL, OR EXPERIMENTAL, METHOD IN THE SOCIAL SCIENCE.\n\n\n\u00a7 1. The laws of the phenomena of society are, and can be, nothing but\nthe laws of the actions and passions of human beings united together in\nthe social state. Men, however, in a state of society, are still men;\ntheir actions and passions are obedient to the laws of individual human\nnature. Men are not, when brought together, converted into another kind\nof substance, with different properties; as hydrogen and oxygen are\ndifferent from water, or as hydrogen, oxygen, carbon, and azote, are\ndifferent from nerves, muscles, and tendons. Human beings in society\nhave no properties but those which are derived from, and may be resolved\ninto, the laws of the nature of individual man. In social phenomena the\nComposition of Causes is the universal law.\n\nNow, the method of philosophizing which may be termed chemical overlooks\nthis fact, and proceeds as if the nature of man as an individual were\nnot concerned at all, or were concerned in a very inferior degree, in\nthe operations of human beings in society. All reasoning in political or\nsocial affairs, grounded on principles of human nature, is objected to\nby reasoners of this sort, under such names as \"abstract theory.\" For\nthe direction of their opinions and conduct, they profess to demand, in\nall cases without exception, specific experience.\n\nThis mode of thinking is not only general with practitioners in\npolitics, and with that very numerous class who (on a subject which no\none, however ignorant, thinks himself incompetent to discuss) profess to\nguide themselves by common sense rather than by science; but is often\ncountenanced by persons with greater pretensions to instruction; persons\nwho, having sufficient acquaintance with books and with the current\nideas to have heard that Bacon taught mankind to follow experience, and\nto ground their conclusions on facts instead of metaphysical\ndogmas--think that, by treating political facts in as directly\nexperimental a method as chemical facts, they are showing themselves\ntrue Baconians, and proving their adversaries to be mere syllogizers and\nschoolmen. As, however, the notion of the applicability of experimental\nmethods to political philosophy cannot coexist with any just conception\nof these methods themselves, the kind of arguments from experience which\nthe chemical theory brings forth as its fruits (and which form the\nstaple, in this country especially, of parliamentary and hustings\noratory,) are such as, at no time since Bacon, would have been admitted\nto be valid in chemistry itself, or in any other branch of experimental\nscience. They are such as these; that the prohibition of foreign\ncommodities must conduce to national wealth, because England has\nflourished under it, or because countries in general which have adopted\nit have flourished; that our laws, or our internal administration, or\nour constitution, are excellent for a similar reason: and the eternal\narguments from historical examples, from Athens or Rome, from the fires\nin Smithfield or the French Revolution.\n\nI will not waste time in contending against modes of argumentation which\nno person, with the smallest practice in estimating evidence, could\npossibly be betrayed into; which draw conclusions of general application\nfrom a single unanalysed instance, or arbitrarily refer an effect to\nsome one among its antecedents, without any process of elimination or\ncomparison of instances. It is a rule both of justice and of good sense\nto grapple not with the absurdest, but with, the most reasonable form of\na wrong opinion. We shall suppose our inquirer acquainted with the true\nconditions of experimental investigation, and competent in point of\nacquirements for realizing them, so far as they can be realized. He\nshall know as much of the facts of history as mere erudition can\nteach--as much as can be proved by testimony, without the assistance of\nany theory; and if those mere facts, properly collated, can fulfil the\nconditions of a real induction, he shall be qualified for the task.\n\nBut, that no such attempt can have the smallest chance of success, has\nbeen abundantly shown in the tenth chapter of the Third Book.[7] We\nthere examined whether effects which depend on a complication of causes\ncan be made the subject of a true induction by observation and\nexperiment; and concluded, on the most convincing grounds, that they\ncannot. Since, of all effects, none depend on so great a complication of\ncauses as social phenomena, we might leave our case to rest in safety on\nthat previous showing. But a logical principle as yet so little familiar\nto the ordinary run of thinkers, requires to be insisted on more than\nonce, in order to make the due impression; and the present being the\ncase which of all others exemplifies it the most strongly, there will be\nadvantage in re-stating the grounds of the general maxim, as applied to\nthe specialities of the class of inquiries now under consideration.\n\n\n\u00a7 2. The first difficulty which meets us in the attempt to apply\nexperimental methods for ascertaining the laws of social phenomena, is\nthat we are without the means of making artificial experiments. Even if\nwe could contrive experiments at leisure, and try them without limit, we\nshould do so under immense disadvantage; both from the impossibility of\nascertaining and taking note of all the facts of each case, and because\n(those facts being in a perpetual state of change) before sufficient\ntime had elapsed to ascertain the result of the experiment, some\nmaterial circumstances would always have ceased to be the same. But it\nis unnecessary to consider the logical objections which would exist to\nthe conclusiveness of our experiments, since we palpably never have the\npower of trying any. We can only watch those which nature produces, or\nwhich are produced for other reasons. We cannot adapt our logical means\nto our wants, by varying the circumstances as the exigencies of\nelimination may require. If the spontaneous instances, formed by\ncotemporary events and by the successions of phenomena recorded in\nhistory, afford a sufficient variation of circumstances, an induction\nfrom specific experience is attainable; otherwise not. The question to\nbe resolved is, therefore, whether the requisites for induction\nrespecting the causes of political effects or the properties of\npolitical agents, are to be met with in history? including under the\nterm, cotemporary history. And in order to give fixity to our\nconceptions, it will be advisable to suppose this question asked in\nreference to some special subject of political inquiry or controversy;\nsuch as that frequent topic of debate in the present century, the\noperation of restrictive and prohibitory commercial legislation upon\nnational wealth. Let this, then, be the scientific question to be\ninvestigated by specific experience.\n\n\n\u00a7 3. In order to apply to the case the most perfect of the methods of\nexperimental inquiry, the Method of Difference, we require to find two\ninstances, which tally in every particular except the one which is the\nsubject of inquiry. If two nations can be found which are alike in all\nnatural advantages and disadvantages; whose people resemble each other\nin every quality, physical and moral, spontaneous and acquired; whose\nhabits, usages, opinions, laws and institutions are the same in all\nrespects, except that one of them has a more protective tariff, or in\nother respects interferes more with the freedom of industry; if one of\nthese nations is found to be rich, and the other poor, or one richer\nthan the other, this will be an _experimentum crucis_: a real proof by\nexperience, which of the two systems is most favourable to national\nriches. But the supposition that two such instances can be met with is\nmanifestly absurd. Nor is such a concurrence even abstractly possible.\nTwo nations which agreed in everything except their commercial policy,\nwould agree also in that. Differences of legislation are not inherent\nand ultimate diversities; are not properties of Kinds. They are effects\nof pre-existing causes. If the two nations differ in this portion of\ntheir institutions, it is from some difference in their position, and\nthence in their apparent interests, or in some portion or other of their\nopinions, habits, and tendencies; which opens a view of further\ndifferences without any assignable limit, capable of operating on their\nindustrial prosperity, as well as on every other feature of their\ncondition, in more ways than can be enumerated or imagined. There is\nthus a demonstrated impossibility of obtaining, in the investigations of\nthe social science, the conditions required for the most conclusive form\nof inquiry by specific experience.\n\nIn the absence of the direct, we may next try, as in other cases, the\nsupplementary resource, called in a former place the Indirect Method of\nDifference: which, instead of two instances differing in nothing but the\npresence or absence of a given circumstance, compares two _classes_ of\ninstances respectively agreeing in nothing but the presence of a\ncircumstance on the one side and its absence on the other. To choose the\nmost advantageous case conceivable, (a case far too advantageous to be\never obtained,) suppose that we compare one nation which has a\nrestrictive policy, with two or more nations agreeing in nothing but in\npermitting free trade. We need not now suppose that either of these\nnations agrees with the first in all its circumstances; one may agree\nwith it in some of its circumstances, and another in the remainder. And\nit may be argued, that if these nations remain poorer than the\nrestrictive nation, it cannot be for want either of the first or of the\nsecond set of circumstances, but it must be for want of the protective\nsystem. If (we might say) the restrictive nation had prospered from the\none set of causes, the first of the free-trade nations would have\nprospered equally; if by reason of the other, the second would: but\nneither has: therefore the prosperity was owing to the restrictions.\nThis will be allowed to be a very favourable specimen of an argument\nfrom specific experience in politics, and if this be inconclusive, it\nwould not be easy to find another preferable to it.\n\nYet, that it is inconclusive, scarcely requires to be pointed out. Why\nmust the prosperous nation have prospered from one cause exclusively?\nNational prosperity is always the collective result of a multitude of\nfavourable circumstances; and of these, the restrictive nation may unite\na greater number than either of the others, though it may have all of\nthose circumstances in common with either one or the other of them. Its\nprosperity may be partly owing to circumstances common to it with one of\nthose nations, and partly with the other, while they, having each of\nthem only half the number of favourable circumstances, have remained\ninferior. So that the closest imitation which can be made, in the social\nscience, of a legitimate induction from direct experience, gives but a\nspecious semblance of conclusiveness, without any real value.\n\n\n\u00a7 4. The Method of Difference in either of its forms being thus\ncompletely out of the question, there remains the Method of Agreement.\nBut we are already aware of how little value this method is, in cases\nadmitting Plurality of Causes: and social phenomena are those in which\nthe plurality prevails in the utmost possible extent.\n\nSuppose that the observer makes the luckiest hit which could be given by\nany conceivable combination of chances: that he finds two nations which\nagree in no circumstance whatever, except in having a restrictive\nsystem, and in being prosperous; or a number of nations, all prosperous,\nwhich have no antecedent circumstances common to them all but that of\nhaving a restrictive policy. It is unnecessary to go into the\nconsideration of the impossibility of ascertaining from history, or even\nfrom cotemporary observation, that such is really the fact: that the\nnations agree in no other circumstance capable of influencing the case.\nLet us suppose this impossibility vanquished, and the fact ascertained\nthat they agree only in a restrictive system as an antecedent, and\nindustrial prosperity as a consequent. What degree of presumption does\nthis raise, that the restrictive system caused the prosperity? One so\ntrifling as to be equivalent to none at all. That some one antecedent is\nthe cause of a given effect, because all other antecedents have been\nfound capable of being eliminated, is a just inference, only if the\neffect can have but one cause. If it admits of several, nothing is more\nnatural than that each of these should separately admit of being\neliminated. Now, in the case of political phenomena, the supposition of\nunity of cause is not only wide of the truth, but at an immeasurable\ndistance from it. The causes of every social phenomenon which we are\nparticularly interested about, security, wealth, freedom, good\ngovernment, public virtue, general intelligence, or their opposites, are\ninfinitely numerous: especially the external or remote causes, which\nalone are, for the most part, accessible to direct observation. No one\ncause suffices of itself to produce any of these phenomena; while there\nare countless causes which have some influence over them, and may\nco-operate either in their production or in their prevention. From the\nmere fact, therefore, of our having been able to eliminate some\ncircumstance, we can by no means infer that this circumstance was not\ninstrumental to the effect in some of the very instances from which we\nhave eliminated it. We can conclude that the effect is sometimes\nproduced without it; but not that, when present, it does not contribute\nits share.\n\nSimilar objections will be found to apply to the Method of Concomitant\nVariations. If the causes which act upon the state of any society\nproduced effects differing from one another in kind; if wealth depended\non one cause, peace on another, a third made people virtuous, a fourth\nintelligent; we might, though unable to sever the causes from one\nanother, refer to each of them that property of the effect which waxed\nas it waxed, and which waned as it waned. But every attribute of the\nsocial body is influenced by innumerable causes; and such is the mutual\naction of the coexisting elements of society, that whatever affects any\none of the more important of them, will by that alone, if it does not\naffect the others directly, affect them indirectly. The effects,\ntherefore, of different agents not being different in quality, while the\nquantity of each is the mixed result of all the agents, the variations\nof the aggregate cannot bear an uniform proportion to those of any one\nof its component parts.\n\n\n\u00a7 5. There remains the Method of Residues; which appears, on the first\nview, less foreign to this kind of inquiry than the three other\nmethods, because it only requires that we should accurately note the\ncircumstances of some one country, or state of society. Making\nallowance, thereupon, for the effect of all causes whose tendencies are\nknown, the residue which those causes are inadequate to explain may\nplausibly be imputed to the remainder of the circumstances which are\nknown to have existed in the case. Something similar to this is the\nmethod which Coleridge[8] describes himself as having followed in his\npolitical essays in the _Morning Post_. \"On every great occurrence I\nendeavoured to discover in past history the event that most nearly\nresembled it. I procured, whenever it was possible, the contemporary\nhistorians, memorialists, and pamphleteers. Then fairly subtracting the\npoints of difference from those of likeness, as the balance favoured the\nformer or the latter, I conjectured that the result would be the same or\ndifferent. As, for instance, in the series of essays entitled 'A\ncomparison of France under Napoleon with Rome under the first C\u00e6sars,'\nand in those which followed, 'on the probable final restoration of the\nBourbons.' The same plan I pursued at the commencement of the Spanish\nRevolution, and with the same success, taking the war of the United\nProvinces with Philip II. as the groundwork of the comparison.\" In this\ninquiry he no doubt employed the Method of Residues; for, in\n\"subtracting the points of difference from those of likeness,\" he\ndoubtless weighed, and did not content himself with numbering, them: he\ndoubtless took those points of agreement only, which he presumed from\ntheir own nature to be capable of influencing the effect, and, allowing\nfor that influence, concluded that the remainder of the result would be\nreferable to the points of difference.\n\nWhatever may be the efficacy of this method, it is, as we long ago\nremarked, not a method of pure observation and experiment; it concludes,\nnot from a comparison of instances, but from the comparison of an\ninstance with the result of a previous deduction. Applied to social\nphenomena, it presupposes that the causes from which part of the effect\nproceeded are already known; and as we have shown that these cannot have\nbeen known by specific experience, they must have been learnt by\ndeduction from principles of human nature; experience being called in\nonly as a supplementary resource, to determine the causes which produced\nan unexplained residue. But if the principles of human nature may be had\nrecourse to for the establishment of some political truths, they may for\nall. If it be admissible to say, England must have prospered by reason\nof the prohibitory system, because after allowing for all the other\ntendencies which have been operating, there is a portion of prosperity\nstill to be accounted for; it must be admissible to go to the same\nsource for the effect of the prohibitory system, and examine what\naccount the laws of human motives and actions will enable us to give of\n_its_ tendencies. Nor, in fact, will the experimental argument amount to\nanything, except in verification of a conclusion drawn from those\ngeneral laws. For we may subtract the effect of one, two, three, or four\ncauses, but we shall never succeed in subtracting the effect of all\ncauses except one: while it would be a curious instance of the dangers\nof too much caution, if, to avoid depending on _\u00e0 priori_ reasoning\nconcerning the effect of a single cause, we should oblige ourselves to\ndepend on as many separate _\u00e0 priori_ reasonings as there are causes\noperating concurrently with that particular cause in some given\ninstance.\n\nWe have now sufficiently characterized the gross misconception of the\nmode of investigation proper to political phenomena, which I have termed\nthe Chemical Method. So lengthened a discussion would not have been\nnecessary, if the claim to decide authoritatively on political doctrines\nwere confined to persons who had competently studied any one of the\nhigher departments of physical science. But since the generality of\nthose who reason on political subjects, satisfactorily to themselves and\nto a more or less numerous body of admirers, know nothing whatever of\nthe methods of physical investigation beyond a few precepts which they\ncontinue to parrot after Bacon, being entirely unaware that Bacon's\nconception of scientific inquiry has done its work, and that science\nhas now advanced into a higher stage; there are probably many to whom\nsuch remarks as the foregoing may still be useful. In an age in which\nchemistry itself, when attempting to deal with the more complex chemical\nsequences, those of the animal or even the vegetable organism, has found\nit necessary to become, and has succeeded in becoming, a Deductive\nScience--it is not to be apprehended that any person of scientific\nhabits, who has kept pace with the general progress of the knowledge of\nnature, can be in danger of applying the methods of elementary chemistry\nto explore the sequences of the most complex order of phenomena in\nexistence.\n\n\n\n\nCHAPTER VIII.\n\nOF THE GEOMETRICAL, OR ABSTRACT METHOD.\n\n\n\u00a7 1. The misconception discussed in the preceding chapter is, as we\nsaid, chiefly committed by persons not much accustomed to scientific\ninvestigation: practitioners in politics, who rather employ the\ncommonplaces of philosophy to justify their practice, than seek to guide\ntheir practice by philosophic principles: or imperfectly educated\npersons, who, in ignorance of the careful selection and elaborate\ncomparison of instances required for the formation of a sound theory,\nattempt to found one upon a few coincidences which they have casually\nnoticed.\n\nThe erroneous method of which we are now to treat, is, on the contrary,\npeculiar to thinking and studious minds. It never could have suggested\nitself but to persons of some familiarity with the nature of scientific\nresearch; who,--being aware of the impossibility of establishing, by\ncasual observation or direct experimentation, a true theory of sequences\nso complex as are those of the social phenomena,--have recourse to the\nsimpler laws which are immediately operative in those phenomena, and\nwhich are no other than the laws of the nature of the human beings\ntherein concerned. These thinkers perceive (what the partisans of the\nchemical or experimental theory do not) that the science of society must\nnecessarily be deductive. But, from an insufficient consideration of the\nspecific nature of the subject matter,--and often because (their own\nscientific education having stopped short in too early a stage) geometry\nstands in their minds as the type of all deductive science, it is to\ngeometry rather than to astronomy and natural philosophy, that they\nunconsciously assimilate the deductive science of society.\n\nAmong the differences between geometry (a science of coexistent facts,\naltogether independent of the laws of the succession of phenomena), and\nthose physical Sciences of Causation which have been rendered deductive,\nthe following is one of the most conspicuous: That geometry affords no\nroom for what so constantly occurs in mechanics and its applications,\nthe case of conflicting forces; of causes which counteract or modify one\nanother. In mechanics we continually find two or more moving forces\nproducing, not motion, but rest; or motion in a different direction from\nthat which would have been produced by either of the generating forces.\nIt is true that the effect of the joint forces is the same when they act\nsimultaneously, as if they had acted one after another, or by turns; and\nit is in this that the difference between mechanical and chemical laws\nconsists. But still the effects, whether produced by successive or by\nsimultaneous action, do, wholly or in part, cancel one another: what the\none force does, the other, partly or altogether, undoes. There is no\nsimilar state of things in geometry. The result which follows from one\ngeometrical principle has nothing that conflicts with the result which\nfollows from another. What is proved true from one geometrical theorem,\nwhat would be true if no other geometrical principles existed, cannot be\naltered and made no longer true by reason of some other geometrical\nprinciple. What is once proved true is true in all cases, whatever\nsupposition may be made in regard to any other matter.\n\nNow a conception, similar to this last, would appear to have been formed\nof the social science, in the minds of the earlier of those who have\nattempted to cultivate it by a deductive method. Mechanics would be a\nscience very similar to geometry, if every motion resulted from one\nforce alone, and not from a conflict of forces. In the geometrical\ntheory of society, it seems to be supposed that this is really the case\nwith the social phenomena; that each of them results always from only\none force, one single property of human nature.\n\nAt the point which we have now reached, it cannot be necessary to say\nanything either in proof or in illustration of the assertion that such\nis not the true character of the social phenomena. There is not, among\nthese most complex and (for that reason) most modifiable of all\nphenomena, any one over which innumerable forces do not exercise\ninfluence; which does not depend on a conjunction of very many causes.\nWe have not, therefore, to prove the notion in question to be an error,\nbut to prove that the error has been committed; that so mistaken a\nconception of the mode in which the phenomena of society are produced,\nhas actually been ascertained.\n\n\n\u00a7 2. One numerous division of the reasoners who have treated social\nfacts according to geometrical methods, not admitting any modification\nof one law by another, must for the present be left out of\nconsideration; because in them this error is complicated with, and is\nthe effect of, another fundamental misconception, of which we have\nalready taken some notice, and which will be further treated of before\nwe conclude. I speak of those who deduce political conclusions not from\nlaws of nature, not from sequences of phenomena, real or imaginary, but\nfrom unbending practical maxims. Such, for example, are all who found\ntheir theory of politics on what is called abstract right, that is to\nsay, on universal precepts; a pretension of which we have already\nnoticed the chimerical nature. Such, in like manner, are those who make\nthe assumption of a social contract, or any other kind of original\nobligation, and apply it to particular cases by mere interpretation. But\nin this the fundamental error is the attempt to treat an art like a\nscience, and to have a deductive art; the irrationality of which will be\nshown in a future chapter. It will be proper to take our exemplification\nof the geometrical theory from those thinkers who have avoided this\nadditional error, and who entertain, so far, a juster idea of the nature\nof political inquiry.\n\nWe may cite, in the first instance, those who assume as the principle of\ntheir political philosophy that government is founded on fear; that the\ndread of each other is the one motive by which human beings were\noriginally brought into a state of society, and are still held in it.\nSome of the earlier scientific inquirers into politics, in particular\nHobbes, assumed this proposition, not by implication, but avowedly, as\nthe foundation of their doctrine, and attempted to build a complete\nphilosophy of politics thereupon. It is true that Hobbes did not find\nthis one maxim sufficient to carry him through the whole of his subject,\nbut was obliged to eke it out by the double sophism of an original\ncontract. I call this a double sophism; first, as passing off a fiction\nfor a fact, and, secondly, assuming a practical principle, or precept,\nas the basis of a theory; which is a _petitio principii_, since (as we\nnoticed in treating of that Fallacy) every rule of conduct, even though\nit be so binding a one as the observance of a promise, must rest its own\nfoundations on the theory of the subject, and the theory, therefore,\ncannot rest upon it.\n\n\n\u00a7 3. Passing over less important instances, I shall come at once to the\nmost remarkable example afforded by our own times of the geometrical\nmethod in politics; emanating from persons who were well aware of the\ndistinction between science and art; who knew that rules of conduct must\nfollow, not precede, the ascertainment of laws of nature, and that the\nlatter, not the former, is the legitimate field for the application of\nthe deductive method. I allude to the interest-philosophy of the Bentham\nschool.\n\nThe profound and original thinkers who are commonly known under this\ndescription, founded their general theory of government on one\ncomprehensive premise, namely, that men's actions are always determined\nby their interests. There is an ambiguity in this last expression; for,\nas the same philosophers, especially Bentham, gave the name of an\ninterest to anything which a person likes, the proposition may be\nunderstood to mean only this, that men's actions are always determined\nby their wishes. In this sense, however, it would not bear out any of\nthe consequences which these writers drew from it; and the word,\ntherefore, in their political reasonings, must be understood to mean\n(which is also the explanation they themselves, on such occasions, gave\nof it) what is commonly termed private, or worldly, interest.\n\nTaking the doctrine, then, in this sense, an objection presents itself\n_in limine_ which might be deemed a fatal one, namely, that so sweeping\na proposition is far from being universally true. Human beings are not\ngoverned in all their actions by their worldly interests. This, however,\nis by no means so conclusive an objection as it at first appears;\nbecause in politics we are for the most part concerned with the conduct\nnot of individual persons, but either of a series of persons (as a\nsuccession of kings) or a body or mass of persons, as a nation, an\naristocracy, or a representative assembly. And whatever is true of a\nlarge majority of mankind, may without much error be taken for true of\nany succession of persons, considered as a whole, or of any collection\nof persons in which the act of the majority becomes the act of the whole\nbody. Although, therefore, the maxim is sometimes expressed in a manner\nunnecessarily paradoxical, the consequences drawn from it will hold\nequally good if the assertion be limited as follows--Any succession of\npersons, or the majority of any body of persons, will be governed in the\nbulk of their conduct by their personal interests. We are bound to allow\nto this school of thinkers the benefit of this more rational statement\nof their fundamental maxim, which is also in strict conformity to the\nexplanations which, when considered to be called for, have been given by\nthemselves.\n\nThe theory goes on to infer, quite correctly, that if the actions of\nmankind are determined in the main by their selfish interests, the only\nrulers who will govern according to the interest of the governed, are\nthose whose selfish interests are in accordance with it. And to this is\nadded a third proposition, namely, that no rulers have their selfish\ninterest identical with that of the governed, unless it be rendered so\nby accountability, that is, by dependence on the will of the governed.\nIn other words (and as the result of the whole), that the desire of\nretaining or the fear of losing their power, and whatever is thereon\nconsequent, is the sole motive which can be relied on for producing on\nthe part of rulers a course of conduct in accordance with the general\ninterest.\n\nWe have thus a fundamental theorem of political science, consisting of\nthree syllogisms, and depending chiefly on two general premises, in each\nof which a certain effect is considered as determined only by one cause,\nnot by a concurrence of causes. In the one, it is assumed that the\nactions of average rulers are determined solely by self-interest; in the\nother, that the sense of identity of interest with the governed, is\nproduced and producible by no other cause than responsibility.\n\nNeither of these propositions is by any means true; the last is\nextremely wide of the truth.\n\nIt is not true that the actions even of average rulers are wholly, or\nanything approaching to wholly, determined by their personal interest,\nor even by their own opinion of their personal interest. I do not speak\nof the influence of a sense of duty, or feelings of philanthropy,\nmotives never to be mainly relied on, though (except in countries or\nduring periods of great moral debasement) they influence almost all\nrulers in some degree, and some rulers in a very great degree. But I\ninsist only on what is true of all rulers, viz. that the character and\ncourse of their actions is largely influenced (independently of personal\ncalculation) by the habitual sentiments and feelings, the general modes\nof thinking and acting, which prevail throughout the community of which\nthey are members; as well as by the feelings, habits, and modes of\nthought which characterize the particular class in that community to\nwhich they themselves belong. And no one will understand or be able to\ndecypher their system of conduct, who does not take all these things\ninto account. They are also much influenced by the maxims and traditions\nwhich have descended to them from other rulers, their predecessors;\nwhich maxims and traditions have been known to retain an ascendancy\nduring long periods, even in opposition to the private interests of the\nrulers for the time being. I put aside the influence of other less\ngeneral causes. Although, therefore, the private interest of the rulers\nor of the ruling class is a very powerful force, constantly in action,\nand exercising the most important influence upon their conduct; there is\nalso, in what they do, a large portion which that private interest by no\nmeans affords a sufficient explanation of: and even the particulars\nwhich constitute the goodness or badness of their government, are in\nsome, and no small degree, influenced by those among the circumstances\nacting upon them, which cannot, with any propriety, be included in the\nterm self-interest.\n\nTurning now to the other proposition, that responsibility to the\ngoverned is the only cause capable of producing in the rulers a sense of\nidentity of interest with the community; this is still less admissible\nas an universal truth, than even the former. I am not speaking of\nperfect identity of interest, which is an impracticable chimera; which,\nmost assuredly, responsibility to the people does not give. I speak of\nidentity in essentials; and the essentials are different at different\nplaces and times. There are a large number of cases in which those\nthings which it is most for the general interest that the rulers should\ndo, are also those which they are prompted to do by their strongest\npersonal interest, the consolidation of their power. The suppression,\nfor instance, of anarchy and resistance to law,--the complete\nestablishment of the authority of the central government, in a state of\nsociety like that of Europe in the middle ages,--is one of the strongest\ninterests of the people, and also of the rulers simply because they are\nthe rulers: and responsibility on their part could not strengthen,\nthough in many conceivable ways it might weaken, the motives prompting\nthem to pursue this object. During the greater part of the reign of\nQueen Elizabeth, and of many other monarchs who might be named, the\nsense of identity of interest between the sovereign and the majority of\nthe people was probably stronger than it usually is in responsible\ngovernments: everything that the people had most at heart, the monarch\nhad at heart too. Had Peter the Great, or the rugged savages whom he\nbegan to civilize, the truest inclination towards the things which were\nfor the real interest of those savages?\n\nI am not here attempting to establish a theory of government, and am not\ncalled upon to determine the proportional weight which ought to be given\nto the circumstances which this school of geometrical politicians left\nout of their system, and those which they took into it. I am only\nconcerned to show that their method was unscientific; not to measure the\namount of error which may have affected their practical conclusions.\n\nIt is but justice to them, however, to remark, that their mistake was\nnot so much one of substance as of form; and consisted in presenting in\na systematic shape, and as the scientific treatment of a great\nphilosophical question, what should have passed for that which it really\nwas, the mere polemics of the day. Although the actions of rulers are by\nno means wholly determined by their selfish interests, it is chiefly as\na security against those selfish interests that constitutional checks\nare required; and for that purpose such checks, in England, and the\nother nations of modern Europe, can in no manner be dispensed with. It\nis likewise true, that in these same nations, and in the present age,\nresponsibility to the governed is the only means practically available\nto create a feeling of identity of interest, in the cases, and on the\npoints, where that feeling does not sufficiently exist. To all this, and\nto the arguments which may be founded on it in favour of measures for\nthe correction of our representative system, I have nothing to object;\nbut I confess my regret, that the small though highly important portion\nof the philosophy of government, which was wanted for the immediate\npurpose of serving the cause of parliamentary reform, should have been\nheld forth by thinkers of such eminence as a complete theory.\n\nIt is not to be imagined possible, nor is it true in point of fact, that\nthese philosophers regarded the few premises of their theory as\nincluding all that is required for explaining social phenomena, or for\ndetermining the choice of forms of government and measures of\nlegislation and administration. They were too highly instructed, of too\ncomprehensive intellect, and some of them of too sober and practical a\ncharacter, for such an error. They would have applied and did apply\ntheir principles with innumerable allowances. But it is not allowances\nthat are wanted. There is little chance of making due amends in the\nsuperstructure of a theory for the want of sufficient breadth in its\nfoundations. It is unphilosophical to construct a science out of a few\nof the agencies by which the phenomena are determined, and leave the\nrest to the routine of practice or the sagacity of conjecture. We either\nought not to pretend to scientific forms, or we ought to study all the\ndetermining agencies equally, and endeavour, so far as it can be done,\nto include all of them within the pale of the science; else we shall\ninfallibly bestow a disproportionate attention upon those which our\ntheory takes into account, while we misestimate the rest, and probably\nunderrate their importance. That the deductions should be from the whole\nand not from a part only of the laws of nature that are concerned, would\nbe desirable even if those omitted were so insignificant in comparison\nwith the others, that they might, for most purposes and on most\noccasions, be left out of the account. But this is far indeed from being\ntrue in the social science. The phenomena of society do not depend, in\nessentials, on some one agency or law of human nature, with only\ninconsiderable modifications from others. The whole of the qualities of\nhuman nature influence those phenomena, and there is not one which\ninfluences them in a small degree. There is not one, the removal or any\ngreat alteration of which would not materially affect the whole aspect\nof society, and change more or less the sequences of social phenomena\ngenerally.\n\nThe theory which has been the subject of these remarks is in this\ncountry at least, the principal cotemporary example of what I have\nstyled the geometrical method of philosophizing in the social science;\nand our examination of it has, for this reason, been more detailed than\nwould otherwise have been suitable to a work like the present. Having\nnow sufficiently illustrated the two erroneous methods, we shall pass\nwithout further preliminary to the true method; that which proceeds\n(conformably to the practice of the more complex physical sciences)\ndeductively indeed, but by deduction from many, not from one or a very\nfew, original premises; considering each effect as (what it really is)\nan aggregate result of many causes, operating sometimes through the\nsame, sometimes through different mental agencies, or laws of human\nnature.\n\n\n\n\nCHAPTER IX.\n\nOF THE PHYSICAL, OR CONCRETE DEDUCTIVE METHOD.\n\n\n\u00a7 1. After what has been said to illustrate the nature of the inquiry\ninto social phenomena, the general character of the method proper to\nthat inquiry is sufficiently evident, and needs only to be\nrecapitulated, not proved. However complex the phenomena, all their\nsequences and coexistences result from the laws of the separate\nelements. The effect produced, in social phenomena, by any complex set\nof circumstances, amounts precisely to the sum of the effects of the\ncircumstances taken singly: and the complexity does not arise from the\nnumber of the laws themselves, which is not remarkably great; but from\nthe extraordinary number and variety of the data or elements--of the\nagents which, in obedience to that small number of laws, co-operate\ntowards the effect. The Social Science, therefore (which, by a\nconvenient barbarism, has been termed Sociology,) is a deductive\nscience; not, indeed, after the model of geometry, but after that of the\nmore complex physical sciences. It infers the law of each effect from\nthe laws of causation on which that effect depends; not, however, from\nthe law merely of one cause, as in the geometrical method; but by\nconsidering all the causes which conjunctly influence the effect, and\ncompounding their laws with one another. Its method, in short, is the\nConcrete Deductive Method; that of which astronomy furnishes the most\nperfect, natural philosophy a somewhat less perfect example, and the\nemployment of which, with the adaptations and precautions required by\nthe subject, is beginning to regenerate physiology.\n\nNor does it admit of doubt, that similar adaptations and precautions are\nindispensable in sociology. In applying, to that most complex of all\nstudies, what is demonstrably the sole method capable of throwing the\nlight of science even upon phenomena of a far inferior degree of\ncomplication, we ought to be aware that the same superior complexity\nwhich renders the instrument of Deduction more necessary, renders it\nalso more precarious; and we must be prepared to meet, by appropriate\ncontrivances, this increase of difficulty.\n\nThe actions and feelings of human beings in the social state, are, no\ndoubt, entirely governed by psychological and ethological laws: whatever\ninfluence any cause exercises upon the social phenomena, it exercises\nthrough those laws. Supposing therefore the laws of human actions and\nfeelings to be sufficiently known, there is no extraordinary difficulty\nin determining from those laws, the nature of the social effects which\nany given cause tends to produce. But when the question is that of\ncompounding several tendencies together, and computing the aggregate\nresult of many coexistent causes; and especially when, by attempting to\npredict what will actually occur in a given case, we incur the\nobligation of estimating and compounding the influences of all the\ncauses which happen to exist in that case; we attempt a task, to proceed\nfar in which, surpasses the compass of the human faculties.\n\nIf all the resources of science are not sufficient to enable us to\ncalculate _\u00e0 priori_, with complete precision, the mutual action of\nthree bodies gravitating towards one another; it may be judged with what\nprospect of success we should endeavour to calculate the result of the\nconflicting tendencies which are acting in a thousand different\ndirections and promoting a thousand different changes at a given instant\nin a given society: although we might and ought to be able, from the\nlaws of human nature, to distinguish correctly enough the tendencies\nthemselves, so far as they depend on causes accessible to our\nobservation; and to determine the direction which each of them, if\nacting alone, would impress upon society, as well as, in a general way\nat least, to pronounce that some of these tendencies are more powerful\nthan others.\n\nBut, without dissembling the necessary imperfections of the _\u00e0 priori_\nmethod when applied to such a subject, neither ought we, on the other\nhand, to exaggerate them. The same objections, which apply to the Method\nof Deduction in this its most difficult employment, apply to it, as we\nformerly showed,[9] in its easiest; and would even there have been\ninsuperable, if there had not existed, as was then fully explained, an\nappropriate remedy. This remedy consists in the process which, under the\nname of Verification, we have characterized as the third essential\nconstituent part of the Deductive Method; that of collating the\nconclusions of the ratiocination either with the concrete phenomena\nthemselves, or, when such are obtainable, with their empirical laws. The\nground of confidence in any concrete deductive science is not the _\u00e0\npriori_ reasoning itself, but the accordance between its results and\nthose of observation _\u00e0 posteriori_. Either of these processes, apart\nfrom the other, diminishes in value as the subject increases in\ncomplication, and this in so rapid a ratio as soon to become entirely\nworthless; but the reliance to be placed in the concurrence of the two\nsorts of evidence, not only does not diminish in anything like the same\nproportion, but is not necessarily much diminished at all. Nothing more\nresults than a disturbance in the order of precedency of the two\nprocesses, sometimes amounting to its actual inversion: insomuch that\ninstead of deducing our conclusions by reasoning, and verifying them by\nobservation, we in some cases begin by obtaining them conjecturally from\nspecific experience, and afterwards connect them with the principles of\nhuman nature by _\u00e0 priori_ reasonings, which reasonings are thus a real\nVerification.\n\nThe only thinker who, with a competent knowledge of scientific methods\nin general, has attempted to characterize the Method of Sociology, M.\nComte, considers this inverse order as inseparably inherent in the\nnature of sociological speculation. He looks upon the social science as\nessentially consisting of generalizations from history, verified, not\noriginally suggested, by deduction from the laws of human nature. Though\nthere is a truth contained in this opinion, of which I shall presently\nendeavour to show the importance, I cannot but think that this truth is\nenunciated in too unlimited a manner, and that there is considerable\nscope in sociological inquiry for the direct, as well as for the\ninverse, Deductive Method.\n\nIt will, in fact, be shown in the next chapter, that there is a kind of\nsociological inquiries to which, from their prodigious complication, the\nmethod of direct deduction is altogether inapplicable, while by a happy\ncompensation it is precisely in these cases that we are able to obtain\nthe best empirical laws: to these inquiries, therefore, the Inverse\nMethod is exclusively adapted. But there are also, as will presently\nappear, other cases in which it is impossible to obtain from direct\nobservation anything worthy the name of an empirical law; and it\nfortunately happens that these are the very cases in which the Direct\nMethod is least affected by the objection which undoubtedly must always\naffect it in a certain degree.\n\nWe shall begin, then, by looking at the Social Science as a science of\ndirect Deduction, and considering what can be accomplished in it, and\nunder what limitations, by that mode of investigation. We shall, then,\nin a separate chapter, examine and endeavour to characterize the inverse\nprocess.\n\n\n\u00a7 2. It is evident, in the first place, that Sociology, considered as a\nsystem of deductions _\u00e0 priori_, cannot be a science of positive\npredictions, but only of tendencies. We may be able to conclude, from\nthe laws of human nature applied to the circumstances of a given state\nof society, that a particular cause will operate in a certain manner\nunless counteracted; but we can never be assured to what extent or\namount it will so operate, or affirm with certainty that it will not be\ncounteracted; because we can seldom know, even approximately, all the\nagencies which may coexist with it, and still less calculate the\ncollective result of so many combined elements. The remark, however,\nmust here be once more repeated, that knowledge insufficient for\nprediction may be most valuable for guidance. It is not necessary for\nthe wise conduct of the affairs of society, no more than of any one's\nprivate concerns, that we should be able to foresee infallibly the\nresults of what we do. We must seek our objects by means which may\nperhaps be defeated, and take precautions against dangers which possibly\nmay never be realized. The aim of practical politics is to surround any\ngiven society with the greatest possible number of circumstances of\nwhich the tendencies are beneficial, and to remove or counteract, as far\nas practicable, those of which the tendencies are injurious. A knowledge\nof the tendencies only, though without the power of accurately\npredicting their conjunct result, gives us to a certain extent this\npower.\n\nIt would, however, be an error to suppose that even with respect to\ntendencies, we could arrive in this manner at any great number of\npropositions which will be true in all societies without exception. Such\na supposition would be inconsistent with the eminently modifiable nature\nof the social phenomena, and the multitude and variety of the\ncircumstances by which they are modified; circumstances never the same,\nor even nearly the same, in two different societies, or in two different\nperiods of the same society. This would not be so serious an obstacle\nif, though the causes acting upon society in general are numerous, those\nwhich influence any one feature of society were limited in number; for\nwe might then insulate any particular social phenomenon, and investigate\nits laws without disturbance from the rest. But the truth is the very\nopposite of this. Whatever affects, in an appreciable degree, any one\nelement of the social state, affects through it all the other elements.\nThe mode of production of all social phenomena is one great case of\nIntermixture of Laws. We can never either understand in theory or\ncommand in practice the condition of a society in any one respect,\nwithout taking into consideration its condition in all other respects.\nThere is no social phenomenon which is not more or less influenced by\nevery other part of the condition of the same society, and therefore by\nevery cause which is influencing any other of the contemporaneous social\nphenomena. There is, in short, what physiologists term a _consensus_,\nsimilar to that existing among the various organs and functions of the\nphysical frame of man and the more perfect animals; and constituting one\nof the many analogies which have rendered universal such expressions as\nthe \"body politic\" and \"body natural.\" It follows from this _consensus_,\nthat unless two societies could be alike in all the circumstances which\nsurround and influence them, (which would imply their being alike in\ntheir previous history,) no portion whatever of the phenomena will,\nunless by accident, precisely correspond; no one cause will produce\nexactly the same effects in both. Every cause, as its effect spreads\nthrough society, comes somewhere in contact with different sets of\nagencies, and thus has its effects on some of the social phenomena\ndifferently modified; and these differences, by their reaction, produce\na difference even in those of the effects which would otherwise have\nbeen the same. We can never, therefore, affirm with certainty that a\ncause which has a particular tendency in one people or in one age will\nhave exactly the same tendency in another, without referring back to our\npremises, and performing over again for the second age or nation, that\nanalysis of the whole of its influencing circumstances which we had\nalready performed for the first. The deductive science of society will\nnot lay down a theorem, asserting in an universal manner the effect of\nany cause; but will rather teach us how to frame the proper theorem for\nthe circumstances of any given case. It will not give the laws of\nsociety in general, but the means of determining the phenomena of any\ngiven society from the particular elements or data of that society.\n\nAll the general propositions which can be framed by the deductive\nscience, are therefore, in the strictest sense of the word,\nhypothetical. They are grounded on some supposititious set of\ncircumstances, and declare how some given cause would operate in those\ncircumstances, supposing that no others were combined with them. If the\nset of circumstances supposed have been copied from those of any\nexisting society, the conclusions will be true of that society,\nprovided, and in as far as, the effect of those circumstances shall not\nbe modified by others which have not been taken into the account. If we\ndesire a nearer approach to concrete truth, we can only aim at it by\ntaking, or endeavouring to take, a greater number of individualizing\ncircumstances into the computation.\n\nConsidering, however, in how accelerating a ratio the uncertainty of our\nconclusions increases, as we attempt to take the effect of a greater\nnumber of concurrent causes into our calculations; the hypothetical\ncombinations of circumstances on which we construct the general theorems\nof the science, cannot be made very complex, without so\nrapidly-accumulating a liability to error as must soon deprive our\nconclusions of all value. This mode of inquiry, considered as a means of\nobtaining general propositions, must, therefore, on pain of frivolity,\nbe limited to those classes of social facts which, though influenced\nlike the rest by all sociological agents, are under the _immediate_\ninfluence, principally at least, of a few only.\n\n\n\u00a7 3. Notwithstanding the universal _consensus_ of the social phenomena,\nwhereby nothing which takes place in any part of the operations of\nsociety is without its share of influence on every other part; and\nnotwithstanding the paramount ascendancy which the general state of\ncivilization and social progress in any given society must hence\nexercise over all the partial and subordinate phenomena; it is not the\nless true that different species of social facts are in the main\ndependent, immediately and in the first resort, on different kinds of\ncauses; and therefore not only may with advantage, but must, be studied\napart: just as in the natural body we study separately the physiology\nand pathology of each of the principal organs and tissues, though every\none is acted upon by the state of all the others: and though the\npeculiar constitution and general state of health of the organism\nco-operates with, and often preponderates over, the local causes, in\ndetermining the state of any particular organ.\n\nOn these considerations is grounded the existence of distinct and\nseparate, though not independent, branches or departments of\nsociological speculation.\n\nThere is, for example, one large class of social phenomena, in which\nthe immediately determining causes are principally those which act\nthrough the desire of wealth; and in which the psychological law mainly\nconcerned is the familiar one, that a greater gain is preferred to a\nsmaller. I mean, of course, that portion of the phenomena of society\nwhich emanate from the industrial, or productive, operations of mankind;\nand from those of their acts through which the distribution of the\nproducts of those industrial operations takes place, in so far as not\neffected by force, or modified by voluntary gift. By reasoning from that\none law of human nature, and from the principal outward circumstances\n(whether universal or confined to particular states of society) which\noperate upon the human mind through that law, we may be enabled to\nexplain and predict this portion of the phenomena of society, so far as\nthey depend on that class of circumstances only; overlooking the\ninfluence of any other of the circumstances of society; and therefore\nneither tracing back the circumstances which we do take into account, to\ntheir possible origin in some other facts in the social state, nor\nmaking allowance for the manner in which any of those other\ncircumstances may interfere with, and counteract or modify, the effect\nof the former. A science may thus be constructed, which has received the\nname of Political Economy.\n\nThe motive which suggests the separation of this portion of the social\nphenomena from the rest, and the creation of a distinct science relating\nto them is,--that they do _mainly_ depend, at least in the first resort,\non one class of circumstances only; and that even when other\ncircumstances interfere, the ascertainment of the effect due to the one\nclass of circumstances alone, is a sufficiently intricate and difficult\nbusiness to make it expedient to perform it once for all, and then allow\nfor the effect of the modifying circumstances; especially as certain\nfixed combinations of the former are apt to recur often, in conjunction\nwith ever-varying circumstances of the latter class.\n\nPolitical Economy, as I have said on another occasion, concerns itself\nonly with \"such of the phenomena of the social state as take place in\nconsequence of the pursuit of wealth. It makes entire abstraction of\nevery other human passion or motive; except those which may be regarded\nas perpetually antagonizing principles to the desire of wealth, namely,\naversion to labour, and desire of the present enjoyment of costly\nindulgences. These it takes, to a certain extent, into its calculations,\nbecause these do not merely, like our other desires, occasionally\nconflict with the pursuit of wealth, but accompany it always as a drag\nor impediment, and are therefore inseparably mixed up in the\nconsideration of it. Political Economy considers mankind as occupied\nsolely in acquiring and consuming wealth; and aims at showing what is\nthe course of action into which mankind, living in a state of society,\nwould be impelled, if that motive, except in the degree in which it is\nchecked by the two perpetual counter-motives above adverted to, were\nabsolute ruler of all their actions. Under the influence of this desire,\nit shows mankind accumulating wealth, and employing that wealth in the\nproduction of other wealth; sanctioning by mutual agreement the\ninstitution of property; establishing laws to prevent individuals from\nencroaching upon the property of others by force or fraud; adopting\nvarious contrivances for increasing the productiveness of their labour;\nsettling the division of the produce by agreement, under the influence\nof competition (competition itself being governed by certain laws, which\nlaws are therefore the ultimate regulators of the division of the\nproduce); and employing certain expedients (as money, credit, &c.) to\nfacilitate the distribution. All these operations, though many of them\nare really the result of a plurality of motives, are considered by\npolitical economy as flowing solely from the desire of wealth. The\nscience then proceeds to investigate the laws which govern these several\noperations, under the supposition that man is a being who is determined,\nby the necessity of his nature, to prefer a greater portion of wealth to\na smaller, in all cases, without any other exception than that\nconstituted by the two counter-motives already specified. Not that any\npolitical economist was ever so absurd as to suppose that mankind are\nreally thus constituted, but because this is the mode in which science\nmust necessarily proceed. When an effect depends on a concurrence of\ncauses, these causes must be studied one at a time, and their laws\nseparately investigated, if we wish, through the causes, to obtain the\npower of either predicting or controlling the effect; since the law of\nthe effect is compounded of the laws of all the causes which determine\nit. The law of the centripetal and that of the projectile force must\nhave been known, before the motions of the earth and planets could be\nexplained, or many of them predicted. The same is the case with the\nconduct of man in society. In order to judge how he will act under the\nvariety of desires and aversions which are concurrently operating upon\nhim, we must know how he would act under the exclusive influence of each\none in particular. There is, perhaps, no action of a man's life in which\nhe is neither under the immediate nor under the remote influence of any\nimpulse but the mere desire of wealth. With respect to those parts of\nhuman conduct of which wealth is not even the principal object, to these\npolitical economy does not pretend that its conclusions are applicable.\nBut there are also certain departments of human affairs, in which the\nacquisition of wealth is the main and acknowledged end. It is only of\nthese that political economy takes notice. The manner in which it\nnecessarily proceeds is that of treating the main and acknowledged end\nas if it were the sole end; which, of all hypotheses equally simple, is\nthe nearest to the truth. The political economist inquires, what are the\nactions which would be produced by this desire, if within the\ndepartments in question it were unimpeded by any other. In this way a\nnearer approximation is obtained than would otherwise be practicable to\nthe real order of human affairs in those departments. This approximation\nhas then to be corrected by making proper allowance for the effects of\nany impulses of a different description, which can be shown to interfere\nwith the result in any particular case. Only in a few of the most\nstriking cases (such as the important one of the principle of\npopulation) are these corrections interpolated into the expositions of\npolitical economy itself; the strictness of purely scientific\narrangement being thereby somewhat departed from, for the sake of\npractical utility. So far as it is known or may be presumed, that the\nconduct of mankind in the pursuit of wealth is under the collateral\ninfluence of any other of the properties of our nature, than the desire\nof obtaining the greatest quantity of wealth with the least labour and\nself-denial, the conclusions of political economy will so far fail of\nbeing applicable to the explanation or prediction of real events, until\nthey are modified by a correct allowance for the degree of influence\nexercised by the other cause.\"[10]\n\nExtensive and important practical guidance may be derived, in any given\nstate of society, from general propositions such as those above\nindicated; even though the modifying influence of the miscellaneous\ncauses which the theory does not take into account, as well as the\neffect of the general social changes in progress, be provisionally\noverlooked. And though it has been a very common error of political\neconomists to draw conclusions from the elements of one state of\nsociety, and apply them to other states in which many of the elements\nare not the same; it is even then not difficult, by tracing back the\ndemonstrations, and introducing the new premises in their proper places,\nto make the same general course of argument which served for the one\ncase, serve for the others too.\n\nFor example, it has been greatly the custom of English political\neconomists to discuss the laws of the distribution of the produce of\nindustry, on a supposition which is scarcely realized anywhere out of\nEngland and Scotland, namely, that the produce is \"shared among three\nclasses, altogether distinct from one another, labourers, capitalists,\nand landlords; and that all these are free agents, permitted in law and\nin fact to set upon their labour, their capital, and their land,\nwhatever price they are able to get for it. The conclusions of the\nscience, being all adapted to a society thus constituted, require to be\nrevised whenever they are applied to any other. They are inapplicable\nwhere the only capitalists are the landlords, and the labourers are\ntheir property, as in slave countries. They are inapplicable where the\nalmost universal landlord is the state as in India. They are\ninapplicable where the agricultural labourer is generally the owner both\nof the land itself and of the capital, as frequently in France, or of\nthe capital only, as in Ireland.\" But though it may often be very justly\nobjected to the existing race of political economists \"that they attempt\nto construct a permanent fabric out of transitory materials; that they\ntake for granted the immutability of arrangements of society, many of\nwhich are in their nature fluctuating or progressive, and enunciate with\nas little qualification as if they were universal and absolute truths,\npropositions which are perhaps applicable to no state of society except\nthe particular one in which the writer happened to live;\" this does not\ntake away the value of the propositions, considered with reference to\nthe state of society from which they were drawn. And even as applicable\nto other states of society, \"it must not be supposed that the science is\nso incomplete and unsatisfactory as this might seem to prove. Though\nmany of its conclusions are only locally true, its method of\ninvestigation is applicable universally; and as whoever has solved a\ncertain number of algebraic equations, can without difficulty solve all\nothers of the same kind, so whoever knows the political economy of\nEngland, or even of Yorkshire, knows that of all nations, actual or\npossible, provided he have good sense enough not to expect the same\nconclusion to issue from varying premises.\" Whoever is thoroughly master\nof the laws which, under free competition, determine the rent, profits,\nand wages, received by landlords, capitalists, and labourers, in a state\nof society in which the three classes are completely separate, will have\nno difficulty in determining the very different laws which regulate the\ndistribution of the produce among the classes interested in it, in any\nof the states of cultivation and landed property set forth in the\nforegoing extract.[11]\n\n\n\u00a7 4. I would not here undertake to decide what other hypothetical or\nabstract sciences similar to Political Economy, may admit of being\ncarved out of the general body of the social science; what other\nportions of the social phenomena are in a sufficiently close and\ncomplete dependence, in the first resort, on a peculiar class of causes,\nto make it convenient to create a preliminary science of those causes;\npostponing the consideration of the causes which act through them, or in\nconcurrence with them, to a later period of the inquiry. There is\nhowever among these separate departments one which cannot be passed over\nin silence, being of a more comprehensive and commanding character than\nany of the other branches into which the social science may admit of\nbeing divided. Like them, it is directly conversant with the causes of\nonly one class of social facts, but a class which exercises, immediately\nor remotely, a paramount influence over the rest. I allude to what may\nbe termed Political Ethology, or the theory of the causes which\ndetermine the type of character belonging to a people or to an age. Of\nall the subordinate branches of the social science, this is the most\ncompletely in its infancy. The causes of national character are scarcely\nat all understood, and the effect of institutions or social arrangements\nupon the character of the people is generally that portion of their\neffects which is least attended to, and least comprehended. Nor is this\nwonderful, when we consider the infant state of the Science of Ethology\nitself, from whence the laws must be drawn, of which the truths of\npolitical ethology can be but results and exemplifications.\n\nYet to whoever well considers the matter, it must appear that the laws\nof national (or collective) character are by far the most important\nclass of sociological laws. In the first place, the character which is\nformed by any state of social circumstances is in itself the most\ninteresting phenomenon which that state of society can possibly present.\nSecondly, it is also a fact which enters largely into the production of\nall the other phenomena. And above all, the character, that is, the\nopinions, feelings, and habits, of the people, though greatly the\nresults of the state of society which precedes them, are also greatly\nthe causes of the state of society which follows them; and are the power\nby which all those of the circumstances of society which are\nartificial, laws and customs for instance, are altogether moulded:\ncustoms evidently, laws no less really, either by the direct influence\nof public sentiment upon the ruling powers, or by the effect which the\nstate of national opinion and feeling has in determining the form of\ngovernment and shaping the character of the governors.\n\nAs might be expected, the most imperfect part of those branches of\nsocial inquiry which have been cultivated as separate sciences, is the\ntheory of the manner in which their conclusions are affected by\nethological considerations. The omission is no defect in them as\nabstract or hypothetical sciences, but it vitiates them in their\npractical application as branches of a comprehensive social science. In\npolitical economy for instance, empirical laws of human nature are\ntacitly assumed by English thinkers, which are calculated only for Great\nBritain and the United States. Among other things, an intensity of\ncompetition is constantly supposed, which, as a general mercantile fact,\nexists in no country in the world except those two. An English political\neconomist, like his countrymen in general, has seldom learned that it is\npossible that men, in conducting the business of selling their goods\nover a counter, should care more about their ease or their vanity than\nabout their pecuniary gain. Yet those who know the habits of the\nContinent of Europe are aware how apparently small a motive often\noutweighs the desire of money-getting, even in the operations which have\nmoney-getting for their direct object. The more highly the science of\nethology is cultivated, and the better the diversities of individual and\nnational character are understood, the smaller, probably, will the\nnumber of propositions become, which it will be considered safe to build\non as universal principles of human nature.\n\nThese considerations show that the process of dividing off the social\nscience into compartments, in order that each may be studied separately,\nand its conclusions afterwards corrected for practice by the\nmodifications supplied by the others, must be subject to at least one\nimportant limitation. Those portions alone of the social phenomena can\nwith advantage be made the subjects, even provisionally, of distinct\nbranches of science, into which the diversities of character between\ndifferent nations or different times enter as influencing causes only in\na secondary degree. Those phenomena, on the contrary, with which the\ninfluences of the ethological state of the people are mixed up at every\nstep (so that the connexion of effects and causes cannot be even rudely\nmarked out without taking those influences into consideration) could not\nwith any advantage, nor without great disadvantage, be treated\nindependently of political ethology, nor, therefore, of all the\ncircumstances by which the qualities of a people are influenced. For\nthis reason (as well as for others which will hereafter appear) there\ncan be no separate Science of Government; that being the fact which, of\nall others, is most mixed up, both as cause and effect, with the\nqualities of the particular people or of the particular age. All\nquestions respecting the tendencies of forms of government must stand\npart of the general science of society, not of any separate branch of\nit.\n\nThis general Science of Society, as distinguished from the separate\ndepartments of the science (each of which asserts its conclusions only\nconditionally, subject to the paramount control of the laws of the\ngeneral science) now remains to be characterized. And as will be shown\npresently, nothing of a really scientific character is here possible,\nexcept by the inverse deductive method. But before we quit the subject\nof those sociological speculations which proceed by way of direct\ndeduction, we must examine in what relation they stand to that\nindispensable element in all deductive sciences, Verification by\nSpecific Experience--comparison between the conclusions of reasoning and\nthe results of observation.\n\n\n\u00a7 5. We have seen that, in most deductive sciences, and among the rest\nin Ethology itself, which is the immediate foundation of the Social\nScience, a preliminary work of preparation is performed on the observed\nfacts, to fit them for being rapidly and accurately collated (sometimes\neven for being collated at all) with the conclusions of theory. This\npreparatory treatment consists in finding general propositions which\nexpress concisely what is common to large classes of observed facts:\nand these are called the empirical laws of the phenomena. We have,\ntherefore, to inquire, whether any similar preparatory process can be\nperformed on the facts of the social science; whether there are any\nempirical laws in history or statistics.\n\nIn statistics, it is evident that empirical laws may sometimes be\ntraced; and the tracing them forms an important part of that system of\nindirect observation on which we must often rely for the data of the\nDeductive Science. The process of the science consists in inferring\neffects from their causes; but we have often no means of observing the\ncauses, except through the medium of their effects. In such cases the\ndeductive science is unable to predict the effects, for want of the\nnecessary data; it can determine what causes are capable of producing\nany given effect, but not with what frequency and in what quantities\nthose causes exist. An instance in point is afforded by a newspaper now\nlying before me. A statement was furnished by one of the official\nassignees in bankruptcy, showing among the various bankruptcies which it\nhad been his duty to investigate, in how many cases the losses had been\ncaused by misconduct of different kinds, and in how many by unavoidable\nmisfortunes. The result was, that the number of failures caused by\nmisconduct greatly preponderated over those arising from all other\ncauses whatever. Nothing but specific experience could have given\nsufficient ground for a conclusion to this purport. To collect,\ntherefore, such empirical laws (which are never more than approximate\ngeneralizations) from direct observation, is an important part of the\nprocess of sociological inquiry.\n\nThe experimental process is not here to be regarded as a distinct road\nto the truth, but as a means (happening accidentally to be the only, or\nthe best, available) for obtaining the necessary data for the deductive\nscience. When the immediate causes of social facts are not open to\ndirect observation, the empirical law of the effects gives us the\nempirical law (which in that case is all that we can obtain) of the\ncauses likewise. But those immediate causes depend on remote causes; and\nthe empirical law, obtained by this indirect mode of observation, can\nonly be relied on as applicable to unobserved cases, so long as there is\nreason to think that no change has taken place in any of the remote\ncauses on which the immediate causes depend. In making use, therefore,\nof even the best statistical generalizations for the purpose of\ninferring (though it be only conjecturally) that the same empirical laws\nwill hold in any new case, it is necessary that we be well acquainted\nwith the remoter causes, in order that we may avoid applying the\nempirical law to cases which differ in any of the circumstances on which\nthe truth of the law ultimately depends. And thus, even where\nconclusions derived from specific observation are available for\npractical inferences in new cases, it is necessary that the deductive\nscience should stand sentinel over the whole process; that it should be\nconstantly referred to, and its sanction obtained to every inference.\n\nThe same thing holds true of all generalizations which can be grounded\non history. Not only there are such generalizations, but it will\npresently be shown that the general science of society, which\ninquires into the laws of succession and coexistence of the\ngreat facts constituting the state of society and civilization\nat any time, can proceed in no other manner than by making such\ngeneralizations--afterwards to be confirmed by connecting them with the\npsychological and ethological laws on which they must really depend.\n\n\n\u00a7 6. But (reserving this question for its proper place) in those more\nspecial inquiries which form the subject of the separate branches of the\nsocial science, this twofold logical process and reciprocal verification\nis not possible: specific experience affords nothing amounting to\nempirical laws. This is particularly the case where the object is to\ndetermine the effect of any one social cause among a great number acting\nsimultaneously; the effect, for example, of corn laws, or of a\nprohibitive commercial system generally. Though it may be perfectly\ncertain, from theory, what _kind_ of effects corn laws must produce, and\nin what general direction their influence must tell upon industrial\nprosperity; their effect is yet of necessity so much disguised by the\nsimilar or contrary effects of other influencing agents, that specific\nexperience can at most only show that on the average of some great\nnumber of instances, the cases where there were corn laws exhibited the\neffect in a greater degree than those where there were not. Now the\nnumber of instances necessary to exhaust the whole round of combinations\nof the various influential circumstances, and thus afford a fair\naverage, never can be obtained. Not only we can never learn with\nsufficient authenticity the facts of so many instances, but the world\nitself does not afford them in sufficient numbers, within the limits of\nthe given state of society and civilization which such inquiries always\npresuppose. Having thus no previous empirical generalizations with which\nto collate the conclusions of theory, the only mode of direct\nverification which remains is to compare those conclusions with the\nresult of an individual experiment or instance. But here the difficulty\nis equally great. For in order to verify a theory by an experiment, the\ncircumstances of the experiment must be exactly the same with those\ncontemplated in the theory. But in social phenomena the circumstances of\nno two cases are exactly alike. A trial of corn laws in another country\nor in a former generation, would go a very little way towards verifying\na conclusion drawn respecting their effect in this generation and in\nthis country. It thus happens, in most cases, that the only individual\ninstance really fitted to verify the predictions of theory is the very\ninstance for which the predictions were made; and the verification comes\ntoo late to be of any avail for practical guidance.\n\nAlthough, however, direct verification is impossible, there is an\nindirect verification, which is scarcely of less value, and which is\nalways practicable. The conclusion drawn as to the individual case, can\nonly be directly verified in that case; but it is verified indirectly,\nby the verification of other conclusions, drawn in other individual\ncases from the same laws. The experience which comes too late to verify\nthe particular proposition to which it refers, is not too late to help\ntowards verifying the general sufficiency of the theory. The test of\nthe degree in which the science affords safe ground for predicting (and\nconsequently for practically dealing with) what has not yet happened, is\nthe degree in which it would have enabled us to predict what has\nactually occurred. Before our theory of the influence of a particular\ncause, in a given state of circumstances, can be entirely trusted, we\nmust be able to explain and account for the existing state of all that\nportion of the social phenomena which that cause has a tendency to\ninfluence. If, for instance, we would apply our speculations in\npolitical economy to the prediction or guidance of the phenomena of any\ncountry, we must be able to explain all the mercantile or industrial\nfacts of a general character, appertaining to the present state of that\ncountry: to point out causes sufficient to account for all of them, and\nprove, or show good ground for supposing, that these causes have really\nexisted. If we cannot do this, it is a proof either that the facts which\nought to be taken into account are not yet completely known to us, or\nthat although we know the facts, we are not masters of a sufficiently\nperfect theory to enable us to assign their consequences. In either case\nwe are not, in the present state of our knowledge, fully competent to\ndraw conclusions, speculative or practical, for that country. In like\nmanner if we would attempt to judge of the effect which any political\ninstitution would have, supposing that it could be introduced into any\ngiven country; we must be able to show that the existing state of the\npractical government of that country, and of whatever else depends\nthereon, together with the particular character and tendencies of the\npeople, and their state in respect to the various elements of social\nwell-being, are such as the institutions they have lived under, in\nconjunction with the other circumstances of their nature or of their\nposition, were calculated to produce.\n\nTo prove (in short) that our science, and our knowledge of the\nparticular case, render us competent to predict the future, we must show\nthat they would have enabled us to predict the present and the past. If\nthere be anything which we could not have predicted, this constitutes a\nresidual phenomenon, requiring further study for the purpose of\nexplanation; and we must either search among the circumstances of the\nparticular case until we find one which, on the principles of our\nexisting theory, accounts for the unexplained phenomenon, or we must\nturn back, and seek the explanation by an extension and improvement of\nthe theory itself.\n\n\n\n\nCHAPTER X.\n\nOF THE INVERSE DEDUCTIVE, OR HISTORICAL METHOD.\n\n\n\u00a7 1. There are two kinds of sociological inquiry. In the first kind, the\nquestion proposed is, what effect will follow from a given cause, a\ncertain general condition of social circumstances being presupposed. As,\nfor example, what would be the effect of imposing or of repealing corn\nlaws, of abolishing monarchy or introducing universal suffrage, in the\npresent condition of society and civilization in any European country,\nor under any other given supposition with regard to the circumstances of\nsociety in general: without reference to the changes which might take\nplace, or which may already be in progress, in those circumstances. But\nthere is also a second inquiry, namely, what are the laws which\ndetermine those general circumstances themselves. In this last the\nquestion is, not what will be the effect of a given cause in a certain\nstate of society, but what are the causes which produce, and the\nphenomena which characterize, States of Society generally. In the\nsolution of this question consists the general Science of Society; by\nwhich the conclusions of the other and more special kind of inquiry must\nbe limited and controlled.\n\n\n\u00a7 2. In order to conceive correctly the scope of this general science,\nand distinguish it from the subordinate departments of sociological\nspeculation, it is necessary to fix the ideas attached to the phrase, \"a\nState of Society.\" What is called a state of society, is the\nsimultaneous state of all the greater social facts or phenomena. Such\nare, the degree of knowledge, and of intellectual and moral culture,\nexisting in the community, and in every class of it; the state of\nindustry, of wealth and its distribution; the habitual occupations of\nthe community; their division into classes, and the relations of those\nclasses to one another; the common beliefs which they entertain on all\nthe subjects most important to mankind, and the degree of assurance with\nwhich those beliefs are held; their tastes, and the character and degree\nof their \u00e6sthetic development; their form of government, and the more\nimportant of their laws and customs. The condition of all these things,\nand of many more which will readily suggest themselves, constitute the\nstate of society or the state of civilization at any given time.\n\nWhen states of society, and the causes which produce them, are spoken of\nas a subject of science, it is implied that there exists a natural\ncorrelation among these different elements; that not every variety of\ncombination of these general social facts is possible, but only certain\ncombinations; that, in short, there exist Uniformities of Coexistence\nbetween the states of the various social phenomena. And such is the\ntruth; as is indeed a necessary consequence of the influence exercised\nby every one of those phenomena over every other. It is a fact implied\nin the _consensus_ of the various parts of the social body.\n\nStates of society are like different constitutions or different ages in\nthe physical frame; they are conditions not of one or a few organs or\nfunctions, but of the whole organism. Accordingly, the information which\nwe possess respecting past ages, and respecting the various states of\nsociety now existing in different regions of the earth, does, when duly\nanalysed, exhibit uniformities. It is found that when one of the\nfeatures of society is in a particular state, a state of many other\nfeatures, more or less precisely determinate, always or usually coexists\nwith it.\n\nBut the uniformities of coexistence obtaining among phenomena which are\neffects of causes, must (as we have so often observed) be corollaries\nfrom the laws of causation by which these phenomena are really\ndetermined. The mutual correlation between the different elements of\neach state of society, is therefore a derivative law, resulting from the\nlaws which regulate the succession between one state of society and\nanother: for the proximate cause of every state of society is the state\nof society immediately preceding it. The fundamental problem, therefore,\nof the social science, is to find the laws according to which any state\nof society produces the state which succeeds it and takes its place.\nThis opens the great and vexed question of the progressiveness of man\nand society; an idea involved in every just conception of social\nphenomena as the subject of a science.\n\n\n\u00a7 3. It is one of the characters, not absolutely peculiar to the\nsciences of human nature and society, but belonging to them in a\npeculiar degree, to be conversant with a subject-matter whose properties\nare changeable. I do not mean changeable from day to day, but from age\nto age; so that not only the qualities of individuals vary, but those of\nthe majority are not the same in one age as in another.\n\nThe principal cause of this peculiarity is the extensive and constant\nreaction of the effects upon their causes. The circumstances in which\nmankind are placed, operating according to their own laws and to the\nlaws of human nature, form the characters of the human beings; but the\nhuman beings, in their turn, mould and shape the circumstances, for\nthemselves and for those who come after them. From this reciprocal\naction there must necessarily result either a cycle or a progress. In\nastronomy also, every fact is at once effect and cause; the successive\npositions of the various heavenly bodies produce changes both in the\ndirection and in the intensity of the forces by which those positions\nare determined. But in the case of the solar system, these mutual\nactions bring round again, after a certain number of changes, the former\nstate of circumstances; which of course leads to the perpetual\nrecurrence of the same series in an unvarying order. Those bodies, in\nshort, revolve in orbits: but there are (or, conformably to the laws of\nastronomy, there might be) others which, instead of an orbit, describe a\ntrajectory--a course not returning into itself. One or other of these\nmust be the type to which human affairs must conform.\n\nOne of the thinkers who earliest conceived the succession of historical\nevents as subject to fixed laws, and endeavoured to discover these laws\nby an analytical survey of history, Vico, the celebrated author of the\n_Scienza Nuova_, adopted the former of these opinions. He conceived the\nphenomena of human society as revolving in an orbit; as going through\nperiodically the same series of changes. Though there were not wanting\ncircumstances tending to give some plausibility to this view, it would\nnot bear a close scrutiny: and those who have succeeded Vico in this\nkind of speculations have universally adopted the idea of a trajectory\nor progress, in lieu of an orbit or cycle.\n\nThe words Progress and Progressiveness are not here to be understood as\nsynonymous with improvement and tendency to improvement. It is\nconceivable that the laws of human nature might determine, and even\nnecessitate, a certain series of changes in man and society, which might\nnot in every case, or which might not on the whole, be improvements. It\nis my belief indeed that the general tendency is, and will continue to\nbe, saving occasional and temporary exceptions, one of improvement; a\ntendency towards a better and happier state. This, however, is not a\nquestion of the method of the social science, but a theorem of the\nscience itself. For our purpose it is sufficient, that there is a\nprogressive change both in the character of the human race, and in their\noutward circumstances so far as moulded by themselves: that in each\nsuccessive age the principal phenomena of society are different from\nwhat they were in the age preceding, and still more different from any\nprevious age: the periods which most distinctly mark these successive\nchanges being intervals of one generation, during which a new set of\nhuman beings have been educated, have grown up from childhood, and taken\npossession of society.\n\nThe progressiveness of the human race is the foundation on which a\nmethod of philosophizing in the social science has been of late years\nerected, far superior to either of the two modes which had previously\nbeen prevalent, the chemical or experimental, and the geometrical modes.\nThis method, which is now generally adopted by the most advanced\nthinkers on the Continent, consists in attempting, by a study and\nanalysis of the general facts of history, to discover (what these\nphilosophers term) the law of progress: which law, once ascertained,\nmust according to them enable us to predict future events, just as after\na few terms of an infinite series in algebra we are able to detect the\nprinciple of regularity in their formation, and to predict the rest of\nthe series to any number of terms we please. The principal aim of\nhistorical speculation in France, of late years, has been to ascertain\nthis law. But while I gladly acknowledge the great services which have\nbeen rendered to historical knowledge by this school, I cannot but deem\nthem to be mostly chargeable with a fundamental misconception of the\ntrue method of social philosophy. The misconception consists in\nsupposing that the order of succession which we may be able to trace\namong the different states of society and civilization which history\npresents to us, even if that order were more rigidly uniform than it has\nyet been proved to be, could ever amount to a law of nature. It can only\nbe an empirical law. The succession of states of the human mind and of\nhuman society cannot have an independent law of its own; it must depend\non the psychological and ethological laws which govern the action of\ncircumstances on men and of men on circumstances. It is conceivable that\nthose laws might be such, and the general circumstances of the human\nrace such, as to determine the successive transformations of man and\nsociety to one given and unvarying order. But even if the case were so,\nit cannot be the ultimate aim of science to discover an empirical law.\nUntil that law could be connected with the psychological and ethological\nlaws on which it must depend, and, by the consilience of deduction _\u00e0\npriori_ with historical evidence, could be converted from an empirical\nlaw into a scientific one, it could not be relied on for the prediction\nof future events, beyond, at most, strictly adjacent cases. M. Comte\nalone, among the new historical school, has seen the necessity of thus\nconnecting all our generalizations from history with the laws of human\nnature.\n\n\n\u00a7 4. But, while it is an imperative rule never to introduce any\ngeneralization from history into the social science unless sufficient\ngrounds can be pointed out for it in human nature, I do not think any\none will contend that it would have been possible, setting out from the\nprinciples of human nature and from the general circumstances of the\nposition of our species, to determine _\u00e0 priori_ the order in which\nhuman development must take place, and to predict, consequently, the\ngeneral facts of history up to the present time. After the first few\nterms of the series, the influence exercised over each generation by the\ngenerations which preceded it, becomes (as is well observed by the\nwriter last referred to) more and more preponderant over all other\ninfluences; until at length what we now are and do, is in a very small\ndegree the result of the universal circumstances of the human race, or\neven of our own circumstances acting through the original qualities of\nour species, but mainly of the qualities produced in us by the whole\nprevious history of humanity. So long a series of actions and reactions\nbetween Circumstances and Man, each successive term being composed of an\never greater number and variety of parts, could not possibly be computed\nby human faculties from the elementary laws which produce it. The mere\nlength of the series would be a sufficient obstacle, since a slight\nerror in any one of the terms would augment in rapid progression at\nevery subsequent step.\n\nIf, therefore, the series of the effects themselves did not, when\nexamined as a whole, manifest any regularity, we should in vain attempt\nto construct a general science of society. We must in that case have\ncontented ourselves with that subordinate order of sociological\nspeculation formerly noticed, namely, with endeavouring to ascertain\nwhat would be the effect of the introduction of any new cause, in a\nstate of society supposed to be fixed; a knowledge sufficient for the\nmore common exigencies of daily political practice, but liable to fail\nin all cases in which the progressive movement of society is one of the\ninfluencing elements; and therefore more precarious in proportion as the\ncase is more important. But since both the natural varieties of mankind,\nand the original diversities of local circumstances, are much less\nconsiderable than the points of agreement, there will naturally be a\ncertain degree of uniformity in the progressive development of the\nspecies and of its works. And this uniformity tends to become greater,\nnot less, as society advances; since the evolution of each people, which\nis at first determined exclusively by the nature and circumstances of\nthat people, is gradually brought under the influence (which becomes\nstronger as civilization advances) of the other nations of the earth,\nand of the circumstances by which they have been influenced. History\naccordingly does, when judiciously examined, afford Empirical Laws of\nSociety. And the problem of general sociology is to ascertain these, and\nconnect them with the laws of human nature, by deductions showing that\nsuch were the derivative laws naturally to be expected as the\nconsequences of those ultimate ones.\n\nIt is, indeed, hardly ever possible, even after history has suggested\nthe derivative law, to demonstrate _\u00e0 priori_ that such was the only\norder of succession or of coexistence in which the effects could,\nconsistently with the laws of human nature, have been produced. We can\nat most make out that there were strong _\u00e0 priori_ reasons for expecting\nit, and that no other order of succession or coexistence would have been\nso likely to result from the nature of man and the general circumstances\nof his position. Often we cannot do even this; we cannot even show that\nwhat did take place was probable _\u00e0 priori_, but only that it was\npossible. This, however,--which, in the Inverse Deductive Method that we\nare now characterizing, is a real process of verification,--is as\nindispensable, as verification by specific experience has been shown to\nbe, where the conclusion is originally obtained by the direct way of\ndeduction. The empirical laws must be the result of but a few instances,\nsince few nations have ever attained at all, and still fewer by their\nown independent development, a high stage of social progress. If,\ntherefore, even one or two of these few instances be insufficiently\nknown, or imperfectly analysed into their elements, and therefore not\nadequately compared with other instances, nothing is more probable than\nthat a wrong empirical law will emerge instead of the right one.\nAccordingly, the most erroneous generalizations are continually made\nfrom the course of history: not only in this country, where history\ncannot yet be said to be at all cultivated as a science, but in other\ncountries, where it is so cultivated, and by persons well versed in it.\nThe only check or corrective is, constant verification by psychological\nand ethological laws. We may add to this, that no one but a person\ncompetently skilled in those laws is capable of preparing the materials\nfor historical generalization, by analysing the facts of history, or\neven by observing the social phenomena of his own time. No other will be\naware of the comparative importance of different facts, nor consequently\nknow what facts to look for, or to observe; still less will he be\ncapable of estimating the evidence of facts which, as is the case with\nmost, cannot be ascertained by direct observation or learnt from\ntestimony, but must be inferred from marks.\n\n\n\u00a7 5. The Empirical Laws of Society are of two kinds; some are\nuniformities of coexistence, some of succession. According as the\nscience is occupied in ascertaining and verifying the former sort of\nuniformities or the latter, M. Comte gives it the title of Social\nStatics, or of Social Dynamics; conformably to the distinction in\nmechanics between the conditions of equilibrium and those of movement;\nor in biology, between the laws of organization and those of life. The\nfirst branch of the science ascertains the conditions of stability in\nthe social union: the second, the laws of progress. Social Dynamics is\nthe theory of Society considered in a state of progressive movement;\nwhile Social Statics is the theory of the _consensus_ already spoken of\nas existing among the different parts of the social organism; in other\nwords, the theory of the mutual actions and reactions of contemporaneous\nsocial phenomena; \"making[12] provisionally, as far as possible,\nabstraction, for scientific purposes, of the fundamental movement which\nis at all times gradually modifying the whole of them.\n\n\"In this first point of view, the provisions of sociology will enable us\nto infer one from another (subject to ulterior verification by direct\nobservation) the various characteristic marks of each distinct mode of\nsocial existence; in a manner essentially analogous to what is now\nhabitually practised in the anatomy of the physical body. This\npreliminary aspect, therefore, of political science, of necessity\nsupposes that (contrary to the existing habits of philosophers) each of\nthe numerous elements of the social state, ceasing to be looked at\nindependently and absolutely, shall be always and exclusively considered\nrelatively to all the other elements, with the whole of which it is\nunited by mutual interdependence. It would be superfluous to insist here\nupon the great and constant utility of this branch of sociological\nspeculation. It is, in the first place, the indispensable basis of the\ntheory of social progress. It may, moreover, be employed, immediately,\nand of itself, to supply the place, provisionally at least, of direct\nobservation, which in many cases is not always practicable for some of\nthe elements of society, the real condition of which may however be\nsufficiently judged of by means of the relations which connect them with\nothers previously known. The history of the sciences may give us some\nnotion of the habitual importance of this auxiliary resource, by\nreminding us, for example, how the vulgar errors of mere erudition\nconcerning the pretended acquirements of the ancient Egyptians in the\nhigher astronomy, were irrevocably dissipated (even before sentence had\nbeen passed on them by a sounder erudition) from the single\nconsideration of the inevitable connexion between the general state of\nastronomy and that of abstract geometry, then evidently in its infancy.\nIt would be easy to cite a multitude of analogous cases, the character\nof which could admit of no dispute. In order to avoid exaggeration,\nhowever, it should be remarked, that these necessary relations among the\ndifferent aspects of society cannot, from their very nature, be so\nsimple and precise that the results observed could only have arisen from\nsome one mode of mutual co-ordination. Such a notion, already too\nnarrow in the science of life, would be completely at variance with the\nstill more complex nature of sociological speculations. But the exact\nestimation of these limits of variation, both in the healthy and in the\nmorbid state, constitutes, at least as much as in the anatomy of the\nnatural body, an indispensable complement to every theory of\nSociological Statics; without which the indirect exploration above\nspoken of would often lead into error.\n\n\"This is not the place for methodically demonstrating the existence of a\nnecessary relation among all the possible aspects of the same social\norganism; a point on which, in principle at least, there is now little\ndifference of opinion among sound thinkers. From whichever of the social\nelements we choose to set out, we may easily recognise that it has\nalways a connexion, more or less immediate, with all the other elements,\neven with those which at first sight appear the most independent of it.\nThe dynamical consideration of the progressive development of civilized\nhumanity, affords, no doubt, a still more efficacious means of effecting\nthis interesting verification of the _consensus_ of the social\nphenomena, by displaying the manner in which every change in any one\npart, operates immediately, or very speedily, upon all the rest. But\nthis indication may be preceded, or at all events followed, by a\nconfirmation of a purely statical kind; for, in politics as in\nmechanics, the communication of motion from one object to another proves\na connexion between them. Without descending to the minute\ninterdependence of the different branches of any one science or art, is\nit not evident that among the different sciences, as well as among most\nof the arts, there exists such a connexion, that if the state of any one\nwell marked division of them is sufficiently known to us, we can with\nreal scientific assurance infer, from their necessary correlation, the\ncontemporaneous state of every one of the others? By a further extension\nof this consideration, we may conceive the necessary relation which\nexists between the condition of the sciences in general and that of the\narts in general, except that the mutual dependence is less intense in\nproportion as it is more indirect. The same is the case when, instead\nof considering the aggregate of the social phenomena in some one people,\nwe examine it simultaneously in different contemporaneous nations;\nbetween which the perpetual reciprocity of influence, especially in\nmodern times, cannot be contested, though the _consensus_ must in this\ncase be ordinarily of a less decided character, and must decrease\ngradually with the affinity of the cases and the multiplicity of the\npoints of contact, so as at last, in some cases, to disappear almost\nentirely; as for example between Western Europe and Eastern Asia, of\nwhich the various general states of society appear to have been hitherto\nalmost independent of one another.\"\n\nThese remarks are followed by illustrations of one of the most\nimportant, and until lately, most neglected, of the general principles\nwhich, in this division of the social science, may be considered as\nestablished; namely, the necessary correlation between the form of\ngovernment existing in any society and the contemporaneous state of\ncivilization: a natural law, which stamps the endless discussions and\ninnumerable theories respecting forms of government in the abstract, as\nfruitless and worthless, for any other purpose than as a preparatory\ntreatment of materials to be afterwards used for the construction of a\nbetter philosophy.\n\nAs already remarked, one of the main results of the science of social\nstatics would be to ascertain the requisites of stable political union.\nThere are some circumstances which, being found in all societies without\nexception, and in the greatest degree where the social union is most\ncomplete, may be considered (when psychological and ethological laws\nconfirm the indication) as conditions of the existence of the complex\nphenomenon called a State. For example, no numerous society has ever\nbeen held together without laws, or usages equivalent to them; without\ntribunals, and an organized force of some sort to execute their\ndecisions. There have always been public authorities whom, with more or\nless strictness and in cases more or less accurately defined, the rest\nof the community obeyed, or according to general opinion were bound to\nobey. By following out this course of inquiry we shall find a number of\nrequisites, which have been present in every society that has maintained\na collective existence, and on the cessation of which it has either\nmerged in some other society, or reconstructed itself on some new basis,\nin which the conditions were conformed to. Although these results,\nobtained by comparing different forms and states of society, amount in\nthemselves only to empirical laws; some of them, when once suggested,\nare found to follow with so much probability from general laws of human\nnature, that the consilience of the two processes raises the evidence to\nproof, and the generalizations to the rank of scientific truths.\n\nThis seems to be affirmable (for instance) of the conclusions arrived at\nin the following passage; extracted, with some alterations, from a\ncriticism on the negative philosophy of the eighteenth century,[13] and\nwhich I quote, though (as in some former instances) from myself, because\nI have no better way of illustrating the conception I have formed of the\nkind of theorems of which sociological statics would consist.\n\n\"The very first element of the social union, obedience to a government\nof some sort, has not been found so easy a thing to establish in the\nworld. Among a timid and spiritless race like the inhabitants of the\nvast plains of tropical countries, passive obedience may be of natural\ngrowth; though even there we doubt whether it has ever been found among\nany people with whom fatalism, or in other words, submission to the\npressure of circumstances as a divine decree, did not prevail as a\nreligious doctrine. But the difficulty of inducing a brave and warlike\nrace to submit their individual _arbitrium_ to any common umpire, has\nalways been felt to be so great, that nothing short of supernatural\npower has been deemed adequate to overcome it; and such tribes have\nalways assigned to the first institution of civil society a divine\norigin. So differently did those judge who knew savage men by actual\nexperience, from those who had no acquaintance with them except in the\ncivilized state. In modern Europe itself, after the fall of the Roman\nempire, to subdue the feudal anarchy and bring the whole people of any\nEuropean nation into subjection to government (though Christianity in\nthe most concentrated form of its influence was co-operating in the\nwork) required thrice as many centuries as have elapsed since that time.\n\n\"Now if these philosophers had known human nature under any other type\nthan that of their own age, and of the particular classes of society\namong whom they lived, it would have occurred to them, that wherever\nthis habitual submission to law and government has been firmly and\ndurably established, and yet the vigour and manliness of character which\nresisted its establishment have been in any degree preserved, certain\nrequisites have existed, certain conditions have been fulfilled, of\nwhich the following may be regarded as the principal.\n\n\"First: there has existed, for all who were accounted citizens,--for all\nwho were not slaves, kept down by brute force,--a system of _education_,\nbeginning with infancy and continued through life, of which whatever\nelse it might include, one main and incessant ingredient was\n_restraining discipline_. To train the human being in the habit, and\nthence the power, of subordinating his personal impulses and aims, to\nwhat were considered the ends of society; of adhering, against all\ntemptation, to the course of conduct which those ends prescribed; of\ncontrolling in himself all feelings which were liable to militate\nagainst those ends, and encouraging all such as tended towards them;\nthis was the purpose, to which every outward motive that the authority\ndirecting the system could command, and every inward power or principle\nwhich its knowledge of human nature enabled it to evoke, were\nendeavoured to be rendered instrumental. The entire civil and military\npolicy of the ancient commonwealths was such a system of training; in\nmodern nations its place has been attempted to be supplied, principally,\nby religious teaching. And whenever and in proportion as the strictness\nof the restraining discipline was relaxed, the natural tendency of\nmankind to anarchy re-asserted itself; the state became disorganized\nfrom within; mutual conflict for selfish ends, neutralized the energies\nwhich were required to keep up the contest against natural causes of\nevil; and the nation, after a longer or briefer interval of progressive\ndecline, became either the slave of a despotism, or the prey of a\nforeign invader.\n\n\"The second condition of permanent political society has been found to\nbe, the existence, in some form or other, of the feeling of allegiance\nor loyalty. This feeling may vary in its objects, and is not confined to\nany particular form of government; but whether in a democracy or in a\nmonarchy, its essence is always the same; viz. that there be in the\nconstitution of the state _something_ which is settled, something\npermanent, and not to be called in question; something which, by general\nagreement, has a right to be where it is, and to be secure against\ndisturbance, whatever else may change. This feeling may attach itself,\nas among the Jews (and in most of the commonwealths of antiquity), to a\ncommon God or gods, the protectors and guardians of their state. Or it\nmay attach itself to certain persons, who are deemed to be, whether by\ndivine appointment, by long prescription, or by the general recognition\nof their superior capacity and worthiness, the rightful guides and\nguardians of the rest. Or it may connect itself with laws; with ancient\nliberties or ordinances. Or, finally, (and this is the only shape in\nwhich the feeling is likely to exist hereafter,) it may attach itself to\nthe principles of individual freedom and political and social equality,\nas realized in institutions which as yet exist nowhere, or exist only in\na rudimentary state. But in all political societies which have had a\ndurable existence, there has been some fixed point: something which\npeople agreed in holding sacred; which, wherever freedom of discussion\nwas a recognised principle, it was of course lawful to contest in\ntheory, but which no one could either fear or hope to see shaken in\npractice; which, in short (except perhaps during some temporary crisis)\nwas in the common estimation placed beyond discussion. And the necessity\nof this may easily be made evident. A state never is, nor until mankind\nare vastly improved, can hope to be, for any long time exempt from\ninternal dissension; for there neither is nor has ever been any state of\nsociety in which collisions did not occur between the immediate\ninterests and passions of powerful sections of the people. What, then,\nenables nations to weather these storms, and pass through turbulent\ntimes without any permanent weakening of the securities for peaceable\nexistence? Precisely this--that however important the interests about\nwhich men fell out, the conflict did not affect the fundamental\nprinciple of the system of social union which happened to exist; nor\nthreaten large portions of the community with the subversion of that on\nwhich they had built their calculations, and with which their hopes and\naims had become identified. But when the questioning of these\nfundamental principles is (not the occasional disease, or salutary\nmedicine, but) the habitual condition of the body politic; and when all\nthe violent animosities are called forth, which spring naturally from\nsuch a situation, the state is virtually in a position of civil war; and\ncan never long remain free from it in act and fact.\n\n\"The third essential condition of stability in political society, is a\nstrong and active principle of cohesion among the members of the same\ncommunity or state. We need scarcely say that we do not mean\nnationality, in the vulgar sense of the term; a senseless antipathy to\nforeigners; indifference to the general welfare of the human race, or an\nunjust preference of the supposed interests of our own country; a\ncherishing of bad peculiarities because they are national, or a refusal\nto adopt what has been found good by other countries. We mean a\nprinciple of sympathy, not of hostility; of union, not of separation. We\nmean a feeling of common interest among those who live under the same\ngovernment, and are contained within the same natural or historical\nboundaries. We mean, that one part of the community do not consider\nthemselves as foreigners with regard to another part; that they set a\nvalue on their connexion--feel that they are one people, that their lot\nis cast together, that evil to any of their fellow-countrymen is evil to\nthemselves, and do not desire selfishly to free themselves from their\nshare of any common inconvenience by severing the connexion. How strong\nthis feeling was in those ancient commonwealths which attained any\ndurable greatness, every one knows. How happily Rome, in spite of all\nher tyranny, succeeded in establishing the feeling of a common country\namong the provinces of her vast and divided empire, will appear when any\none who has given due attention to the subject shall take the trouble to\npoint it out. In modern times the countries which have had that feeling\nin the strongest degree have been the most powerful countries; England,\nFrance, and, in proportion to their territory and resources, Holland and\nSwitzerland; while England in her connexion with Ireland, is one of the\nmost signal examples of the consequences of its absence. Every Italian\nknows why Italy is under a foreign yoke; every German knows what\nmaintains despotism in the Austrian empire; the evils of Spain flow as\nmuch from the absence of nationality among the Spaniards themselves, as\nfrom the presence of it in their relations with foreigners: while the\ncompletest illustration of all is afforded by the republics of South\nAmerica, where the parts of one and the same state adhere so slightly\ntogether, that no sooner does any province think itself aggrieved by the\ngeneral government than it proclaims itself a separate nation.\"\n\n\n\u00a7 6. While the derivative laws of social statics are ascertained by\nanalysing different states of society, and comparing them with one\nanother, without regard to the order of their succession; the\nconsideration of the successive order is, on the contrary, predominant\nin the study of social dynamics, of which the aim is to observe and\nexplain the sequences of social conditions. This branch of the social\nscience would be as complete as it can be made, if every one of the\nleading general circumstances of each generation were traced to its\ncauses in the generation immediately preceding. But the _consensus_ is\nso complete, (especially in modern history,) that in the filiation of\none generation and another, it is the whole which produces the whole,\nrather than any part a part. Little progress, therefore, can be made in\nestablishing the filiation, directly from laws of human nature, without\nhaving first ascertained the immediate or derivative laws according to\nwhich social states generate one another as society advances; the\n_axiomata media_ of General Sociology.\n\nThe empirical laws which are most readily obtained by generalization\nfrom history do not amount to this. They are not the \"middle principles\"\nthemselves, but only evidence towards the establishment of such\nprinciples. They consist of certain general tendencies which may be\nperceived in society; a progressive increase of some social elements and\ndiminution of others, or a gradual change in the general character of\ncertain elements. It is easily seen, for instance, that as society\nadvances, mental tend more and more to prevail over bodily qualities,\nand masses over individuals: that the occupation of all that portion of\nmankind who are not under external restraint is at first chiefly\nmilitary, but society becomes progressively more and more engrossed with\nproductive pursuits, and the military spirit gradually gives way to the\nindustrial; to which many similar truths might be added. And with\ngeneralizations of this description, ordinary inquirers, even of the\nhistorical school now predominant on the Continent, are satisfied. But\nthese and all such results are still at too great a distance from the\nelementary laws of human nature on which they depend,--too many links\nintervene, and the concurrence of causes at each link is far too\ncomplicated,--to enable these propositions to be presented as direct\ncorollaries from those elementary principles. They have, therefore, in\nthe minds of most inquirers, remained in the state of empirical laws,\napplicable only within the bounds of actual observation; without any\nmeans of determining their real limits, and of judging whether the\nchanges which have hitherto been in progress are destined to continue\nindefinitely, or to terminate, or even to be reversed.\n\n\n\u00a7 7. In order to obtain better empirical laws, we must not rest\nsatisfied with noting the progressive changes which manifest themselves\nin the separate elements of society, and in which nothing is indicated\nbut the relation of fragments of the effect to corresponding fragments\nof the cause. It is necessary to combine the statical view of social\nphenomena with the dynamical, considering not only the progressive\nchanges of the different elements, but the contemporaneous condition of\neach; and thus obtain empirically the law of correspondence not only\nbetween the simultaneous states, but between the simultaneous changes,\nof those elements. This law of correspondence it is, which, duly\nverified _\u00e0 priori_, would become the real scientific derivative law of\nthe development of humanity and human affairs.\n\nIn the difficult process of observation and comparison which is here\nrequired, it would evidently be a great assistance if it should happen\nto be the fact, that some one element in the complex existence of social\nman is pre-eminent over all others as the prime agent of the social\nmovement. For we could then take the progress of that one element as the\ncentral chain, to each successive link of which, the corresponding links\nof all the other progressions being appended, the succession of the\nfacts would by this alone be presented in a kind of spontaneous order,\nfar more nearly approaching to the real order of their filiation than\ncould be obtained by any other merely empirical process.\n\nNow, the evidence of history and that of human nature combine, by a\nstriking instance of consilience, to show that there really is one\nsocial element which is thus predominant, and almost paramount, among\nthe agents of the social progression. This is, the state of the\nspeculative faculties of mankind; including the nature of the beliefs\nwhich by any means they have arrived at, concerning themselves and the\nworld by which they are surrounded.\n\nIt would be a great error, and one very little likely to be committed,\nto assert that speculation, intellectual activity, the pursuit of truth,\nis among the more powerful propensities of human nature, or holds a\npredominating place in the lives of any, save decidedly exceptional,\nindividuals. But, notwithstanding the relative weakness of this\nprinciple among other sociological agents, its influence is the main\ndetermining cause of the social progress; all the other dispositions of\nour nature which contribute to that progress, being dependent on it for\nthe means of accomplishing their share of the work. Thus (to take the\nmost obvious case first,) the impelling force to most of the\nimprovements effected in the arts of life, is the desire of increased\nmaterial comfort; but as we can only act upon external objects in\nproportion to our knowledge of them, the state of knowledge at any time\nis the limit of the industrial improvements possible at that time; and\nthe progress of industry must follow, and depend on, the progress of\nknowledge. The same thing may be shown to be true, though it is not\nquite so obvious, of the progress of the fine arts. Further, as the\nstrongest propensities of uncultivated or half-cultivated human nature\n(being the purely selfish ones, and those of a sympathetic character\nwhich partake most of the nature of selfishness) evidently tend in\nthemselves to disunite mankind, not to unite them,--to make them rivals,\nnot confederates; social existence is only possible by a disciplining of\nthose more powerful propensities, which consists in subordinating them\nto a common system of opinions. The degree of this subordination is the\nmeasure of the completeness of the social union, and the nature of the\ncommon opinions determines its kind. But in order that mankind should\nconform their actions to any set of opinions, these opinions must exist,\nmust be believed by them. And thus, the state of the speculative\nfaculties, the character of the propositions assented to by the\nintellect, essentially determines the moral and political state of the\ncommunity, as we have already seen that it determines the physical.\n\nThese conclusions, deduced from the laws of human nature, are in entire\naccordance with the general facts of history. Every considerable change\nhistorically known to us in the condition of any portion of mankind,\nwhen not brought about by external force, has been preceded by a change,\nof proportional extent, in the state of their knowledge, or in their\nprevalent beliefs. As between any given state of speculation, and the\ncorrelative state of everything else, it was almost always the former\nwhich first showed itself; though the effects, no doubt, reacted\npotently upon the cause. Every considerable advance in material\ncivilization has been preceded by an advance in knowledge: and when any\ngreat social change has come to pass, either in the way of gradual\ndevelopment or of sudden conflict, it has had for its precursor a great\nchange in the opinions and modes of thinking of society. Polytheism,\nJudaism, Christianity, Protestantism, the critical philosophy of modern\nEurope, and its positive science--each of these has been a primary agent\nin making society what it was at each successive period, while society\nwas but secondarily instrumental in making _them_, each of them (so far\nas causes can be assigned for its existence) being mainly an emanation\nnot from the practical life of the period, but from the previous state\nof belief and thought. The weakness of the speculative propensity in\nmankind generally, has not, therefore, prevented the progress of\nspeculation from governing that of society at large; it has only, and\ntoo often, prevented progress altogether, where the intellectual\nprogression has come to an early stand for want of sufficiently\nfavourable circumstances.\n\nFrom this accumulated evidence, we are justified in concluding, that the\norder of human progression in all respects will mainly depend on the\norder of progression in the intellectual convictions of mankind, that\nis, on the law of the successive transformations of human opinions. The\nquestion remains, whether this law can be determined; at first from\nhistory as an empirical law, then converted into a scientific theorem by\ndeducing it _\u00e0 priori_ from the principles of human nature. As the\nprogress of knowledge and the changes in the opinions of mankind are\nvery slow, and manifest themselves in a well-defined manner only at long\nintervals; it cannot be expected that the general order of sequence\nshould be discoverable from the examination of less than a very\nconsiderable part of the duration of the social progress. It is\nnecessary to take into consideration the whole of past time, from the\nfirst recorded condition of the human race, to the memorable phenomena\nof the last and present generations.\n\n\n\u00a7 8. The investigation which I have thus endeavoured to characterize,\nhas been systematically attempted, up to the present time, by M. Comte\nalone. His work is hitherto the only known example of the study of\nsocial phenomena according to this conception of the Historical Method.\nWithout discussing here the worth of his conclusions, and especially of\nhis predictions and recommendations with respect to the Future of\nsociety, which appear to me greatly inferior in value to his\nappreciation of the Past, I shall confine myself to mentioning one\nimportant generalization, which M. Comte regards as the fundamental law\nof the progress of human knowledge. Speculation he conceives to have, on\nevery subject of human inquiry, three successive stages; in the first of\nwhich it tends to explain the phenomena by supernatural agencies, in the\nsecond by metaphysical abstractions, and in the third or final state\nconfines itself to ascertaining their laws of succession and similitude.\nThis generalization appears to me to have that high degree of scientific\nevidence, which is derived from the concurrence of the indications of\nhistory with the probabilities derived from the constitution of the\nhuman mind. Nor could it be easily conceived, from the mere enunciation\nof such a proposition, what a flood of light it lets in upon the whole\ncourse of history; when its consequences are traced, by connecting with\neach of the three states of human intellect which it distinguishes, and\nwith each successive modification of those three states, the correlative\ncondition of other social phenomena.[14]\n\nBut whatever decision competent judges may pronounce on the results\narrived at by any individual inquirer, the method now characterized is\nthat by which the derivative laws of social order and of social progress\nmust be sought. By its aid we may hereafter succeed not only in looking\nfar forward into the future history of the human race, but in\ndetermining what artificial means may be used, and to what extent, to\naccelerate the natural progress in so far as it is beneficial; to\ncompensate for whatever may be its inherent inconveniences or\ndisadvantages; and to guard against the dangers or accidents to which\nour species is exposed from the necessary incidents of its progression.\nSuch practical instructions, founded on the highest branch of\nspeculative sociology, will form the noblest and most beneficial portion\nof the Political Art.\n\nThat of this science and art even the foundations are but beginning to\nbe laid, is sufficiently evident. But the superior minds are fairly\nturning themselves towards that object. It has become the aim of really\nscientific thinkers to connect by theories the facts of universal\nhistory: it is acknowledged to be one of the requisites of a general\nsystem of social doctrine, that it should explain, so far as the data\nexist, the main facts of history; and a Philosophy of History is\ngenerally admitted to be at once the verification, and the initial form,\nof the Philosophy of the Progress of Society.\n\nIf the endeavours now making in all the more cultivated nations, and\nbeginning to be made even in England (usually the last to enter into the\ngeneral movement of the European mind) for the construction of a\nPhilosophy of History, shall be directed and controlled by those views\nof the nature of sociological evidence which I have (very briefly and\nimperfectly) attempted to characterize; they cannot fail to give birth\nto a sociological system widely removed from the vague and conjectural\ncharacter of all former attempts, and worthy to take its place, at last,\namong the sciences. When this time shall come, no important branch of\nhuman affairs will be any longer abandoned to empiricism and\nunscientific surmise: the circle of human knowledge will be complete,\nand it can only thereafter receive further enlargement by perpetual\nexpansion from within.\n\n\n\n\nCHAPTER XI.\n\nADDITIONAL ELUCIDATIONS OF THE SCIENCE OF HISTORY.\n\n\n\u00a7 1. The doctrine which the preceding chapters were intended to enforce\nand elucidate--that the collective series of social phenomena, in other\nwords the course of history, is subject to general laws, which\nphilosophy may possibly detect--has been familiar for generations to the\nscientific thinkers of the Continent, and has for the last quarter of a\ncentury passed out of their peculiar domain, into that of newspapers and\nordinary political discussion. In our own country, however, at the time\nof the first publication of this Treatise, it was almost a novelty, and\nthe prevailing habits of thought on historical subjects were the very\nreverse of a preparation for it. Since then a great change has taken\nplace, and has been eminently promoted by the important work of Mr.\nBuckle; who, with characteristic energy, flung down this great\nprinciple, together with many striking exemplifications of it, into the\narena of popular discussion, to be fought over by a sort of combatants,\nin the presence of a sort of spectators, who would never even have been\naware that there existed such a principle if they had been left to learn\nits existence from the speculations of pure science. And hence has\narisen a considerable amount of controversy, tending not only to make\nthe principle rapidly familiar to the majority of cultivated minds, but\nalso to clear it from the confusions and misunderstandings by which it\nwas but natural that it should for a time be clouded, and which impair\nthe worth of the doctrine to those who accept it, and are the\nstumbling-block of many who do not.\n\nAmong the impediments to the general acknowledgment, by thoughtful\nminds, of the subjection of historical facts to scientific laws, the\nmost fundamental continues to be that which is grounded on the doctrine\nof Free Will, or in other words, on the denial that the law of\ninvariable Causation holds true of human volitions: for if it does not,\nthe course of history, being the result of human volitions, cannot be a\nsubject of scientific laws, since the volitions on which it depends can\nneither be foreseen, nor reduced to any canon of regularity even after\nthey have occurred. I have discussed this question, as far as seemed\nsuitable to the occasion, in a former chapter: and I only think it\nnecessary to repeat, that the doctrine of the Causation of human\nactions, improperly called the doctrine of Necessity, affirms no\nmysterious _nexus_, or overruling fatality: it asserts only that men's\nactions are the joint result of the general laws and circumstances of\nhuman nature, and of their own particular characters; those characters\nagain being the consequence of the natural and artificial circumstances\nthat constituted their education, among which circumstances must be\nreckoned their own conscious efforts. Any one who is willing to take (if\nthe expression may be permitted) the trouble of thinking himself into\nthe doctrine as thus stated, will find it, I believe, not only a\nfaithful interpretation of the universal experience of human conduct,\nbut a correct representation of the mode in which he himself, in every\nparticular case, spontaneously interprets his own experience of that\nconduct.\n\nBut if this principle is true of individual man, it must be true of\ncollective man. If it is the law of human life, the law must be realized\nin history. The experience of human affairs when looked at _en masse_,\nmust be in accordance with it if true, or repugnant to it if false. The\nsupport which this _\u00e0 posteriori_ verification affords to the law, is\nthe part of the case which has been most clearly and triumphantly\nbrought out by Mr. Buckle.\n\nThe facts of statistics, since they have been made a subject of careful\nrecordation and study, have yielded conclusions, some of which have been\nvery startling to persons not accustomed to regard moral actions as\nsubject to uniform laws. The very events which in their own nature\nappear most capricious and uncertain, and which in any individual case\nno attainable degree of knowledge would enable us to foresee, occur,\nwhen considerable numbers are taken into the account, with a degree of\nregularity approaching to mathematical. What act is there which all\nwould consider as more completely dependent on individual character, and\non the exercise of individual free will, than that of slaying a fellow\ncreature? Yet in any large country, the number of murders, in proportion\nto the population, varies (it has been found) very little from one year\nto another, and in its variations never deviates widely from a certain\naverage. What is still more remarkable, there is a similar approach to\nconstancy in the proportion of these murders annually committed with\nevery particular kind of instrument. There is a like approximation to\nidentity, as between one year and another, in the comparative number of\nlegitimate and of illegitimate births. The same thing is found true of\nsuicides, accidents, and all other social phenomena of which the\nregistration is sufficiently perfect; one of the most curiously\nillustrative examples being the fact, ascertained by the registers of\nthe London and Paris post-offices, that the number of letters posted\nwhich the writers have forgotten to direct, is nearly the same, in\nproportion to the whole number of letters posted, in one year as in\nanother. \"Year after year,\" says Mr. Buckle, \"the same proportion of\nletter-writers forget this simple act; so that for each successive\nperiod we can actually foretell the number of persons whose memory will\nfail them in regard to this trifling, and as it might appear, accidental\noccurrence.\"[15]\n\nThis singular degree of regularity _en masse_, combined with the extreme\nof irregularity in the cases composing the mass, is a felicitous\nverification _\u00e0 posteriori_ of the law of causation in its application\nto human conduct. Assuming the truth of that law, every human action,\nevery murder for instance, is the concurrent result of two sets of\ncauses. On the one part, the general circumstances of the country and\nits inhabitants; the moral, educational, economical, and other\ninfluences operating on the whole people, and constituting what we term\nthe state of civilization. On the other part, the great variety of\ninfluences special to the individual: his temperament, and other\npeculiarities of organization, his parentage, habitual associates,\ntemptations, and so forth. If we now take the whole of the instances\nwhich occur within a sufficiently large field to exhaust all the\ncombinations of these special influences, or in other words, to\neliminate chance; and if all these instances have occurred within such\nnarrow limits of time, that no material change can have taken place in\nthe general influences constituting the state of civilization of the\ncountry; we may be certain, that if human actions are governed by\ninvariable laws, the aggregate result will be something like a constant\nquantity. The number of murders committed within that space and time,\nbeing the effect partly of general causes which have not varied, and\npartly of partial causes the whole round of whose variations has been\nincluded, will be, practically speaking, invariable.\n\nLiterally and mathematically invariable it is not, and could not be\nexpected to be: because the period of a year is too short to include\n_all_ the possible combinations of partial causes, while it is, at the\nsame time, sufficiently long to make it probable that in some years at\nleast, of every series, there will have been introduced new influences\nof a more or less general character; such as a more vigorous or a more\nrelaxed police; some temporary excitement from political or religious\ncauses; or some incident generally notorious, of a nature to act\nmorbidly on the imagination. That in spite of these unavoidable\nimperfections in the data, there should be so very trifling a margin of\nvariation in the annual results, is a brilliant confirmation of the\ngeneral theory.\n\n\n\u00a7 2. The same considerations which thus strikingly corroborate the\nevidence of the doctrine, that historical facts are the invariable\neffects of causes, tend equally to clear that doctrine from various\nmisapprehensions, the existence of which has been put in evidence by the\nrecent discussions. Some persons, for instance, seemingly imagine the\ndoctrine to imply, not merely that the total number of murders committed\nin a given space and time, is entirely the effect of the general\ncircumstances of society, but that every particular murder is so too:\nthat the individual murderer is, so to speak, a mere instrument in the\nhands of general causes; that he himself has no option, or if he has,\nand chose to exercise it, some one else would be necessitated to take\nhis place: that if any one of the actual murderers had abstained from\nthe crime, some person who would otherwise have remained innocent, would\nhave committed an extra murder to make up the average. Such a corollary\nwould certainly convict any theory which necessarily led to it of\nabsurdity. It is obvious, however, that each particular murder depends,\nnot on the general state of society only, but on that combined with\ncauses special to the case, which are generally much more powerful: and\nif these special causes, which have greater influence than the general\nones in causing every particular murder, have no influence on the number\nof murders in a given period, it is because the field of observation is\nso extensive as to include all possible combinations of the special\ncauses--all varieties of individual character and individual temptation\ncompatible with the general state of society. The collective experiment,\nas it may be termed, exactly separates the effect of the general from\nthat of the special causes, and shows the net result of the former: but\nit declares nothing at all respecting the amount of influence of the\nspecial causes, be it greater or smaller, since the scale of the\nexperiment extends to the number of cases within which the effects of\nthe special causes balance one another, and disappear in that of the\ngeneral causes.\n\nI will not pretend that all the defenders of the theory have always kept\ntheir language free from this same confusion, and have shown no tendency\nto exalt the influence of general causes at the expense of special. I am\nof opinion, on the contrary, that they have done so in a very great\ndegree, and by so doing have encumbered their theory with difficulties,\nand laid it open to objections, which do not necessarily affect it.\nSome, for example (among whom is Mr. Buckle himself), have inferred, or\nallowed it to be supposed that they inferred, from the regularity in\nthe recurrence of events which depend on moral qualities, that the\nmoral qualities of mankind are little capable of being improved, or are\nof little importance in the general progress of society, compared with\nintellectual or economic causes. But to draw this inference is to forget\nthat the statistical tables, from which the invariable averages are\ndeduced, were compiled from facts occurring within narrow geographical\nlimits and in a small number of successive years; that is, from a field\nthe whole of which was under the operation of the same general causes,\nand during too short a time to allow of much change therein. All moral\ncauses but those common to the country generally, have been eliminated\nby the great number of instances taken; and those which are common to\nthe whole country have not varied considerably, in the short space of\ntime comprised in the observations. If we admit the supposition that\nthey have varied; if we compare one age with another, or one country\nwith another, or even one part of a country with another, differing in\nposition and character as to the moral elements, the crimes committed\nwithin a year give no longer the same, but a widely different numerical\naggregate. And this cannot but be the case: for inasmuch as every single\ncrime committed by an individual mainly depends on his moral qualities,\nthe crimes committed by the entire population of the country must depend\nin an equal degree on their collective moral qualities. To render this\nelement inoperative upon the large scale, it would be necessary to\nsuppose that the general moral average of mankind does not vary from\ncountry to country or from age to age; which is not true, and even if it\nwere true, could not possibly be proved by any existing statistics. I do\nnot on this account the less agree in the opinion of Mr. Buckle, that\nthe intellectual element in mankind, including in that expression the\nnature of their beliefs, the amount of their knowledge, and the\ndevelopment of their intelligence, is the predominant circumstance in\ndetermining their progress. But I am of this opinion, not because I\nregard their moral or economical condition either as less powerful or\nless variable agencies, but because these are in a great degree the\nconsequences of the intellectual condition, and are, in all cases,\nlimited by it; as was observed in the preceding chapter. The\nintellectual changes are the most conspicuous agents in history, not\nfrom their superior force, considered in themselves, but because\npractically they work with the united power belonging to all three.[16]\n\n\n\u00a7 3. There is another distinction often neglected in the discussion of\nthis subject, which it is extremely important to observe. The theory of\nthe subjection of social progress to invariable laws, is often held in\nconjunction with the doctrine, that social progress cannot be materially\ninfluenced by the exertions of individual persons, or by the acts of\ngovernments. But though these opinions are often held by the same\npersons, they are two very different opinions, and the confusion between\nthem is the eternally recurring error of confounding Causation with\nFatalism. Because whatever happens will be the effect of causes, human\nvolitions among the rest, it does not follow that volitions, even those\nof peculiar individuals, are not of great efficacy as causes. If any one\nin a storm at sea, because about the same number of persons in every\nyear perish by shipwreck, should conclude that it was useless for him to\nattempt to save his own life, we should call him a Fatalist; and should\nremind him that the efforts of shipwrecked persons to save their lives\nare so far from being immaterial, that the average amount of those\nefforts is one of the causes on which the ascertained annual number of\ndeaths by shipwreck depend. However universal the laws of social\ndevelopment may be, they cannot be more universal or more rigorous than\nthose of the physical agencies of nature; yet human will can convert\nthese into instruments of its designs, and the extent to which it does\nso makes the chief difference between savages and the most highly\ncivilized people. Human and social facts, from their more complicated\nnature, are not less, but more, modifiable, than mechanical and chemical\nfacts; human agency, therefore, has still greater power over them. And\naccordingly, those who maintain that the evolution of society depends\nexclusively, or almost exclusively, on general causes, always include\namong these the collective knowledge and intellectual development of the\nrace. But if of the race, why not also of some powerful monarch or\nthinker, or of the ruling portion of some political society, acting\nthrough its government? Though the varieties of character among ordinary\nindividuals neutralize one another on any large scale, exceptional\nindividuals in important positions do not in any given age neutralize\none another; there was not another Themistocles, or Luther, or Julius\nC\u00e6sar, of equal powers and contrary dispositions, who exactly balanced\nthe given Themistocles, Luther, and C\u00e6sar, and prevented them from\nhaving any permanent effect. Moreover, for aught that appears, the\nvolitions of exceptional persons, or the opinions and purposes of the\nindividuals who at some particular time compose a government, may be\nindispensable links in the chain of causation by which even the general\ncauses produce their effects; and I believe this to be the only tenable\nform of the theory.\n\nLord Macaulay, in a celebrated passage of one of his early essays (let\nme add that it was one which he did not himself choose to reprint),\ngives expression to the doctrine of the absolute inoperativeness of\ngreat men, more unqualified, I should think, than has been given to it\nby any writer of equal abilities. He compares them to persons who\nmerely stand on a loftier height, and thence receive the sun's rays a\nlittle earlier, than the rest of the human race. \"The sun illuminates\nthe hills while it is still below the horizon, and truth is discovered\nby the highest minds a little before it becomes manifest to the\nmultitude. This is the extent of their superiority. They are the first\nto catch and reflect a light which, without their assistance, must in a\nshort time be visible to those who lie far beneath them.\"[17] If this\nmetaphor is to be carried out, it follows that if there had been no\nNewton, the world would not only have had the Newtonian system, but\nwould have had it equally soon; as the sun would have risen just as\nearly to spectators in the plain if there had been no mountain at hand\nto catch still earlier rays. And so it would be, if truths, like the\nsun, rose by their own proper motion, without human effort; but not\notherwise. I believe that if Newton had not lived, the world must have\nwaited for the Newtonian philosophy until there had been another Newton,\nor his equivalent. No ordinary man, and no succession of ordinary men,\ncould have achieved it. I will not go the length of saying that what\nNewton did in a single life, might not have been done in successive\nsteps by some of those who followed him, each singly inferior to him in\ngenius. But even the least of those steps required a man of great\nintellectual superiority. Eminent men do not merely see the coming light\nfrom the hill-top, they mount on the hill-top and evoke it; and if no\none had ever ascended thither, the light, in many cases, might never\nhave risen upon the plain at all. Philosophy and religion are abundantly\namenable to general causes; yet few will doubt, that had there been no\nSocrates, no Plato, and no Aristotle, there would have been no\nphilosophy for the next two thousand years, nor in all probability then;\nand that if there had been no Christ, and no St. Paul, there would have\nbeen no Christianity.\n\nThe point in which, above all, the influence of remarkable individuals\nis decisive, is in determining the celerity of the movement. In most\nstates of society it is the existence of great men which decides even\nwhether there shall be any progress. It is conceivable that Greece, or\nthat Christian Europe, might have been progressive in certain periods of\ntheir history through general causes only: but if there had been no\nMahomet, would Arabia have produced Avicenna or Averroes, or Caliphs of\nBagdad or of Cordova? In determining, however, in what manner and order\nthe progress of mankind shall take place if it take place at all, much\nless depends on the character of individuals. There is a sort of\nnecessity established in this respect by the general laws of human\nnature; by the constitution of the human mind. Certain truths cannot be\ndiscovered, or inventions made, unless certain others have been made\nfirst; certain social improvements, from the nature of the case, can\nonly follow, and not precede, others. The order of human progress,\ntherefore, may to a certain extent have definite laws assigned to it:\nwhile as to its celerity, or even as to its taking place at all, no\ngeneralization, extending to the human species generally, can possibly\nbe made; but only some very precarious approximate generalizations,\nconfined to the small portion of mankind in whom there has been anything\nlike consecutive progress within the historical period, and deduced from\ntheir special position, or collected from their particular history. Even\nlooking to the _manner_ of progress, the order of succession of social\nstates, there is need of great flexibility in our generalizations. The\nlimits of variation in the possible development of social, as of animal\nlife, are a subject of which little is yet understood, and are one of\nthe great problems in social science. It is, at all events, a fact, that\ndifferent portions of mankind, under the influence of different\ncircumstances, have developed themselves in a more or less different\nmanner and into different forms; and among these determining\ncircumstances, the individual character of their great speculative\nthinkers or practical organizers may well have been one. Who can tell\nhow profoundly the whole subsequent history of China may have been\ninfluenced by the individuality of Confucius? and of Sparta (and hence\nof Greece and the world) by that of Lycurgus?\n\nConcerning the nature and extent of what a great man under favourable\ncircumstances can do for mankind, as well as of what a government can do\nfor a nation, many different opinions are possible; and every shade of\nopinion on these points is consistent with the fullest recognition that\nthere are invariable laws of historical phenomena. Of course the degree\nof influence which has to be assigned to these more special agencies,\nmakes a great difference in the precision which can be given to the\ngeneral laws, and in the confidence with which predictions can be\ngrounded on them. Whatever depends on the peculiarities of individuals,\ncombined with the accident of the positions they hold, is necessarily\nincapable of being foreseen. Undoubtedly these casual combinations might\nbe eliminated like any others, by taking a sufficiently large cycle: the\npeculiarities of a great historical character make their influence felt\nin history sometimes for several thousand years, but it is highly\nprobable that they may make no difference at all at the end of fifty\nmillions. Since, however, we cannot obtain an average of the vast length\nof time necessary to exhaust all the possible combinations of great men\nand circumstances, as much of the law of evolution of human affairs as\ndepends upon this average, is and remains inaccessible to us: and within\nthe next thousand years, which are of considerably more importance to us\nthan the whole remainder of the fifty millions, the favourable and\nunfavourable combinations which will occur will be to us purely\naccidental. We cannot foresee the advent of great men. Those who\nintroduce new speculative thoughts or great practical conceptions into\nthe world, cannot have their epoch fixed beforehand. What science can\ndo, is this. It can trace through past history the general causes which\nhad brought mankind into that preliminary state, which when the right\nsort of great man appeared, rendered them accessible to his influence.\nIf this state continues, experience renders it tolerably certain that in\na longer or shorter period the great man will be produced; provided that\nthe general circumstances of the country and people are (which very\noften they are not) compatible with his existence; of which point also,\nscience can in some measure judge. It is in this manner that the results\nof progress, except as to the celerity of their production, can be, to\na certain extent, reduced to regularity and law. And the belief that\nthey can be so, is equally consistent with assigning very great, or very\nlittle efficacy, to the influence of exceptional men, or of the acts of\ngovernments. And the same may be said of all other accidents and\ndisturbing causes.\n\n\n\u00a7 4. It would nevertheless be a great error to assign only a trifling\nimportance to the agency of eminent individuals, or of governments. It\nmust not be concluded that the influence of either is small, because\nthey cannot bestow what the general circumstances of society, and the\ncourse of its previous history, have not prepared it to receive. Neither\nthinkers nor governments effect all that they intend, but in\ncompensation they often produce important results which they did not in\nthe least foresee. Great men, and great actions, are seldom wasted: they\nsend forth a thousand unseen influences, more effective than those which\nare seen; and though nine out of every ten things done, with a good\npurpose, by those who are in advance of their age, produce no material\neffect, the tenth thing produces effects twenty times as great as any\none would have dreamed of predicting from it. Even the men who for want\nof sufficiently favourable circumstances left no impress at all upon\ntheir own age, have often been of the greatest value to posterity. Who\ncould appear to have lived more entirely in vain, than some of the early\nheretics? They were burnt or massacred, their writings extirpated, their\nmemory anathematized, and their very names and existence left for seven\nor eight centuries in the obscurity of musty manuscripts--their history\nto be gathered, perhaps, only from the sentences by which they were\ncondemned. Yet the memory of these men--men who resisted certain\npretensions or certain dogmas of the Church in the very age in which the\nunanimous assent of Christendom was afterwards claimed as having been\ngiven to them, and asserted as the ground of their authority--broke the\nchain of tradition, established a series of precedents for resistance,\ninspired later Reformers with the courage, and armed them with the\nweapons, which they needed when mankind were better prepared to follow\ntheir impulse. To this example from men, let us add another from\ngovernments. The comparatively enlightened rule of which Spain had the\nbenefit during a considerable part of the eighteenth century, did not\ncorrect the fundamental defects of the Spanish people; and in\nconsequence, though it did great temporary good, so much of that good\nperished with it, that it may plausibly be affirmed to have had no\npermanent effect. The case has been cited as a proof how little\ngovernments can do, in opposition to the causes which have determined\nthe general character of the nation. It does show how much there is\nwhich they cannot do; but not that they can do nothing. Compare what\nSpain was at the beginning of that half century of liberal government,\nwith what she had become at its close. That period fairly let in the\nlight of European thought upon the more educated classes; and it never\nafterwards ceased to go on spreading. Previous to that time the change\nwas in an inverse direction; culture, light, intellectual and even\nmaterial activity, were becoming extinguished. Was it nothing to arrest\nthis downward and convert it into an upward course? How much that\nCharles the Third and Aranda could not do, has been the ultimate\nconsequence of what they did! To that half century Spain owes that she\nhas got rid of the Inquisition, that she has got rid of the monks, that\nshe now has parliaments and (save in exceptional intervals) a free\npress, and the feelings of freedom and citizenship, and is acquiring\nrailroads and all the other constituents of material and economical\nprogress. In the Spain which preceded that era there was not a single\nelement at work, which could have led to these results in any length of\ntime, if the country had continued to be governed as it was by the last\nprinces of the Austrian dynasty, or if the Bourbon rulers had been from\nthe first what, both in Spain and in Naples, they afterwards became.\n\nAnd if a government can do much, even when it seems to have done little,\nin causing positive improvement, still greater are the issues dependent\non it in the way of warding off evils, both internal and external, which\nelse would stop improvement altogether. A good or a bad counsellor, in a\nsingle city at a particular crisis, has affected the whole subsequent\nfate of the world. It is as certain as any contingent judgment\nrespecting historical events can be, that if there had been no\nThemistocles there would have been no victory of Salamis; and had there\nnot, where would have been all our civilization? How different again\nwould have been the issue if Epaminondas, or Timoleon, or even\nIphicrates, instead of Chares and Lysicles, had commanded at Ch\u00e6roneia.\nAs is well said in the second of two Essays on the Study of History,[18]\nin my judgment the soundest and most philosophical productions which the\nrecent controversies on this subject have called forth; historical\nscience authorizes not absolute, but only conditional predictions.\nGeneral causes count for much, but individuals also \"produce great\nchanges in history, and colour its whole complexion long after their\ndeath.... No one can doubt that the Roman republic would have subsided\ninto a military despotism if Julius C\u00e6sar had never lived;\" (thus much\nwas rendered practically certain by general causes): \"but is it at all\nclear that in that case Gaul would ever have formed a province of the\nempire? Might not Varus have lost his three legions on the banks of the\nRhone? and might not that river have become the frontier instead of the\nRhine? This might well have happened if C\u00e6sar and Crassus had changed\nprovinces; and it is surely impossible to say that in such an event the\nvenue (as lawyers say) of European civilization might not have been\nchanged. The Norman Conquest in the same way was as much the act of a\nsingle man, as the writing of a newspaper article; and knowing as we do\nthe history of that man and his family, we can retrospectively predict\nwith all but infallible certainty, that no other person\" (no other in\nthat age, I presume, is meant), \"could have accomplished the enterprise.\nIf it had not been accomplished, is there any ground to suppose that\neither our history or our national character would have been what they\nare?\"\n\nAs is most truly remarked by the same writer, the whole stream of\nGrecian history, as cleared up by Mr. Grote, is one series of examples\nhow often events on which the whole destiny of subsequent civilization\nturned, were dependent on the personal character for good or evil of\nsome one individual. It must be said, however, that Greece furnishes the\nmost extreme example of this nature to be found in history, and is a\nvery exaggerated specimen of the general tendency. It has happened only\nthat once, and will probably never happen again, that the fortunes of\nmankind depended upon keeping a certain order of things in existence in\na single town, or a country scarcely larger than Yorkshire; capable of\nbeing ruined or saved by a hundred causes, of very slight magnitude in\ncomparison with the general tendencies of human affairs. Neither\nordinary accidents, nor the characters of individuals, can ever again be\nso vitally important as they then were. The longer our species lasts,\nand the more civilized it becomes, the more, as Comte remarks, does the\ninfluence of past generations over the present, and of mankind _en\nmasse_ over every individual in it, predominate over other forces: and\nthough the course of affairs never ceases to be susceptible of\nalteration both by accidents and by personal qualities, the increasing\npreponderance of the collective agency of the species over all minor\ncauses, is constantly bringing the general evolution of the race into\nsomething which deviates less from a certain and preappointed track.\nHistorical science, therefore, is always becoming more possible: not\nsolely because it is better studied, but because, in every generation,\nit becomes better adapted for study.\n\n\n\n\nCHAPTER XII.\n\nOF THE LOGIC OF PRACTICE, OR ART; INCLUDING MORALITY AND POLICY.\n\n\n\u00a7 1. In the preceding chapters we have endeavoured to characterize the\npresent state of those among the branches of knowledge called Moral,\nwhich are sciences in the only proper sense of the term, that is,\ninquiries into the course of nature. It is customary, however, to\ninclude under the term moral knowledge, and even (though improperly)\nunder that of moral science, an inquiry the results of which do not\nexpress themselves in the indicative, but in the imperative mood, or in\nperiphrases equivalent to it; what is called the knowledge of duties;\npractical ethics, or morality.\n\nNow, the imperative mood is the characteristic of art, as distinguished\nfrom science. Whatever speaks in rules, or precepts, not in assertions\nrespecting matters of fact, is art: and ethics, or morality, is properly\na portion of the art corresponding to the sciences of human nature and\nsociety.[19]\n\nThe Method, therefore, of Ethics, can be no other than that of Art, or\nPractice, in general: and the portion yet uncompleted, of the task which\nwe proposed to ourselves in the concluding Book, is to characterize the\ngeneral Method of Art, as distinguished from Science.\n\n\n\u00a7 2. In all branches of practical business, there are cases in which\nindividuals are bound to conform their practice to a pre-established\nrule, while there are others in which it is part of their task to find\nor construct the rule by which they are to govern their conduct. The\nfirst, for example, is the case of a judge, under a definite written\ncode. The judge is not called upon to determine what course would be\nintrinsically the most advisable in the particular case in hand, but\nonly within what rule of law it falls; what the legislator has ordained\nto be done in the kind of case, and must therefore be presumed to have\nintended in the individual case. The method must here be wholly and\nexclusively one of ratiocination, or syllogism; and the process is\nobviously, what in our analysis of the syllogism we showed that all\nratiocination is, namely the interpretation of a formula.\n\nIn order that our illustration of the opposite case may be taken from\nthe same class of subjects as the former, we will suppose, in contrast\nwith the situation of the judge, the position of a legislator. As the\njudge has laws for his guidance, so the legislator has rules, and maxims\nof policy; but it would be a manifest error to suppose that the\nlegislator is bound by these maxims in the same manner as the judge is\nbound by the laws, and that all he has to do is to argue down from them\nto the particular case, as the judge does from the laws. The legislator\nis bound to take into consideration the reasons or grounds of the maxim;\nthe judge has nothing to do with those of the law, except so far as a\nconsideration of them may throw light upon the intention of the\nlaw-maker, where his words have left it doubtful. To the judge, the\nrule, once positively ascertained, is final; but the legislator, or\nother practitioner, who goes by rules rather than by their reasons, like\nthe old-fashioned German tacticians who were vanquished by Napoleon, or\nthe physician who preferred that his patients should die by rule rather\nthan recover contrary to it, is rightly judged to be a mere pedant, and\nthe slave of his formulas.\n\nNow, the reasons of a maxim of policy, or of any other rule of art, can\nbe no other than the theorems of the corresponding science.\n\nThe relation in which rules of art stand to doctrines of science may be\nthus characterized. The art proposes to itself an end to be attained,\ndefines the end, and hands it over to the science. The science receives\nit, considers it as a phenomenon or effect to be studied, and having\ninvestigated its causes and conditions, sends it back to art with a\ntheorem of the combination of circumstances by which it could be\nproduced. Art then examines these combinations of circumstances, and\naccording as any of them are or are not in human power, pronounces the\nend attainable or not. The only one of the premises, therefore, which\nArt supplies, is the original major premise, which asserts that the\nattainment of the given end is desirable. Science then lends to Art the\nproposition (obtained by a series of inductions or of deductions) that\nthe performance of certain actions will attain the end. From these\npremises Art concludes that the performance of these actions is\ndesirable, and finding it also practicable, converts the theorem into a\nrule or precept.\n\n\n\u00a7 3. It deserves particular notice, that the theorem or speculative\ntruth is not ripe for being turned into a precept, until the whole, and\nnot a part merely, of the operation which belongs to science, has been\nperformed. Suppose that we have completed the scientific process only up\nto a certain point; have discovered that a particular cause will produce\nthe desired effect, but have not ascertained all the negative conditions\nwhich are necessary, that is, all the circumstances which, if present,\nwould prevent its production. If, in this imperfect state of the\nscientific theory, we attempt to frame a rule of art, we perform that\noperation prematurely. Whenever any counteracting cause, overlooked by\nthe theorem, takes place, the rule will be at fault: we shall employ the\nmeans and the end will not follow. No arguing from or about the rule\nitself will then help us through the difficulty: there is nothing for it\nbut to turn back and finish the scientific process which should have\npreceded the formation of the rule. We must re-open the investigation,\nto inquire into the remainder of the conditions on which the effect\ndepends; and only after we have ascertained the whole of these, are we\nprepared to transform the completed law of the effect into a precept, in\nwhich those circumstances or combinations of circumstances which the\nscience exhibits as conditions, are prescribed as means.\n\nIt is true that, for the sake of convenience, rules must be formed from\nsomething less than this ideally perfect theory; in the first place,\nbecause the theory can seldom be made ideally perfect; and next,\nbecause, if all the counteracting contingencies, whether of frequent or\nof rare occurrence, were included, the rules would be too cumbrous to be\napprehended and remembered by ordinary capacities, on the common\noccasions of life. The rules of art do not attempt to comprise more\nconditions than require to be attended to in ordinary cases; and are\ntherefore always imperfect. In the manual arts, where the requisite\nconditions are not numerous, and where those which the rules do not\nspecify are generally either plain to common observation or speedily\nlearnt from practice, rules may often be safely acted on by persons who\nknow nothing more than the rule. But in the complicated affairs of life,\nand still more in those of states and societies, rules cannot be relied\non, without constantly referring back to the scientific laws on which\nthey are founded. To know what are the practical contingencies which\nrequire a modification of the rule, or which are altogether exceptions\nto it, is to know what combinations of circumstances would interfere\nwith, or entirely counteract, the consequences of those laws: and this\ncan only be learnt by a reference to the theoretic grounds of the rule.\n\nBy a wise practitioner, therefore, rules of conduct will only be\nconsidered as provisional. Being made for the most numerous cases, or\nfor those of most ordinary occurrence, they point out the manner in\nwhich it will be least perilous to act, where time or means do not exist\nfor analysing the actual circumstances of the case, or where we cannot\ntrust our judgment in estimating them. But they do not at all supersede\nthe propriety of going through (when circumstances permit) the\nscientific process requisite for framing a rule from the data of the\nparticular case before us. At the same time, the common rule may very\nproperly serve as an admonition that a certain mode of action has been\nfound by ourselves and others to be well adapted to the cases of most\ncommon occurrence; so that if it be unsuitable to the case in hand, the\nreason of its being so will be likely to arise from some unusual\ncircumstance.\n\n\n\u00a7 4. The error is therefore apparent, of those who would deduce the line\nof conduct proper to particular cases, from supposed universal practical\nmaxims; overlooking the necessity of constantly referring back to the\nprinciples of the speculative science, in order to be sure of attaining\neven the specific end which the rules have in view. How much greater\nstill, then, must the error be, of setting up such unbending principles,\nnot merely as universal rules for attaining a given end, but as rules of\nconduct generally; without regard to the possibility, not only that some\nmodifying cause may prevent the attainment of the given end by the means\nwhich the rule prescribes, but that success itself may conflict with\nsome other end, which may possibly chance to be more desirable.\n\nThis is the habitual error of many of the political speculators whom I\nhave characterized as the geometrical school; especially in France,\nwhere ratiocination from rules of practice forms the staple commodity of\njournalism and political oratory; a misapprehension of the functions of\nDeduction which has brought much discredit, in the estimation of other\ncountries, upon the spirit of generalization so honourably\ncharacteristic of the French mind. The common-places of politics, in\nFrance, are large and sweeping practical maxims, from which, as ultimate\npremises, men reason downwards to particular applications, and this they\ncall being logical and consistent. For instance, they are perpetually\narguing that such and such a measure ought to be adopted, because it is\na consequence of the principle on which the form of government is\nfounded; of the principle of legitimacy, or the principle of the\nsovereignty of the people. To which it may be answered, that if these be\nreally practical principles, they must rest on speculative grounds; the\nsovereignty of the people (for example) must be a right foundation for\ngovernment, because a government thus constituted tends to produce\ncertain beneficial effects. Inasmuch, however, as no government produces\nall possible beneficial effects, but all are attended with more or fewer\ninconveniences; and since these cannot usually be combated by means\ndrawn from the very causes which produce them; it would be often a much\nstronger recommendation of some practical arrangement, that it does not\nfollow from what is called the general principle of the government, than\nthat it does. Under a government of legitimacy, the presumption is far\nrather in favour of institutions of popular origin; and in a democracy,\nin favour of arrangements tending to check the impetus of popular will.\nThe line of argumentation so commonly mistaken in France for political\nphilosophy, tends to the practical conclusion that we should exert our\nutmost efforts to aggravate, instead of alleviating, whatever are the\ncharacteristic imperfections of the system of institutions which we\nprefer, or under which we happen to live.\n\n\n\u00a7 5. The grounds, then, of every rule of art, are to be found in the\ntheorems of science. An art, or a body of art, consists of the rules,\ntogether with as much of the speculative propositions as comprises the\njustification of those rules. The complete art of any matter, includes a\nselection of such a portion from the science, as is necessary to show on\nwhat conditions the effects, which the art aims at producing, depend.\nAnd Art in general, consists of the truths of Science, arranged in the\nmost convenient order for practice, instead of the order which is the\nmost convenient for thought. Science groups and arranges its truths, so\nas to enable us to take in at one view as much as possible of the\ngeneral order of the universe. Art, though it must assume the same\ngeneral laws, follows them only into such of their detailed consequences\nas have led to the formation of rules of conduct; and brings together\nfrom parts of the field of science most remote from one another, the\ntruths relating to the production of the different and heterogeneous\nconditions necessary to each effect which the exigencies of practical\nlife require to be produced.\n\nScience, therefore, following one cause to its various effects, while\nart traces one effect to its multiplied and diversified causes and\nconditions; there is need of a set of intermediate scientific truths,\nderived from the higher generalities of science, and destined to serve\nas the generalia or first principles of the various arts. The scientific\noperation of framing these intermediate principles, M. Comte\ncharacterizes as one of those results of philosophy which are reserved\nfor futurity. The only complete example which he points out as actually\nrealized, and which can be held up as a type to be imitated in more\nimportant matters, is the general theory of the art of Descriptive\nGeometry, as conceived by M. Monge. It is not, however, difficult to\nunderstand what the nature of these intermediate principles must\ngenerally be. After framing the most comprehensive possible conception\nof the end to be aimed at, that is, of the effect to be produced, and\ndetermining in the same comprehensive manner the set of conditions on\nwhich that effect depends; there remains to be taken, a general survey\nof the resources which can be commanded for realizing this set of\nconditions; and when the result of this survey has been embodied in the\nfewest and most extensive propositions possible, those propositions will\nexpress the general relation between the available means and the end,\nand will constitute the general scientific theory of the art; from which\nits practical methods will follow as corollaries.\n\n\n\u00a7 6. But though the reasonings which connect the end or purpose of every\nart with its means, belong to the domain of Science, the definition of\nthe end itself belongs exclusively to Art, and forms its peculiar\nprovince. Every art has one first principle, or general major premise,\nnot borrowed from science; that which enunciates the object aimed at,\nand affirms it to be a desirable object. The builder's art assumes that\nit is desirable to have buildings; architecture (as one of the fine\narts), that it is desirable to have them beautiful or imposing. The\nhygienic and medical arts assume, the one that the preservation of\nhealth, the other that the cure of disease, are fitting and desirable\nends. These are not propositions of science. Propositions of science\nassert a matter of fact: an existence, a coexistence, a succession, or a\nresemblance. The propositions now spoken of do not assert that anything\nis, but enjoin or recommend that something should be. They are a class\nby themselves. A proposition of which the predicate is expressed, by the\nwords _ought_ or _should be_, is generically different from one which is\nexpressed by _is_, or _will be_. It is true that, in the largest sense\nof the words, even these propositions assert something as a matter of\nfact. The fact affirmed in them is, that the conduct recommended excites\nin the speaker's mind the feeling of approbation. This, however, does\nnot go to the bottom of the matter; for the speaker's approbation is no\nsufficient reason why other people should approve; nor ought it to be a\nconclusive reason even with himself. For the purposes of practice, every\none must be required to justify his approbation: and for this there is\nneed of general premises, determining what are the proper objects of\napprobation, and what the proper order of precedence among those\nobjects.\n\nThese general premises, together with the principal conclusions which\nmay be deduced from them, form (or rather might form) a body of\ndoctrine, which is properly the Art of Life, in its three departments,\nMorality, Prudence or Policy, and \u00c6sthetics; the Right, the Expedient,\nand the Beautiful or Noble, in human conduct and works. To this art,\n(which, in the main, is unfortunately still to be created,) all other\narts are subordinate; since its principles are those which must\ndetermine whether the special aim of any particular art is worthy and\ndesirable, and what is its place in the scale of desirable things. Every\nart is thus a joint result of laws of nature disclosed by science, and\nof the general principles of what has been called Teleology, or the\nDoctrine of Ends;[20] which, borrowing the language of the German\nmetaphysicians, may also be termed, not improperly, the Principles of\nPractical Reason.\n\nA scientific observer or reasoner, merely as such, is not an adviser\nfor practice. His part is only to show that certain consequences follow\nfrom certain causes, and that to obtain certain ends, certain means are\nthe most effectual. Whether the ends themselves are such as ought to be\npursued, and if so, in what cases and to how great a length, it is no\npart of his business as a cultivator of science to decide, and science\nalone will never qualify him for the decision. In purely physical\nscience, there is not much temptation to assume this ulterior office;\nbut those who treat of human nature and society invariably claim it;\nthey always undertake to say, not merely what is, but what ought to be.\nTo entitle them to do this, a complete doctrine of Teleology is\nindispensable. A scientific theory, however perfect, of the subject\nmatter, considered merely as part of the order of nature, can in no\ndegree serve as a substitute. In this respect the various subordinate\narts afford a misleading analogy. In them there is seldom any visible\nnecessity for justifying the end, since in general its desirableness is\ndenied by nobody, and it is only when the question of precedence is to\nbe decided between that end and some other, that the general principles\nof Teleology have to be called in: but a writer on Morals and Politics\nrequires those principles at every step. The most elaborate and\nwell-digested exposition of the laws of succession and coexistence among\nmental or social phenomena, and of their relation to one another as\ncauses and effects, will be of no avail towards the art of Life or of\nSociety, if the ends to be aimed at by that art are left to the vague\nsuggestions of the _intellectus sibi permissus_, or are taken for\ngranted without analysis or questioning.\n\n\n\u00a7 7. There is, then, a Philosophia Prima peculiar to Art, as there is\none which belongs to Science. There are not only first principles of\nKnowledge, but first principles of Conduct. There must be some standard\nby which to determine the goodness or badness, absolute and comparative,\nof ends, or objects of desire. And whatever that standard is, there can\nbe but one: for if there were several ultimate principles of conduct,\nthe same conduct might be approved by one of those principles and\ncondemned by another; and there would be needed some more general\nprinciple, as umpire between them.\n\nAccordingly, writers on moral philosophy have mostly felt the necessity\nnot only of referring all rules of conduct, and all judgments of praise\nand blame, to principles, but of referring them to some one principle;\nsome rule, or standard, with which all other rules of conduct were\nrequired to be consistent, and from which by ultimate consequence they\ncould all be deduced. Those who have dispensed with the assumption of\nsuch an universal standard, have only been enabled to do so by supposing\nthat a moral sense, or instinct, inherent in our constitution, informs\nus, both what principles of conduct we are bound to observe, and also in\nwhat order these should be subordinated to one another.\n\nThe theory of the foundations of morality is a subject which it would be\nout of place, in a work like this, to discuss at large, and which could\nnot to any useful purpose be treated incidentally. I shall content\nmyself therefore with saying, that the doctrine of intuitive moral\nprinciples, even if true, would provide only for that portion of the\nfield of conduct which is properly called moral. For the remainder of\nthe practice of life some general principle, or standard, must still be\nsought; and if that principle be rightly chosen, it will be found, I\napprehend, to serve quite as well for the ultimate principle of\nMorality, as for that of Prudence, Policy, or Taste.\n\nWithout attempting in this place to justify my opinion, or even to\ndefine the kind of justification which it admits of, I merely declare my\nconviction, that the general principle to which all rules of practice\nought to conform, and the test by which they should be tried, is that of\nconduciveness to the happiness of mankind, or rather, of all sentient\nbeings: in other words, that the promotion of happiness is the ultimate\nprinciple of Teleology.[21]\n\nI do not mean to assert that the promotion of happiness should be\nitself the end of all actions, or even of all rules of action. It is the\njustification, and ought to be the controller, of all ends, but is not\nitself the sole end. There are many virtuous actions, and even virtuous\nmodes of action (though the cases are, I think, less frequent than is\noften supposed) by which happiness in the particular instance is\nsacrificed, more pain being produced than pleasure. But conduct of which\nthis can be truly asserted, admits of justification only because it can\nbe shown that on the whole more happiness will exist in the world, if\nfeelings are cultivated which will make people, in certain cases,\nregardless of happiness. I fully admit that this is true: that the\ncultivation of an ideal nobleness of will and conduct, should be to\nindividual human beings an end, to which the specific pursuit either of\ntheir own happiness or of that of others (except so far as included in\nthat idea) should, in any case of conflict, give way. But I hold that\nthe very question, what constitutes this elevation of character, is\nitself to be decided by a reference to happiness as the standard. The\ncharacter itself should be, to the individual, a paramount end, simply\nbecause the existence of this ideal nobleness of character, or of a near\napproach to it, in any abundance, would go further than all things else\ntowards making human life happy; both in the comparatively humble sense,\nof pleasure and freedom from pain, and in the higher meaning, of\nrendering life, not what it now is almost universally, puerile and\ninsignificant--but such as human beings with highly developed faculties\ncan care to have.\n\n\n\u00a7 8. With these remarks we must close this summary view of the\napplication of the general logic of scientific inquiry to the moral and\nsocial departments of science. Notwithstanding the extreme generality of\nthe principles of method which I have laid down, (a generality which, I\ntrust, is not, in this instance, synonymous with vagueness) I have\nindulged the hope that to some of those on whom the task will devolve of\nbringing those most important of all sciences into a more satisfactory\nstate, these observations may be useful; both in removing erroneous, and\nin clearing up the true, conceptions of the means by which, on subjects\nof so high a degree of complication, truth can be attained. Should this\nhope be realized, what is probably destined to be the great intellectual\nachievement of the next two or three generations of European thinkers\nwill have been in some degree forwarded.\n\nFOOTNOTES:\n\n[1] Some arguments and explanations, supplementary to those in the text,\nwill be found in _An Examination of Sir William Hamilton's Philosophy_,\nchap. xxvi.\n\n[2] Supra, p. 137.\n\n[3] When this chapter was written, Mr. Bain had not yet published even\nthe first part (\"The Senses and the Intellect\") of his profound Treatise\non the Mind. In this, the laws of association have been more\ncomprehensively stated and more largely exemplified than by any previous\nwriter; and the work, having been completed by the publication of \"The\nEmotions and the Will,\" may now be referred to as incomparably the most\ncomplete analytical exposition of the mental phenomena, on the basis of\na legitimate Induction, which has yet been produced.\n\nMany striking applications of the laws of association to the explanation\nof complex mental phenomena, are also to be found in Mr. Herbert\nSpencer's \"Principles of Psychology.\"\n\n[4] In the case of the moral sentiments the place of direct experiment\nis to a considerable extent supplied by historical experience, and we\nare able to trace with a tolerable approach to certainty the particular\nassociations by which those sentiments are engendered. This has been\nattempted, so far as respects the sentiment of justice, in a little work\nby the present author, entitled _Utilitarianism_.\n\n[5] The most favourable cases for making such approximate\ngeneralizations are what may be termed collective instances; where we\nare fortunately enabled to see the whole class respecting which we are\ninquiring, in action at once; and, from the qualities displayed by the\ncollective body, are able to judge what must be the qualities of the\nmajority of the individuals composing it. Thus the character of a nation\nis shown in its acts as a nation; not so much in the acts of its\ngovernment, for those are much influenced by other causes; but in the\ncurrent popular maxims, and other marks of the general direction of\npublic opinion; in the character of the persons or writings that are\nheld in permanent esteem or admiration; in laws and institutions, so far\nas they are the work of the nation itself, or are acknowledged and\nsupported by it; and so forth. But even here there is a large margin of\ndoubt and uncertainty. These things are liable to be influenced by many\ncircumstances: they are partly determined by the distinctive qualities\nof that nation or body of persons, but partly also by external causes\nwhich would influence any other body of persons in the same manner. In\norder, therefore, to make the experiment really complete, we ought to be\nable to try it without variation upon other nations: to try how\nEnglishmen would act or feel if placed in the same circumstances in\nwhich we have supposed Frenchmen to be placed; to apply, in short, the\nMethod of Difference as well as that of Agreement. Now these experiments\nwe cannot try, nor even approximate to.\n\n[6] \"To which,\" says Dr. Whewell, \"we may add, that it is certain from\nthe history of the subject, that in that case the hypothesis would never\nhave been framed at all.\"\n\nDr. Whewell (_Philosophy of Discovery_, pp. 277-282) defends Bacon's\nrule against the preceding strictures. But his defence consists only in\nasserting and exemplifying a proposition which I had myself stated, viz.\nthat though the largest generalizations may be the earliest made, they\nare not at first seen in their entire generality, but acquire it by\ndegrees, as they are found to explain one class after another of\nphenomena. The laws of motion, for example, were not known to extend to\nthe celestial regions, until the motions of the celestial bodies had\nbeen deduced from them. This however does not in any way affect the\nfact, that the middle principles of astronomy, the central force for\nexample, and the law of the inverse square, could not have been\ndiscovered, if the laws of motion, which are so much more universal, had\nnot been known first. On Bacon's system of step-by-step generalization,\nit would be impossible in any science to ascend higher than the\nempirical laws; a remark which Dr. Whewell's own Inductive Tables,\nreferred to by him in support of his argument, amply bear out.\n\n[7] Vol. i. p. 494 to the end of the chapter.\n\n[8] _Biographia Literaria_, i. 214.\n\n[9] Supra, vol. i. p. 500.\n\n[10] _Essays on some Unsettled Questions of Political Economy_, pp.\n137-140.\n\n[11] The quotations in this paragraph are from a paper written by the\nauthor, and published in a periodical in 1834.\n\n[12] _Cours de Philosophie Positive_, iv. 325-9.\n\n[13] Since reprinted entire in _Dissertations and Discussions_, as the\nconcluding paper of the first volume.\n\n[14] This great generalization is often unfavourably criticised (as by\nDr. Whewell for instance) under a misapprehension of its real import.\nThe doctrine, that the theological explanation of phenomena belongs only\nto the infancy of our knowledge of them, ought not to be construed as if\nit was equivalent to the assertion, that mankind, as their knowledge\nadvances, will necessarily cease to believe in any kind of theology.\nThis was M. Comte's opinion; but it is by no means implied in his\nfundamental theorem. All that is implied is, that in an advanced state\nof human knowledge, no other Ruler of the World will be acknowledged\nthan one who rules by universal laws, and does not at all, or does not\nunless in very peculiar cases, produce events by special interpositions.\nOriginally all natural events were ascribed to such interpositions. At\npresent every educated person rejects this explanation in regard to all\nclasses of phenomena of which the laws have been fully ascertained;\nthough some have not yet reached the point of referring all phenomena to\nthe idea of Law, but believe that rain and sunshine, famine and\npestilence, victory and defeat, death and life, are issues which the\nCreator does not leave to the operation of his general laws, but\nreserves to be decided by express acts of volition. M. Comte's theory is\nthe negation of this doctrine.\n\nDr. Whewell equally misunderstands M. Comte's doctrine respecting the\nsecond, or metaphysical stage of speculation. M. Comte did not mean that\n\"discussions concerning ideas\" are limited to an early stage of inquiry,\nand cease when science enters into the positive stage. (_Philosophy of\nDiscovery_, pp. 226 et seq.) In all M. Comte's speculations as much\nstress is laid on the process of clearing up our conceptions, as on the\nascertainment of facts. When M. Comte speaks of the metaphysical stage\nof speculation, he means the stage in which men speak of \"Nature\" and\nother abstractions as if they were active forces, producing effects;\nwhen Nature is said to do this, or forbid that; when Nature's horror of\na vacuum, Nature's non-admission of a break, Nature's _vis medicatrix_,\nwere offered as explanations of phenomena; when the qualities of things\nwere mistaken for real entities dwelling in the things; when the\nphenomena of living bodies were thought to be accounted for by being\nreferred to a \"vital force;\" when, in short, the abstract names of\nphenomena were mistaken for the causes of their existence. In this sense\nof the word it cannot be reasonably denied that the metaphysical\nexplanation of phenomena, equally with the theological, gives way before\nthe advance of real science.\n\nThat the final, or positive stage, as conceived by M. Comte, has been\nequally misunderstood, and that, notwithstanding some expressions open\nto just criticism, M. Comte never dreamed of denying the legitimacy of\ninquiry into all causes which are accessible to human investigation, I\nhave pointed out in a former place.\n\n[15] Buckle's _History of Civilization_, i. 30.\n\n[16] I have been assured by an intimate friend of Mr. Buckle that he\nwould not have withheld his assent from these remarks, and that he never\nintended to affirm or imply that mankind are not progressive in their\nmoral as well as in their intellectual qualities. \"In dealing with his\nproblem, he availed himself of the artifice resorted to by the Political\nEconomist, who leaves out of consideration the generous and benevolent\nsentiments, and founds his science on the proposition that mankind are\nactuated by acquisitive propensities alone,\" not because such is the\nfact, but because it is necessary to begin by treating the principal\ninfluence as if it was the sole one, and make the due corrections\nafterwards. \"He desired to make abstraction of the intellect as the\ndetermining and dynamical element of the progression, eliminating the\nmore dependent set of conditions, and treating the more active one as if\nit were an entirely independent variable.\"\n\nThe same friend of Mr. Buckle states that when he used expressions which\nseemed to exaggerate the influence of general at the expense of special\ncauses, and especially at the expense of the influence of individual\nminds, Mr. Buckle really intended no more than to affirm emphatically\nthat the greatest men cannot effect great changes in human affairs\nunless the general mind has been in some considerable degree prepared\nfor them by the general circumstances of the age; a truth which, of\ncourse, no one thinks of denying. And there certainly are passages in\nMr. Buckle's writings which speak of the influence exercised by great\nindividual intellects in as strong terms as could be desired.\n\n[17] Essay on Dryden, in Miscellaneous Writings, i. 186.\n\n[18] In the _Cornhill Magazine_ for June and July 1861.\n\n[19] It is almost superfluous to observe, that there is another meaning\nof the word Art, in which it may be said to denote the poetical\ndepartment or aspect of things in general, in contradistinction to the\nscientific. In the text, the word is used in its older, and I hope, not\nyet obsolete sense.\n\n[20] The word Teleology is also, but inconveniently and improperly,\nemployed by some writers as a name for the attempt to explain the\nphenomena of the universe from final causes.\n\n[21] For an express discussion and vindication of this principle, see\nthe little volume entitled \"Utilitarianism.\"\n\n\nTHE END.\n\n\n\n\nTranscriber's Notes.\n\n\nSpelling irregularities where there was no obviously preferred version\nwere left as is. Variants include: \"cotemporary\" and \"contemporary;\"\n\"commonplaces\" and \"common-places;\" \"dependents\" and \"dependants;\"\n\"dreamed\" and \"dreamt;\" derivatives of \"enclose\" and \"inclose;\" \"e. g.\"\nand \"e.g.\"; \"i. e.\" and \"i.e.\"; \"misestimate\" and \"mis-estimate;\"\n\"recal\" and \"recall\" (and derivatives); derivatives of \"paraphrase\" and\n\"periphrase;\" \"subclass\" and \"sub-class\" (and derivatives).\n\nChanged \"Phemomena\" to \"Phenomena\" on page xv: \"Successions of Social\nPhenomena.\"\n\nChanged page reference for section 4 of Chapter XI on page xv of the\nTable of Contents from \"539\" to \"540.\"\n\nChanged \"oberved\" to \"observed\" on page 17: \"the observed facts.\"\n\nA closing double quotation mark is missing on page 17. It was added\nafter the sentence that ends with \"object of the inquiry.\"\n\nChanged \"neverthless\" to \"nevertheless\" on page 104: \"phenomena would\nnevertheless.\"\n\nFor the mathematical formulas appearing on pages 152 and 153:\nparentheses were added to make the linear form of the formula correct;\nand the radical sign was replaced by \"[root of].\" The equal sign was\npreserved in \"arc (sin = x),\" although it makes more sense without it.\n\nPage 240 contains the word \"'Squire.\" It intentionally begins with an\napostrophe, not an unmatched single quotation mark, and was left as\noriginally printed.\n\nChanged \"eupiditatibus\" to \"cupiditatibus\" on page 401: \"de\ncupiditatibus finiendis.\" And shortly thereafter, changed \"eupiditas\" to\n\"cupiditas:\" \"An potest cupiditas finiri.\" And then a bit further on,\nchanged \"h\u00e6e\" to \"h\u00e6c:\" \"h\u00e6c desideria natur\u00e6.\"\n\n\n\n\n\n
","title":"A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. II","tradition":"philosophy-ethics","translated_text":null,"word_count":196619}