{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_30866/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_30866","id":"gutenberg_30866","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/30866","summary":null,"tags":["Category: Language & Communication","Category: Philosophy & Ethics","Logic, Modern -- 19th century","Mill, John Stuart, 1806-1873","Philosophy"],"text":"Produced by David Clarke, Martin Pettit and the Online\nDistributed Proofreading Team at http://www.pgdp.net (This\nfile was produced from images generously made available\nby The Internet Archive/Million Book Project)\n\n\n\n\n\n\nANALYSIS OF MR. MILL'S SYSTEM OF LOGIC.\n\n       *       *       *       *       *\n\nWORKS BY JOHN STUART MILL, M.P. FOR WESTMINSTER.\n\n\n     A SYSTEM of LOGIC, RATIOCINATIVE and INDUCTIVE. Sixth Edition. 2\n     vols. 8vo. 25_s._\n\n     An EXAMINATION of SIR WILLIAM HAMILTON'S PHILOSOPHY, and of the\n     Principal Philosophical Questions discussed in his Writings. Third\n     Edition, revised. 8vo. 14_s._\n\n     PRINCIPLES of POLITICAL ECONOMY, with some of their Applications to\n     Social Philosophy. Sixth Edition. 2 vols. 8vo. 30_s._\n\n     PRINCIPLES of POLITICAL ECONOMY. By JOHN STUART MILL, M.P. People's\n     Edition. Crown 8vo. 5_s._\n\n     CONSIDERATIONS on REPRESENTATIVE GOVERNMENT. Third Edition. 8vo.\n     9_s._\n\n     On REPRESENTATIVE GOVERNMENT. By JOHN STUART MILL, M.P. People's\n     Edition. Crown 8vo. 2_s._\n\n     On LIBERTY. Third Edition. Post 8vo. 7_s._ 6_d._\n\n     On LIBERTY. By JOHN STUART MILL, M.P. People's Edition. Crown 8vo.\n     1_s._ 4_d._\n\n     DISSERTATIONS and DISCUSSIONS, POLITICAL, PHILOSOPHICAL, and\n     HISTORICAL. Second Edition of VOLS. I. and II. price 24_s._; VOL.\n     III., price 12_s._\n\n     INAUGURAL ADDRESS delivered to the University of St. Andrew's, Feb.\n     1, 1867. By JOHN STUART MILL, M.P. Rector of the University.\n     Library Edition (the Second), post 8vo. 5_s._ People's Edition,\n     crown 8vo. 1_s._\n\n     UTILITARIANISM. Second Edition. 8vo. 5_s._\n\n     THOUGHTS on PARLIAMENTARY REFORM. Second Edition, with SUPPLEMENT.\n     8vo. 1_s._ 6_d._\n\n\nLondon: LONGMANS and CO. Paternoster Row.\n\n       *       *       *       *       *\n\nANALYSIS OF MR. MILL'S SYSTEM OF LOGIC.\n\nBY\n\nW. STEBBING, M.A.\n\nFELLOW OF WORCESTER COLLEGE, OXFORD.\n\n_NEW EDITION._\n\nLONDON:\nLONGMANS, GREEN, AND CO.\n1867.\n\n\nLONDON\n\nPRINTED BY SPOTTISWOODE AND CO.\n\nNEW-STREET SQUARE\n\n\n\n\nPREFACE TO THE SECOND EDITION.\n\n\nThe author's aim has been to produce such a condensation of the original\nwork as may recall its contents to those who have read it, and may serve\nthose who are now reading it in the place of a full body of marginal\nnotes. Mr. Mill's conclusions on the true province and method of Logic\nhave a high substantive value, independent even of the arguments and\nillustrations by which they are supported; and these conclusions may be\nadequately, and, it is believed, with much practical utility, embodied\nin an epitome. The processes of reasoning on which they depend, can, on\nthe other hand, be represented in outline only. But it is hoped that the\nsubstance of every paragraph, necessary for the due comprehension of the\nseveral steps by which the results have been reached, will be here\nfound at all events suggested.\n\nThe author may be allowed to add, that Mr. Mill, before publication,\nexpressed a favourable opinion of the manner in which the work had been\nexecuted. Without such commendation the volume would hardly have been\noffered to the public.\n\nLONDON: _Dec. 21, 1865_.\n\n\n\n\nCONTENTS.\n                                                                 PAGE\n\nINTRODUCTION                                                        1\n\n\nBOOK I.\n\nNAMES AND PROPOSITIONS.\n\nCHAP.\n\n      I. On the Necessity of commencing with an Analysis of\n          Language in Logic                                         3\n\n     II. Names                                                      3\n\n    III. The Things denoted by Names                                7\n\n     IV. Propositions                                              17\n\n      V. The Import of Propositions                                19\n\n     VI. Propositions merely Verbal                                24\n\n    VII. The Nature of Classification, and the Five Predicables    26\n\n   VIII. Definition                                                30\n\n\nBOOK II.\n\nREASONING.\n\n      I. Inference, or Reasoning in General                        35\n\n     II. Ratiocination, or Syllogism                               36\n\n    III. The Functions and Logical Value of the Syllogism          39\n\n     IV. Trains of Reasoning, and Deductive Sciences               43\n\nV. & VI. Demonstration and Necessary Truths                        46\n\n\nBOOK III.\n\nINDUCTION.\n\n      I. Preliminary Observations on Induction in general          53\n\n     II. Inductions improperly so called                           54\n\n    III. The ground of Induction                                   57\n\n     IV. Laws of Nature                                            58\n\n      V. The Law of Universal Causation                            60\n\n     VI. The Composition of Causes                                 66\n\n    VII. Observation and Experiment                                67\n\n   VIII. & Note to IX. The Four Methods of Experimental\n          Enquiry                                                  69\n\n      X. Plurality of Causes, and intermixture of Effects          73\n\n     XI. The Deductive Method                                      76\n\n    XII. & XIII. The Explanation and Examples of the Explanation\n          of Laws of Nature                                        77\n\n    XIV. The Limits to the Explanation of Laws of Nature;\n          and Hypotheses                                           79\n\n     XV. Progressive Effects, and continued Action of\n          Causes                                                   81\n\n    XVI. Empirical Laws                                            83\n\n   XVII. Chance, and its Elimination                               85\n\n  XVIII. The Calculation of Chances                                87\n\n    XIX. The Extension of Derivative Laws to Adjacent Cases        89\n\n     XX. Analogy                                                   91\n\n     XXI. The Evidence of the Law of Universal Causation           92\n\n    XXII. Uniformities of Coexistence not dependent on Causation   94\n\n   XXIII. Approximate Generalisations, and Probable Evidence       96\n\n    XXIV. The remaining Laws of Nature                             99\n\n     XXV. The grounds of Disbelief                                103\n\n\nBOOK IV.\n\nOPERATIONS SUBSIDIARY TO INDUCTION.\n\n      I. Observation and Description                              107\n\n     II. Abstraction, or the Formation of Conceptions             108\n\n    III. Naming as Subsidiary to Induction                        111\n\n     IV. The Requisites of a Philosophical Language, and the\n          Principles of Definition                                112\n\n      V. The Natural History of the Variation in the Meaning\n          of Terms                                                115\n\n     VI. Terminology and Nomenclature                             117\n\n    VII. Classification, as Subsidiary to Induction               121\n\n   VIII. Classification by Series                                 124\n\n\nBOOK V.\n\nFALLACIES.\n\n      I. Fallacies in general                                     127\n\n     II. Classification of Fallacies                              128\n\n    III. Fallacies of Simple Inspection; or, a priori Fallacies   130\n\n     IV. Fallacies of Observation                                 134\n\n      V. Fallacies of Generalisation                              137\n\n     VI. Fallacies of Ratiocination                               141\n\n    VII. Fallacies of Confusion                                   143\n\n\nBOOK VI.\n\nON THE LOGIC OF THE MORAL SCIENCES.\n\n      I. Introductory Remarks                                     148\n\n     II. Liberty and Necessity                                    148\n\n    III. There is, or may be, a Science of Human Nature           150\n\n     IV. The Laws of Mind                                         151\n\n      V. Ethology, or the Science of the Formation of Character   153\n\n     VI. General Considerations on the Social Science             155\n\n    VII. The Chemical, or Experimental, Method in the Social\n          Science                                                 156\n\n   VIII. The Geometrical, or Abstract Method                      157\n\n     IX. The Physical, or Concrete Deductive Method               158\n\n      X. The Inverse Deductive, or Historical Method              161\n\n     XI. The Logic of Practice, or Art; including Morality\n          and Policy                                              165\n\n\n\n\nANALYSIS OF MILL'S LOGIC.\n\n\n\n\nINTRODUCTION.\n\n\nNo adequate definition is possible till the properties of the thing to\nbe defined are known. Previously we can define only the scope of the\ninquiry. Now, Logic has been considered as both the science of\nreasoning, i.e. the analysis of the mental process when we reason, and\nthe art of reasoning, i.e. the rules for the process. The term\n_reasoning_, however, is not wide enough. _Reasoning_ means either\nsyllogising, or (and this is its truer sense) the drawing inferences\nfrom assertions already admitted. But the Aristotelian or Scholastic\nlogicians included in Logic terms and propositions, and the Port Royal\nlogicians spoke of it as equivalent to the art of thinking. Even\npopularly, accuracy of classification, and the extent of command over\npremisses, are thought clearer signs of logical powers than accuracy of\ndeduction. On the other hand, the definition of logic as a 'science\ntreating of the operations of the understanding in the search of truth,'\nthough wide enough, would err through including truths known from\nintuition; for, though doubtless many seeming intuitions are processes\nof inference, questions as to what facts are _real intuitions_ belong\nto Metaphysics, not to Logic.\n\nLogic is the science, not of Belief, but of Proof, or Evidence. Almost\nall knowledge being matter of inference, the fields of Logic and of\nKnowledge coincide; but the two differ in so far that Logic does not\nfind evidence, but only judges of it. All science is composed of data,\nand conclusions thence: Logic shows what relations must subsist between\nthem. All inferential knowledge is true or not, according as the laws of\nLogic have been obeyed or not. Logic is Bacon's _Ars Artium_, the\nscience of sciences. Genius sometimes employs laws unconsciously; but\nonly genius: as a rule, the advances of a science have been ever found\nto be preceded by a fuller knowledge of the laws of Logic applicable to\nit. Logic, then, may be described as the science of the operations of\nthe understanding which aid in the estimation of evidence. It includes\nnot only the process of proceeding from the known to the unknown, but,\nas auxiliary thereto, Naming, Definition, and Classification.\nConception, Memory, and other like faculties, are not treated by it; but\nit presupposes them. Our object, therefore, must be to analyse the\nprocess of inference and the subsidiary operations, besides framing\ncanons to test any given evidence. We need not, however, carry the\nanalysis beyond what is necessary for the practical uses of Logic; for\none step in analysis is good without a second, and our purpose is simply\nto see the difference between good and ill processes of inference.\nMinuter analysis befits Metaphysics; though even that science, when\nstepping beyond the interrogation of our consciousness, or rather of our\nmemory, is, as all other sciences, amenable to Logic.\n\n\n\n\nBOOK I\n\nNAMES AND PROPOSITIONS.\n\n\n\n\nCHAPTER I.\n\nON THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE IN LOGIC.\n\n\nThe fact of Logic being a portion of the art of thinking, and of\nthought's chief instrument being words, is one reason why we must first\ninquire into the right use of words. But further, the import of\npropositions cannot really be examined apart from that of words; and\n(since whatever can be an object of belief assumes the form of a\nproposition, and in propositions all truth and error lie) this is a\nparamount reason why we must, as a preliminary, consider the import of\nnames, the neglecting which, and confining ourselves to things, would\nindeed be to discard all past experience. The right method is, to take\nmen's classifications of things as shown by names, correcting them as we\nproceed.\n\n\n\n\nCHAPTER II.\n\nNAMES.\n\n\nHobbes's assertion that a name is a sign, not of a thing, but of our\nconception of it, is untrue (unless he merely mean that the conception,\nand not the thing itself, is imparted to the hearer); for we intend by\na name, not only to make men conceive what we conceive, but to inform\nthem what we believe as to the things themselves.\n\nNames may be divided according to five principles of classification. The\n_first_ way of dividing them is into General (not as equivalent to\nCollective) and Individual names; the _second_, into Concrete, i.e. the\nnames of objects, and Abstract, i.e. the names of attributes (though\nLocke improperly extends the term to all names gained by abstraction,\nthat is, to all general names). An abstract name is sometimes general,\ne.g. colour, and sometimes singular, e.g. milk-whiteness. It may be\nobjected to calling attributes abstract, that also concrete adjectives,\ne.g. white, are attributes. But a word is the name of the things of\nwhich it can be predicated. Hence, white is the name of all things so\ncoloured, given indeed because of the quality, but really the name of\nthe thing, and no more the name of the quality than are names generally,\nsince every one of them, if it signifies anything at all, must imply an\nattribute.\n\nThe _third_ division is into Connotative and Non-connotative (the latter\nbeing wrongly called Absolute). By _connotative_ are meant, not (as Mr.\nJames Mill explains it) words which, pointing directly to one thing,\ntacitly refer to another, but words which denote a subject and imply an\nattribute; while _non-connotatives_ signify a subject only, or attribute\nonly. All concrete general names are connotative. They are also called\n_denominative_, because the subject denoted receives a common name (e.g.\nsnow is named white) from the attribute connoted. Even some abstracts\nare connotative, for attributes may have attributes ascribed to them,\nand a word which denotes attributes may connote an attribute of them;\ne.g. fault connotes hurtfulness. Proper names, on the other hand, though\nconcrete, are not connotative. They are merely distinguishing marks,\ngiven perhaps originally for a reason, but, when once given, independent\nof it, since the reason is proved to be no part of the sense of the word\nby the fact that the name is still used when the reason is forgotten.\nBut other individual names are connotative. Some of these, viz. those\nconnoting some attribute or some set of attributes possessed by one\nobject only, e.g. Sun, God, are really general names, though happening\nto be predicable only of a single object. But there are also real\nconnotative individual names, part of whose meaning is, that there\nexists only one individual with the connoted attribute, e.g. The first\nEmperor, The father of Socrates; and it is so with many-worded names,\nmade up of a general name limited by other words, e.g. The present Prime\nMinister of England. In short, the meaning of all names, which have any\nmeaning, resides, not in what they denote, but in what they connote.\nThere perpetually, however, arises a difficulty of deciding how much\nthey do connote, that is, what difference in the object would make a\ndifference in the name. This vagueness comes from our learning the\nconnotation, through a rude generalisation and analysis, from the\nobjects denoted. Thus, men use a name without any precise reference to a\ndefinite set of attributes, applying it to new objects on account of\nsuperficial resemblance, so that at length all common meaning\ndisappears. Even scientific writers, from ignorance, or from the\naversion which men at large feel to the use of new names, often force\nold terms to express an ever-growing number of distinctions. But every\nconcrete general name should be given a definite connotation with the\nleast possible change in the denotation; and this is what is aimed at in\nevery definition of a general name already in use. But we must not\nconfound the use of names of indeterminate connotation, which is so\ngreat an evil, with the employment, necessitated by the paucity of names\nas compared with the demand, of the same words with different\nconnotations in different relations.\n\nA _fourth_ division of names is into Positive and Negative. When the\npositive is connotative, so is the corresponding negative, for the\nnon-possession of an attribute is itself an attribute. Names negative in\nform, e.g. unpleasant, are often really positive; and others, e.g. idle,\nsober, though seemingly positive, are really negative. Privatives are\nnames which are equivalent each to a positive and a negative name taken\ntogether. They connote both the absence of certain attributes, and the\npresence of others, whence the presence of the defaulting ones might\nhave been expected. Thus, blind would be applied only to a non-seeing\nmember of a seeing class.\n\nThe _fifth_ division is into Relative and (that we may economise the\nterm Absolute for an occasion when none other is available) Non-relative\nnames. Correlatives, when concrete, are of course connotative. A\nrelation arises from two individuals being concerned in the same series\nof facts, so that the signification of neither name can be explained\nexcept by mentioning another: and any two correlatives connote, not the\nsame attribute indeed, but just this series of facts, which is exactly\nthe same in both cases.\n\nSome make a _sixth_ division, viz. Univocals, i.e. names predicated of\ndifferent individuals in the same sense, and AEquivocals, i.e. names\npredicated of different individuals in different senses. But these are\nnot two kinds of names, but only two modes of using them; for an\naequivocal name is two names accidentally coinciding in sound. An\nintermediate case is that of a name used analogically or metaphorically,\nthat is, in two senses, one its primary, the other its secondary sense.\nThe not perceiving that such a word is really two has produced many\nfallacies.\n\n\n\n\nCHAPTER III.\n\nTHE THINGS DENOTED BY NAMES.\n\n\nLogic is the theory of Proof, and everything provable can be exhibited\nas a proposition, propositions alone being objects of belief. Therefore,\nthe import of propositions, that is, the import of predication, must be\nascertained. But, as to make a proposition, i.e. to predicate, is to\nassert one _thing_ of another _thing_, the way to learn the import of\npredication is, by discovering what are the _things_ signified by names\nwhich are capable of being subject or predicate. It was with this object\nthat Aristotle formed his Categories, i.e. an attempted enumeration of\nall nameable things by the _summa genera_ or highest predicates, one or\nother of which must, he asserted, be predicable of everything. His,\nhowever, is a rude catalogue, without philosophical analysis of the\nrationale even of familiar distinctions. For instance, his Relation\nproperly includes Action, Passivity, and Local Situation, and also the\ntwo categories of Position [Greek: pote] and [Greek: pou], while the\ndifference between [Greek: pou] and [Greek: keisthai] is only verbal,\nand [Greek: echein] is not a _summum genus_ at all. Besides--only\nsubstantives and attributes being there considered--there is no category\nfor sensation and other mental states, since, though these may rightly\nbe placed, so far as they express their relation, if active, to their\nobjects, if passive to their causes, in the Categories of Actio and\nPassio, the things, viz., the mental states, do not belong there.\n\nThe absence of a well-defined concrete name answering to the abstract\n_existence_, is one great obstacle to renewing Aristotle's attempt. The\nwords used for the purpose commonly denote substances only, though\nattributes and feelings are equally existences. Even _being_ is\ninadequate, since it denotes only _some_ existences, being used by\ncustom as synonymous with _substance_, both material and spiritual. That\nis, it is applied to what excites feelings and has attributes, but not\nto feelings and attributes themselves; and if we called extension,\nvirtue, &c., _beings_, we should be accused of believing in the Platonic\nself-existing ideas, or Epicurus's sensible forms--in short, of deeming\nattributes substances. To fill this gap, the abstract, _entity_, was\nmade into a concrete, equivalent to _being_. Yet even _entity_ implies,\nthough not so much as _being_, the notion of substance. In fact, every\nword originally connoting simply existence, gradually enlarges its\nconnotation to mean _separate_ existence, i.e. existence freed from the\ncondition of belonging to a substance, so as to exclude attributes and\nfeelings. Since, then, all the terms are ambiguous, that among them (and\nthe same principle applies to terms generally) will be employed here\nwhich seems on each occasion to be _least_ ambiguous: and terms will be\nused even in improper senses, when these by familiar association convey\nthe proper meaning.\n\n_Nameable things_ are--I. Feelings or States of Consciousness.--A\nfeeling, being anything of which the mind is conscious, is synonymous\nwith _state of consciousness_. It is commonly confined to the sensations\nand emotions, or to the emotions alone; but it is properly a genus,\nhaving for species, Sensation, Emotion, Thought, and Volition. By\nthought is meant all that we are internally conscious of when we think;\ne.g. the idea of the sun, and not the sun itself, is a thought; and so,\nnot even an imaginary thing like a ghost, but only the idea of it, is a\nthought. In like manner, a sensation differs both from the object\ncausing it, and the attribute ascribed to the object. Yet language\n(except in the case of the sensations of hearing) has seldom provided\nthe sensations with separate names; so that we have to name the\nsensation from the object or the attribute exciting it, though we might\n_conceive_ the sensation to exist, though it never actually does,\nwithout an exciting cause. Again, another distinction has to be attended\nto, viz. the difference between the sensation and the state of the\nbodily organs, which is the physical agency producing it. This\ndistinction escapes notice partly by reason of the division of the\nfeelings into bodily and mental. But really there is no such division,\neven sensations being states of the sentient mind, and not of the body.\nThe difference, in fact, between sensations, thoughts, and emotions, is\nonly in the different agency producing the feeling; it being, in the\ncase of the sensations, a bodily, and, for the other two, a mental\nstate. Some suppose, after the sensation, in which, they say, the mind\nis passive, a distinct active process called perception, which is the\ndirect recognition of an external object, as the cause of the sensation.\nProbably, perceptions are simply cases of belief claiming to be\nintuitive, i.e. free of external evidence. But, at any rate, any\nquestion as to their nature is irrelevant to an inquiry like the\npresent, viz. how we get the non-original part of our knowledge. And so\nalso is the distinction in German metaphysics, between the mind's _acts_\nand its passive _states_. Enough for us now that they are all states of\nthe mind.\n\nII. Substances.--Logicians think they have defined substance and\nattribute, when they have shown merely what difference the use of them\nrespectively makes in the grammar of a sentence. They say an attribute\nmust be an attribute _of_ something, but that a substance is\nself-existent (being followed, if a relative, by _of_, not _qua_\nsubstance, but _qua_ the relation). But this _of_, as distinguishing\nattributes, itself needs explanation: besides, we can no more conceive a\nsubstance independent of attributes, than an attribute independent of a\nsubstance. Metaphysicians go deeper into the distinction than logicians.\nSubstances, most of them say, are either bodies or minds; and, of these,\na body is the external cause to which we ascribe sensations. Berkeley\nand the Idealists, however, deny that there exists any cause of\nsensations (except, indeed, a First Cause). They argue that the _whole_\nof our notion of a body consists of a number of our own or others'\nsensations occurring together habitually (so that, the thought of one\nbeing associated with the thought of the others, we get what Hartley and\nLocke call a complex idea). They deny that a residuum would remain if\nall the attributes were pared off; for that, though the sensations are\nbound together by a law, the existence of a _substratum_ is but one of\nmany forms of mentally realising the connection. And they ask how it\nis,--since so long as the sensations occurred in the old order, we\nshould not miss such a _substratum_, supposing it to have once existed\n_and to have perished_--that we can know it exists even now? Their\nopponents used formerly to reply, that the uniform order of sensations\nimplies an external cause determining the law of the order; and that the\nattributes _inhere_ in this external cause or substratum, viz. matter.\nBut at last it was seen that the existence of matter could not be proved\nby extrinsic evidence; consequently, now the answer to the idealist\nargument simply is, that the belief in an external cause of sensations\nis universal, and as intuitive as our knowledge of sensations\nthemselves. Even Kant allows this (notwithstanding his belief in the\nexistence of a universe of _things in themselves_, i.e. Nouemena, as\ncontrasted with the mental representation of them, where the sensations,\nhe thinks, furnish the matter, and the laws of the mind, the form).\nBrown even traced up to the sensations of touch, combined with the\nsensations seated in the muscular frame, those very properties, viz.,\nextension and figure, which Reid referred to as proving that some\nqualities must exist, not in the sensations, but in the things\nthemselves, _since_ they cannot possibly be copies of any impression on\nthe senses. We have, in truth, no right to consider a thing's sensible\nqualities akin to its nature, unless we suppose an absurdity, viz. that\na cause must, as such, resemble its effects. In any case, the question\nwhether Ontology be a possible science, concerns, not Logic, but the\nnature and laws of intuitive knowledge. And the question as to the\nnature of Mind is as out of place here as that about Body. As body is\nthe unknown exciting cause of sensations, so mind, the other kind of\nsubstance, is the unknown recipient both of the sensations and of all\nthe other feelings. Though I call a something _myself_, as distinct from\nthe series of feelings, the 'thread of consciousness,' yet this self\nshows itself only through its capacity of feeling or being conscious;\nand I can, with my present faculties, conceive the gaining no new\ninformation but about as yet unknown faculties of feeling. In short, as\nbody is the unsentient cause of all feelings, so mind is the sentient\n_subject_ (in the German sense) of them, viz. that which feels them.\nAbout this inner nature we know nothing, and Logic cares nothing.\n\nIII. Attributes.--Qualities are the first class of attributes. Now, if\nwe know nothing about bodies but the sensations they excite, we can mean\nnothing by the attributes of bodies but sensations. Against this it has\nbeen urged that, though we know nothing of sensible objects except the\nsensations, the quality which we ascribe on the _ground_ of the\nsensation may yet be a real hidden power or quality in the object, of\nwhich the sensation is only the evidence. Seemingly, this doctrine\narises only from the tendency to suppose that there must be two\ndifferent things to answer to two names when not quite synonymous.\nQuality and sensation are probably names for the same thing viewed in\ndifferent lights. The doctrine of an entity _per se_, called quality, is\na relic of the scholastic _occult causes_; the only intelligible cause\nof sensation being the presence of the assemblage of phenomena, called\nthe _object_. Why the presence of the object causes the sensation, we\nknow not; and, granting an _occult cause_, we are still in the dark as\nto how _that_ produces the effect. However, the question belongs to\nmetaphysics; and it suits this doctrine, as well as the opposed one, to\nsay that a quality has for its _foundation_ a sensation.\n\nRelations form the second class of attributes. In all cases of relation\nthere exists some fact into which the relatives enter as parties\nconcerned; and this is the _fundamentum relationis_. Whenever two things\nare involved in some one fact, we may ascribe to them a relation\ngrounded on it, however general the fact may be. As, then, a quality is\nan attribute based on the fact of a sensation, so a relation is an\nattribute based on a fact into which two objects enter jointly. This\nfact in both is always composed entirely of states of consciousness; and\nthis, whether it be complicated, as in many legal relations, or simple,\nas in the relations expressed by _antecedent_ and _consequent_ and by\n_simultaneous_, where the fact consists merely of the two things so\nrelated, since the consciousness either of the succession or of the\nsimultaneousness of the two sensations which represent the things, is a\nfeeling not added to, but involved in _them_, being a condition under\nwhich we must suppose things. And so, likewise, with the relations of\nlikeness and unlikeness. The feeling of these sometimes cannot be\nanalysed, when the _fundamentum relationis_ is, as in the case of two\nsimple sensations, e.g. two sensations of white, only the two sensations\nthemselves, the consequent feeling of their resemblance being, like that\nof their succession or simultaneousness, apparently involved in the\nsensations themselves. Sometimes, again, the likeness or unlikeness is\ncomplex, and therefore can be analysed into simpler cases. In any case,\nlikeness or unlikeness must resolve itself into likeness or unlikeness\nbetween states of our own or some other mind; and this, whether the\nfeeling of the resemblance or dissimilarity relate to bodies or to\nattributes, since the former we know only through the sensations they\nare supposed to excite, and the latter through the sensations on which\nthey are grounded. And so, again, when we say that two relations are\nalike (one of the many senses of analogy), we simply assert resemblance\nbetween the facts constituting the two _fundamenta relationis_. Several\nrelations, called by different names, are really cases of resemblance.\nThus, equality, i.e. the exact resemblance existing between things in\nrespect of their quantity, is often called identity.\n\nThe _third_ species of attributes is Quantity. The assertion of likeness\nor unlikeness in quantity, as in quality, is always founded on a\nlikeness or unlikeness in the sensations excited. What the difference is\nall who have had the sensations know, but it cannot be explained to\nthose who never had them.\n\nIn fine, all the attributes classed under Quality and Quantity are the\npowers bodies have of exciting certain sensations. So, Relation\ngenerally is but the power which an object has of joining its\ncorrelative in producing the series of sensations, which is the only\nsign of the existence of the fact on which they both are grounded. The\nrelations of succession and simultaneousness, indeed, are not based on\nany fact (i.e. any feeling) distinct from the related objects. But these\nrelations are themselves states of consciousness; resemblance, for\nexample, being nothing but our feeling of resemblance: at least, we\nascribe these relations to objects or attributes simply because they\nhold between the feelings which the objects excite and on which the\nattributes are grounded. And as with the attributes of bodies, so also\nthose of minds are grounded on states of consciousness. Considered in\nitself, we can predicate of a mind only the series of its own feelings:\ne.g. by _devout_ we mean that the feelings implied in that word form an\noft-recurring part of the series of feelings filling up the sentient\nexistence of that mind. Again, attributes may be ascribed to a mind as\nto a body, as grounded on the thoughts or emotions (not the sensations,\nfor only bodies excite them) which it excites in others: e.g. when we\ncall a character admirable, we mean that it causes feelings in us of\nadmiration. Sometimes, under one word really two attributes are\npredicated, one a state of the mind, the other of other minds affected\nby thinking of it: e.g. He is generous. Sometimes, even bodies have the\nattribute of producing an emotion: e.g. That statue is beautiful.\n\nThe general result is, that there are three chief kinds of nameable\nthings:--1. Feelings distinct from the objects exciting and the organs\nsupposed to convey them, and divisible into four classes, perceptions\nbeing only a particular case of belief, which is itself a sort of\nthought, while actions are only volitions followed by an effect. 2.\nSubstances, i.e. the unknown cause and the unknown recipient of our\nsensations. 3. Attributes, subdivisible into Quality, Relation,\nQuantity. Of these ([Greek: a]) qualities, like substances, are known\nonly by the states of consciousness which they excite, and on which they\nare based, and by which alone, though they are treated as a distinct\nclass, they can be described. ([Greek: b]) Relations also, with four\nexceptions, are based on some fact, i.e. a series of states of\nconsciousness. ([Greek: g]) Quantity is, in the same way, based on our\nsensations. In short, all attributes are only our sensations and other\nfeelings, or something involved in them. We may, then, classify nameable\nthings thus:--1, Feelings; 2, Minds; 3, Bodies, together with the\nproperties whereby they are _popularly_ (though the evidence is very\ndeficient) supposed to excite sensations; 4, the relations of Succession\nand Coexistence, Likeness and Unlikeness, which subsist really only\nbetween states of consciousness.\n\nThese four classes are a substitute for Aristotle's abortive Categories.\nAs they comprise all nameable things, every fact is made up of them or\nsome of them; those that are called _subjective_ facts being composed\nwholly of feelings as such, and the _objective_ facts, though composed\nwholly or partly of substances and attributes, being grounded on\ncorresponding subjective facts.\n\n\n\n\nCHAPTER IV.\n\nPROPOSITIONS.\n\n\nThe copula is a mere sign of predication, though it is often confounded\nwith _to be_, the verb of existence (and that not merely by Greeks, but\neven by moderns, whose larger experience how one word in one language\noften answers to several in another, should have saved them from\nthinking that things with a common name must have a common nature). The\n_first_ division of propositions is into Affirmative and Negative, the\ncopula in the latter being _is not_. Hobbes and others, by joining the\n_not_ to the predicate, made the latter what they call a _negative\nname_. But as a negative name is one expressing the _absence_ of an\nattribute, we thus in fact merely deny its presence, and therefore the\naffirmative guise these thinkers give to negative propositions is only a\nfiction. Again, _modal_ propositions cannot be reduced to the common\nform by joining the modality to the predicate, and turning, e.g. The sun\n_did_ rise, into, The sun is a thing having risen; for the past time is\nnot a particular kind of rising, and it affects not the predicate, but\nthe predication, i.e. the applicability of the predicate to the subject.\nThere are, however, certain cases in which the qualification may be\ndetached from the copula; e.g. in such expressions as, _may be_, _is\nperhaps_; for, then we really do not mean to assert anything about the\nfact, but only about the state of our mind about it, so that it is not\nthe predication which is affected: e.g. Caesar _may be_ dead, may\nproperly be rendered, I am not sure that he is alive.\n\nThe _second_ division is into Simple and Complex. Several propositions\njoined by a conjunction do not make a complex proposition. The\nconjunction, so far from making the two one, adds another, as being an\nabbreviation generally of an additional proposition: e.g. _and_ is an\nabbreviation of one additional proposition, viz. We must think of the\ntwo together; while _but_ is an abbreviation of two additional\npropositions, viz. We must think of them together, and we must recollect\nthere is a contrast between them. But hypothetical propositions, i.e.\nboth disjunctives and conditionals, are true complex propositions, since\nwith several terms they contain but a single assertion. Thus, in, If the\nKoran comes from God, Mahomet is God's prophet, we do not assert the\ntruth of either of the simple propositions therein contained (viz. the\nKoran comes from God, and Mahomet is God's prophet), but only the\ninferribility of one from the other. The only difference, then, between\na hypothetical and a categorical proposition, is that the former is\nalways an assertion about an assertion (though some categoricals are so\nlikewise; e.g. That the whole is greater than its parts, is an axiom).\nTheir conspicuous place in treatises on Logic arises from this attribute\nwhich they predicate of a proposition (for a proposition, like other\nthings, has attributes), viz. its being an inference from something\nelse, being, with reference to Logic, its chief attribute.\n\nThe _third_ common division is into Universal, Particular, Indefinite,\nand Singular. A proposition whose subject is an individual name, even if\nnot a proper name, is singular, e.g. The founder of Rome was killed. In\nparticular propositions, if the part of the class meant by the _some_\nwere specified, the proposition would become either singular, or\nuniversal with a different subject including all the part. Indefinite in\nLogic is a solecism like _doubtful gender_ in grammar, for the speaker\nmust mean to make either a particular or a universal assertion.\n\n\n\n\nCHAPTER V.\n\nTHE IMPORT OF PROPOSITIONS.\n\n\nThe object of an inquiry into the nature of propositions must be to\nanalyse, either, 1, the state of mind called belief, or 2, what is\nbelieved. Philosophers have usually, but wrongly, thought the former,\ni.e. an analysis of the act of judgment, the chief duty of Logic,\nconsidering a proposition to consist in the denying or affirming one\n_idea_ of another. True, we must have the two ideas in the mind\ntogether, in order to believe the assertion about the two _things_; but\nso we must also in order to disbelieve it. True also, that besides the\nputting the ideas together, there may be a mental process; but this has\nnothing to do with the import of propositions, since they are assertions\nabout things, i.e. facts of external nature, not about the ideas of\nthem, i.e. facts in our mental history. Logic has suffered from stress\nbeing laid on the relation between the ideas rather than the phenomena,\nnature thus coming to be studied by logicians second-hand, that is to\nsay, as represented in our minds. Our present object, therefore, must\nbe to investigate judgments, not judgment, and to inquire what it is\nwhich we assert when we make a proposition.\n\nHobbes (though he certainly often shows his belief that all propositions\nare not merely about the meaning of words, and that general names are\ngiven to things on account of their attributes) declares that what we\nassert, is our belief that the subject and predicate are names of the\nsame thing. This is, indeed, a property of all true propositions, and\nthe only one true of all. But it is not the scientific definition of\npropositions; for though the mere collocation which makes a proposition\na proposition, signifies only this, yet that _form_, combined with other\n_matter_, conveys much more meaning. Hobbes's principle accounts _fully_\nonly for propositions where both terms are proper names. He applied it\nto others, through attending, like all nominalists, to the denotation,\nand not the connotation of words, holding them to be, like proper names,\nmere marks put upon individuals. But when saying that, e.g. Socrates is\nwise, is a true proposition, because of the conformity of import between\nthe terms, he should have asked himself why _Socrates_ and _wise_ are\nnames of the same person. He ought to have seen that they are given to\nthe same person, not because of the intention of the maker of each word,\nbut from the resemblance of their connotation, since a word means\nproperly certain attributes, and, only secondarily, objects denoted by\nit. What we really assert, therefore, in a proposition, is, that where\nwe find certain attributes, we shall find a certain other one, which is\na question not of the meaning of names, but of the laws of nature.\n\nAnother theory virtually identical with Hobbes's, is that commonly\nreceived, which makes predication consist in referring things to a\n_class_; that is (since a class is only an indefinite number of\nindividuals denoted by a general name), in viewing them as some of those\nto be called by that general name. This view is the basis of the _dictum\nde omni et nullo_, on which is supposed to rest the validity of all\nreasoning. Such a theory is an example of [Greek: hysteron proteron]: it\nexplains the cause by the effect, since the predicate cannot be known\nfor a class name which includes the subject, till several propositions\nhaving it for predicate have been first assented to. This doctrine seems\nto suppose all individuals to have been made into parcels, with the\ncommon name outside; so that, to know if a general name can be\npredicated correctly of the subject, we need only search the roll so\nentitled. But the truth is, that general names are marks put, not upon\ndefinite objects, but upon collections of objects ever fluctuating. We\nmay frame a class without knowing a single individual belonging to it:\nthe individual is placed in the class because the proposition is true;\nthe proposition is not made true by the individual being placed there.\n\nAnalysis of different propositions shows what is the real import of\npropositions not simply verbal. Thus, we find that even a proposition\nwith a proper name for subject, means to assert that an individual thing\nhas the attributes connoted by the predicate, the name being thought of\nonly as means for giving information of a physical fact. This is still\nmore the case in propositions with connotative subjects. In these the\ndenoted objects are indicated by some of their attributes, and the\nassertion really is, that the predicate's set of attributes constantly\naccompanies the subject's set. But as every attribute is grounded on\nsome fact or phenomenon, a proposition, when asserting the attendance of\none or some attributes on others, really asserts simply the attendance\nof one phenomenon on another; e.g. When we say Man is mortal, we mean\nthat where certain physical and moral facts called humanity are found,\nthere also will be found the physical and moral facts called death. But\nanalysis shows that propositions assert other things besides (although\nthis is indeed their ordinary import) this coexistence or sequence of\ntwo phenomena, viz. two states of consciousness. Assertions in\npropositions about those unknowable entities (_nouemena_) which are the\nhidden causes of phenomena, are made, indeed, only in virtue of the\nknowable _phenomena_. Still, such propositions do, besides asserting the\nsequence or coexistence of the phenomena, assert further the _existence_\nof the nouemena; and, moreover, in affirming the existence of a nouemenon,\nwhich is an unknowable _cause_, they assert _causation_ also. Lastly,\npropositions sometimes assert _resemblance_ between two phenomena. It is\nnot true that, as some contend, every proposition whose predicate is a\ngeneral name affirms resemblance to the other members of the class; for\nsuch propositions generally assert only the possession by the subject of\ncertain common peculiarities; and the assertion would be true though\nthere were no members of the class besides those denoted by the\nsubject. Nevertheless, _resemblance alone_ is _sometimes_ predicated.\nThus, when individuals are put into a class as belonging to it, not\nabsolutely, but rather than to any other, the assertion is, not that\nthey have the attributes connoted, but that they resemble those having\nthem more than they do other objects. So, again, _only resemblance_ is\npredicated, when, though the predicate is a class name, the class is\nbased on general unanalysable resemblance. The classes in question are\nthose of the simple feelings; the names of feelings being, like all\nconcrete general names, connotative, but only of a mere resemblance.\n\nIn short, one of _five_ things, viz. Existence, Coexistence (or, to be\nmore particular, Order in Place), Sequence (or, more particularly, Order\nin Time, which comprises also the _mere fact of Coexistence_),\nCausation, and Resemblance, is asserted or denied in every proposition.\nThis division is an exhaustive classification with respect to all things\nthat can be believed. Although only propositions with concrete terms\nhave been spoken of, it is equally the fact that, in propositions with\nan abstract term or terms, we predicate one of these same _five_ things.\nThere cannot be any difference in the import of these two classes of\npropositions, since there is none in the import of their terms, for the\nreal signification of a concrete term resides in its connotation (so\nthat in a concrete proposition we really predicate an attribute), and\nwhat the concrete term connotes forms the whole sense of the abstract.\nThus, all propositions with abstract terms can be turned into equivalent\nones with concrete, the new terms being either the names which connote\nthe attributes, or names of the facts which are the _fundamenta_ of the\nattributes: e.g. Thoughtlessness is danger, is equivalent to,\nThoughtless actions (the _fundamentum_) are dangerous.\n\nFinally, as these _five_ are the only things affirmable, so are they the\nonly things deniable.\n\n\n\n\nCHAPTER VI.\n\nPROPOSITIONS MERELY VERBAL.\n\n\nThe object of Logic is to find how propositions are to be proved. As\npreliminary to this, it has been already shown that the Conceptualist\nview of propositions, viz. that they assert a relation between two\nideas, and the Nominalist, that they assert agreement or disagreement\nbetween the meanings of two names, are both wrong as general theories:\nfor that _generally_ the import of propositions is, to affirm or deny\nrespecting a phenomenon, or its hidden source, one of five kinds of\nfacts. There is, however, a class of propositions which relate not to\nmatter of fact, but to the meaning of names, and which, therefore, as\nnames and their meanings are arbitrary, admit not of truth or falsity,\nbut only of agreement or disagreement with usage. These _verbal_\npropositions are not only those in which both terms are proper names,\nbut also some, viz. _essential_ propositions, thought to be more closely\nrelated to things than any others. The Aristotelians' belief that\nobjects are made what they are called by the inherence of a certain\n_general substance_ in the individuals which get from it all their\nessential properties, prevented even Porphyry (though more reasonable\nthan the mediaeval Realists) from seeing that the only difference between\naltering a non-essential (or _accidental_) property, which, he says,\nmakes the thing [Greek: alloion], and altering an essential one, which\nmakes it [Greek: allo] (i.e. a different thing), is, that the latter\nchange makes the object change its name. But even when it was no longer\nbelieved that there are real entities answering to general terms, the\ndoctrine based upon it, viz. that a thing's essence is that without\nwhich the thing could neither be, nor be conceived to be, was still\ngenerally held, till Locke convinced most thinkers that the supposed\nessences of classes are simply the significations of their _names_. Yet\neven Locke supposed that, though the essences of classes are _nominal_,\n_individuals_ have _real_ essences, which, though unknown, are the\ncauses of their sensible properties.\n\nAn accidental proposition (i.e. in which a property not connoted by the\nsubject is predicated of it) tacitly asserts the existence of a thing\ncorresponding to the subject; otherwise, such a proposition, as it does\nnot explain the name, would assert nothing at all. But an essential\nproposition (i.e. in which a property connoted by the subject is\npredicated of it) is identical. The only use of such propositions is to\n_define_ words by unfolding the meaning involved in a name. When, as in\nmathematics, important consequences seem to follow from them, such\nreally follow from the tacit assumption, through the ambiguity of the\ncopula, of the real existence of the _object_ named.\n\nAccidental propositions include, 1, those with a proper name for\nsubject, since an individual has no essence (although the schoolmen,\nand rightly, according to their view of genera and species as entities\ninhering in the individuals, attributed to the individual the essence of\nhis class); and, 2, all general or particular propositions in which the\npredicate connotes any attribute not connoted by the subject. Accidental\npropositions may be called _real_; they add to our knowledge. Their\nimport may be expressed (according as the attention is directed mainly,\neither to what the proposition means, or to the way in which it is to be\nused), either, by the formula: The attributes of the subject are always\n(or never) accompanied by those signified by the predicate; or, by the\nformula: The attributes of the subject are evidence, or a mark, of the\npresence of those of the predicate. For the purposes of reasoning, since\npropositions enter into _that_, not as ultimate results, but as means\nfor establishing other propositions, the latter formula is preferable.\n\n\n\n\nCHAPTER VII.\n\nTHE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.\n\n\nIt is merely an accident when general names are names of classes of real\nobjects: e.g. The unity of God, in the Christian sense, and the\nnon-existence of the things called dragons, do not prevent those names\nbeing general names. The using a name to connote attributes, turns the\nthings, whether real or imaginary, into a class. But, in predicating the\nname, we predicate only the attributes; and even when a name (as, e.g.\nthose in Cuvier's system) is introduced as a means of grouping certain\nobjects together, and not, as usually, as a means of predication, it\nstill signifies nothing but the possession of certain attributes.\n\nClassification (as resulting from the use of general language) is the\nsubject of the Aristotelians' Five Predicables, viz. _Genus_, _Species_,\n_Differentia_, _Proprium_, _Accidens_. These are a division of general\nnames, not based on a distinction in their meaning, i.e. in the\nattributes connoted, but on a distinction in the class denoted. They\nexpress, not the meaning of the predicate itself, but its relation (a\nvarying one) to the subject. Commonly, the names of any two classes (or,\npopularly, the classes themselves), one of which includes all the other\nand more, are called respectively _genus_ and _species_. But the\nAristotelians, i.e. the schoolmen, meant by _differences in kind_\n(_genere_ or _specie_) something which was in its nature (and not merely\nwith reference to the connotation of the name) distinct from\n_differences_ in the _accidents_. Now, it is the fact that, though a\nfresh class may be founded on the smallest distinction in attributes,\nyet that some classes have, to separate them from other classes, no\ncommon attributes except those connoted by the name, while others have\ninnumerable common qualities (from which we have to select a few samples\nfor connotation) not referrible to a common source. The ends of language\nand of classification would be subverted if the latter (not if the\nformer) sorts of _difference_ were disregarded. Now, it was these only\nthat the Aristotelians called _kinds_ (_genera_ or _species_), holding\n_differences_ made up of _certain_ and _definite_ properties to be\n_differences_ in the _accidents_ of things. In conformity with this\ndistinction--and it is a true one--any class, e.g. negro as opposed to\nwhite man, may, according as physiology shall show the _differences_ to\nbe infinite or finite, be discovered to be a distinct _kind_ or\n_species_ (though not according to the naturalist's construction of\n_species_, as including all descended from the same stock), or merely a\nsubdivision of the _kind_ or _species_, Man. Among _kinds_, a _genus_ is\na class divisible into other _kinds_, though it may be itself a species\nin reference to higher _genera_; that which is not so divisible, is an\nindividual's _proximate kind_ or _infima species_ (_species\npraedicabilis_ and also _subjicibilis_), whose common properties must\ninclude all the common properties of every other real _kind_ to which\nthe individual can be referred.\n\nThe Aristotelians said that the _differentia_ must be of the _essence_\nof the subject. They vaguely understood, indeed, by the _essence_ of a\nthing, that which makes it the _kind_ of thing that it is. But, as a\n_kind_ is such from innumerable qualities not flowing from a common\nsource, logicians selected the qualities which make the thing be what it\nis called, and termed these the essence, not merely of the _species_,\nbut, in the case of the _infima species_, of the individual also. Hence,\nthe distinction between the predicables, Differentia, Proprium, and\nAccidens, is founded, not on the nature of things, but on the\nconnotation of names. The _specific difference_ is that which must be\nadded to the connotation of the _genus_ to complete the connotation of\nthe _species_. A _species_ may have various _differences_, according to\nthe principle of the particular classification. A _kind_, and not\nmerely a class, may be founded on any one of these, if there be a host\nof properties behind, of which this one is the index, and not the\nsource. Sometimes a name has a technical as well as an ordinary\nconnotation (e.g. the name Man, in the Linnaean system, connotes a\ncertain number of incisor and canine teeth, instead of its usual\nconnotation of rationality and a certain general form); and then the\nword is in fact ambiguous, i.e. two names. _Genus_ and _Differentia_ are\nsaid to be of the essence; that is, the properties signified by them are\nconnoted by the name denoting the _species_. But both _proprium_ and\n_accidens_ are said to be predicated of the species _accidentally_. A\nproprium of the species, however, is predicated of the species\nnecessarily being an attribute, not indeed connoted by the name, but\nfollowing from an attribute connoted by it. It follows, either by way of\ndemonstration as a conclusion from premisses, or by way of causation as\neffect from cause; but, in either case, _necessarily_. Inseparable\naccidents, on the other hand, are attributes universal, so far as we\nknow, to the species (e.g. blackness to crows), but not _necessary_;\ni.e. neither involved in the meaning of the name of the species, nor\nfollowing from attributes which are. Separable accidents do not belong\nto all, or if to all, not at all times (e.g. the fact of being born, to\nman), and sometimes are not constant even in the same individual (e.g.\nto be hot or cold).\n\n\n\n\nCHAPTER VIII.\n\nDEFINITION.\n\n\nA definition is a proposition declaring either the special or the\nordinary meaning, i.e. in the case of connotative names, the\nconnotation, of a word. This may be effected by stating directly the\nattributes connoted; but it is more usual to predicate of the subject of\ndefinition one name of synonymous, or several which, when combined, are\nof equivalent, connotation. So that, a definition of a name being thus\ngenerally the sum total of the essential propositions which could be\nframed with that name for subject, is really, as Condillac says, an\n_analysis_. Even when a name connotes only a single attribute, it (and\nalso the corresponding abstract name itself) can yet be defined (in this\nsense of being analysed or resolved into its elements) by declaring the\nconnotation of that attribute, whether, if it be a union of several\nattributes (e.g. Humanity), by enumerating them, or, if only one (e.g.\nEloquence), by dissecting the fact which is its foundation. Even when\nthe fact which is the foundation of the attribute is a simple feeling,\nand therefore incapable of analysis, still, if the simple feeling have a\nname, the attribute and the object possessing it may be defined by\nreference to the fact: e.g. a white object is definable as one exciting\nthe sensation of white; and whiteness, as the power of exciting that\nsensation. The only names, abstract or concrete, incapable of analysis,\nand therefore of definition, are proper names, as having no meaning, and\nalso the names of the simple feelings themselves, since these can be\nexplained only by the resemblance of the feelings to former feelings\ncalled by the same or by an exactly synonymous name, which consequently\nequally needs definition.\n\nThough the only accurate definition is one declaring all the facts\ninvolved in the name, i.e. its connotation, men are usually satisfied\nwith anything which will serve as an index to its denotation, so as to\nguard them from applying it inconsistently. This was the object of\nlogicians when they laid down that a species must be defined _per genus\net differentiam_, meaning by the _differentia one_ attribute included in\nthe essence, i.e. in the connotation. And, in fact, one attribute, e.g.\nin defining man, Rationality (Swift's Houyhnhms having not been as yet\ndiscovered) often does sufficiently mark out the objects denoted. But,\nbesides that a definition of this kind ought, in order to be complete,\nto be _per genus et differentias_, i.e. by _all_ the connoted attributes\nnot implied in the name of the _genus_, still, even if all were given, a\n_summum genus_ could not be so defined, since it has no superior genus.\nAnd for merely marking out the objects denoted, Description, in which\nnone of the connoted attributes are given, answers as well as logicians'\nso-called _essential_ definition. In Description, any one or a\ncombination of attributes may be given, the object being to make it\nexactly coextensive with the name, so as to be predicable of the same\nthings. Such a description may be turned into an essential definition by\na change of the connotation (not the denotation) of the name; and, in\nfact, thus are manufactured almost all scientific definitions, which,\nbeing landmarks of classification, and not meant to declare the meaning\nof the name (though, in fact, they do declare it in its new use), are\never being modified (as is the definition of a science itself) with the\nadvance of knowledge. Thus, a technical definition helps to expound the\nartificial classification from which it grows; but ordinary definition\ncannot expound, as the Aristotelians fancied it could, the natural\nclassification of things, i.e. explain their division into _kinds_, and\nthe relations among the _kinds_: for the properties of every _kind_ are\ninnumerable, and all that definition can do is to state the connotation\nof the name.\n\nBoth these two modes, viz. the essential but incomplete Definition, and\nthe accidental, or Description, are imperfect; but the Realists'\ndistinction between definition of names and of things is quite\nerroneous. Their doctrine is now exploded; but many propositions\nconsistent with it alone (e.g. that the science of geometry is deduced\nfrom definitions) have been retained by Nominalists, such as Hobbes.\nReally a definition, as such, cannot explain a thing's nature, being\nmerely an identical proposition explaining the meaning of a word. But\ndefinitions of names _known to be names of really existing objects_, as\nin geometry, include two propositions, one a definition and another a\npostulate. The latter affirms the existence of a thing answering to the\nname. The science is based on the postulates (whether they rest on\nintuition or proof), for the demonstration appeals to them alone, and\nnot on the definitions, which indeed might, though at some cost of\nbrevity, be dispensed with entirely. It has been argued that, at any\nrate, definitions are premisses of science, _provided_ they give such\nmeanings to terms as suit existing things: but even so, the inference\nwould obviously be from the existence, not of the name which means, but\nof the thing which has the properties.\n\nOne reason for the belief that demonstrative truths follow from the\ndefinitions, not from the postulates, was because the postulates are\nnever quite true (though in reality so much of them is true as is true\nof the conclusions). Philosophers, therefore, searching for something\nmore accurately true, surmised that definitions must be statements and\nanalyses, neither of words nor of things, as such, but of ideas; and\nthey supposed the subject-matter of all demonstrative sciences to be\nabstractions of the mind. But even allowing this (though, in fact, the\nmind cannot so abstract one property, e.g. length, from all others; it\nonly _attends_ to the one exclusively), yet the conclusions would still\nfollow, not from the mere definitions, but from the postulates of the\nreal existence of the ideas.\n\nDefinitions, in short, are of names, not things: yet they are not\ntherefore arbitrary; and to determine what _should be_ the meaning of a\nterm, it is often necessary to look at the objects. The obscurity as to\nthe connotation arises through the objects being named before the\nattributes (though it is from the latter that the concrete general terms\nget their meaning), and through the same name being popularly applied to\ndifferent objects on the ground of general resemblance, without any\ndistinct perception of their common qualities, especially when these are\ncomplex. The philosopher, indeed, uses general names with a definite\nconnotation; but philosophers do not make language--it grows: so that,\nby degrees, the same name often ceases to connote even general\nresemblance. The object in remodelling language is to discover if the\nthings denoted have common qualities, i.e. if they form a class; and, if\nthey do not, to form one artificially for them. A language's rude\nclassifications often serve, when retouched, for philosophy. The\ntransitions in signification, which often go on till the different\nmembers of the group seem to connote nought in common, indicate, at any\nrate, a striking resemblance among the objects denoted, and are\nfrequently an index to a real connection; so that arguments turning\napparently on the double meaning of a term, may perhaps depend on the\nconnection of two ideas. To ascertain the link of connection, and to\nprocure for the name a distinct connotation, the resemblances of things\nmust be considered. Till the name has got a distinct connotation, it\ncannot be defined. The philosopher chooses for his connotation of the\nname the attributes most important, either directly, or as the\ndifferentiae leading to the most interesting propria. The enquiry into\nthe more hidden agreement on which these obvious agreements depend,\noften itself arises under the guise of enquiries into the definition of\na name.\n\n\n\n\nBOOK II.\n\nREASONING.\n\n\n\n\nCHAPTER I.\n\nINFERENCE, OR REASONING IN GENERAL.\n\n\nThe preceding book treated, not of the proper subject of logic, viz. the\nnature of proof, but of assertion. Assertions (as, e.g. definitions)\nwhich relate to the meaning of words, are, since _that_ is arbitrary,\nincapable of truth or falsehood, and therefore of proof or disproof. But\nthere are assertions which are subjects for proof or disproof, viz. the\npropositions (the real, and not the verbal) whose subject is some fact\nof consciousness, or its hidden cause, about which is predicated, in the\naffirmative or negative, one of five things, viz. existence, order in\nplace, order in time, causation, resemblance: in which, in short, it is\nasserted, that some given subject does or does not possess some\nattribute, or that two attributes, or sets of attributes, do or do not\n(constantly or occasionally) coexist.\n\nA proposition not believed on its own evidence, but inferred from\nanother, is said to be _proved_; and this process of inferring, whether\nsyllogistically or not, is _reasoning_. But whenever, as in the\ndeduction of a particular from a universal, or, in Conversion, the\nassertion in the new proposition is the same as the whole or part of\nthe assertion in the original proposition, the inference is only\napparent; and such processes, however useful for cultivating a habit of\ndetecting quickly the concealed identity of assertions, are not\nreasoning.\n\nReasoning, or Inference, properly so called, is, 1, Induction, when a\nproposition is inferred from another, which, whether particular or\ngeneral, is less general than itself; 2, Ratiocination, or Syllogism,\nwhen a proposition is inferred from others equally or more general; 3, a\nkind which falls under neither of these descriptions, yet is the basis\nof both.\n\n\n\n\nCHAPTER II.\n\nRATIOCINATION, OR SYLLOGISM.\n\n\nThe syllogistic figures are determined by the position of the middle\nterm. There are four, or, if the fourth be classed under the first,\nthree. But syllogisms in the other figures can be reduced to the first\nby conversion. Such reduction may not indeed be necessary, for different\narguments are suited to different figures; the first figure, says\nLambert, being best adapted to the discovery or proof of the properties\nof things; the second, of the distinctions between things; the third, of\ninstances and exceptions; the fourth, to the discovery or exclusion of\nthe different species of a genus. Still, as the premisses of the first\nfigure, got by reduction, are really the same as the original ones, and\nas the only arguments of great scientific importance, viz. those in\nwhich the conclusion is a universal affirmative, can be proved in the\nfirst figure alone, it is best to hold that the two elementary forms of\nthe first figure are the universal types, the one in affirmatives, the\nother in negatives, of all correct ratiocination.\n\nThe _dictum de omni et nullo_, viz. that whatever can be affirmed or\ndenied of a class can be affirmed or denied of everything included in\nthe class, which is a true account generalised of the constituent parts\nof the syllogism in the first figure, was thought the basis of the\nsyllogistic theory. The fact is, that when universals were supposed to\nhave an independent objective existence, this dictum stated a supposed\nlaw, viz. that the _substantia secunda_ formed part of the properties of\neach individual substance bearing the name. But, now that we know that a\nclass or universal is nothing but the individuals in the class, the\ndictum is nothing but the identical proposition, that whatever is true\nof certain objects is true of each of them, and, to mean anything, must\nbe considered, not as an axiom, but as a circuitous definition of the\nword _class_.\n\nIt was the attempt to combine the nominalist view of the signification\nof general terms with the retention of the dictum as the basis of all\nreasoning, that led to the self-contradictory theories disguised under\nthe ultra-nominalism of Hobbes and Condillac, the ontology of the later\nKantians, and (in a less degree) the abstract ideas of Locke. It was\nfancied that the process of inferring new truths was only the\nsubstitution of one arbitrary sign for another; and Condillac even\ndescribed science as _une langue bien faite_. But language merely\nenables us to remember and impart our thoughts; it strengthens, like an\nartificial memory, our power of thought, and is thought's powerful\ninstrument, but not its exclusive subject. If, indeed, propositions in a\nsyllogism did nothing but refer something to or exclude it from a class,\nthen certainly syllogisms might have the dictum for their basis, and\nimport only that the classification is consistent with itself. But such\nis not the primary object of propositions (and it is on this account, as\nwell as because men will never be persuaded in common discourse to\n_quantify_ the predicate, that Mr. De Morgan's or Sir William Hamilton's\n_quantification of the predicate_ is a device of little value). What is\nasserted in every proposition which conveys real knowledge, is a fact\ndependent, not on artificial classification, but on the laws of nature;\nand as ratiocination is a mode of gaining real knowledge, the principle\nor law of all syllogisms, with propositions not purely verbal, must be,\nfor affirmative syllogisms, that; Things coexisting with the same thing\ncoexist with one another; and for negative, that; A thing coexisting\nwith another, with which a third thing does not coexist, does not\ncoexist with that third thing. But if (see _supra_, p. 26) propositions\n(and, of course, all combinations of them) be regarded, not\nspeculatively, as portions of our knowledge of nature, but as memoranda\nfor practical guidance, to enable us, when we know that a thing has one\nof two attributes, to infer it has the other, these two axioms may be\ntranslated into one, viz. Whatever has any mark has that which it is a\nmark of; or, if both premisses are universal, Whatever is a mark of any\nmark, is a mark of that of which this last is a mark.\n\n\n\n\nCHAPTER III.\n\nTHE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.\n\n\nThe question is, whether the syllogistic process is one of inference,\ni.e. a process from the known to the unknown. Its assailants say, and\ntruly, that in every syllogism, considered as an argument to prove the\nconclusion, there is a _petitio principii_; and Dr. Whately's defence of\nit, that its object is to unfold assertions wrapped up and implied (i.e.\nin fact, _asserted unconsciously_) in those with which we set out,\nrepresents it as a sort of trap. Yet, though no reasoning from generals\nto particulars can, as such, prove anything, the conclusion _is_ a _bona\nfide_ inference, though not an inference from the general proposition.\nThe general proposition (i.e. in the first figure, the major premiss)\ncontains not only a record of many particular facts which we have\nobserved or inferred, but also instructions for making inferences in\nunforeseen cases. Thus the inference is completed in the major premiss;\nand the rest of the syllogism serves only to decipher, as it were, our\nown notes.\n\nDr. Whately fails to make out that syllogising, i.e. reasoning from\ngenerals to particulars, is the _only_ mode of reasoning. No additional\nevidence is gained by interpolating a general proposition, and therefore\nwe may, if we please, reason directly from the individual cases, since\nit is on these alone that the general proposition, if made, would rest.\nIndeed, thus are in fact drawn, as well the inferences of children and\nsavages, and of animals (which latter having no signs, can frame no\ngeneral propositions), as even those drawn by grown men generally, from\npersonal experience, and particularly the inferences of men of high\npractical genius, who, not having been trained to generalise, can apply,\nbut not state, their principles of action. Even when we have general\npropositions we need not use them. Thus Dugald Stewart showed that the\naxioms need not be expressly adverted to in order to make good the\ndemonstrations in Euclid; though he held, inconsistently, that the\ndefinitions must be. All general propositions, whether called axioms, or\ndefinitions, or laws of nature, are merely abridged statements of the\nparticular facts, which, as occasion arises, we either think we may\nproceed on as proved, or intend to assume.\n\nIn short, all inference is from particulars to particulars; and general\npropositions are both registers or memoranda of such former inferences,\nand also short formulae for making more. The major premiss is such a\nformula; and the conclusion is an inference drawn, not from, but\naccording to that formula. The _actual_ premisses are the particular\nfacts whence the general proposition was collected inductively; and the\nsyllogistic rules are to guide us in reading the register, so as to\nascertain what it was that we formerly thought might be inferred from\nthose facts. Even where ratiocination is independent of induction, as,\nwhen we accept from a man of science the doctrine that all A is B; or\nfrom a legislator, the law that all men shall do this or that, the\noperation of drawing thence any particular conclusion is a process, not\nof inference, but of interpretation. In fact, whether the premisses are\ngiven by authority, or derived from our own (or predecessors')\nobservation, the object is always simply to interpret, by reference to\ncertain marks, an intention, whether that of the propounder of the\nprinciple or enactment, or that which we or our predecessors had when we\nframed the general proposition, so that we may draw no inferences that\nwere not _intended_ to be drawn. We assent to the conclusion in a\nsyllogism on account of its consistency with what we interpret to have\nbeen the intention of the framer of the major premiss, and not, as Dr.\nWhately held, because the supposition of a false conclusion from the\npremisses involves a contradiction, since, in fact, the denial, e.g.\nthat an individual now living will die, is not _in terms_ contradictory\nto the assertion that his ancestors and their contemporaries (to which\nthe general proposition, as a record of facts, really amounts) have all\ndied.\n\nBut the syllogistic form, though the process of inference, which there\nalways is when a syllogism is used, lies not in this form, but in the\nact of generalisation, is yet a great collateral security for the\ncorrectness of that generalisation. When all possible inferences from a\ngiven set of particulars are thrown into one general expression (and, if\nthe particulars support one inference, they always will support an\nindefinite number), we are more likely both to feel the need of weighing\ncarefully the sufficiency of the experience, and also, through seeing\nthat the general proposition would equally support some conclusion which\nwe _know_ to be false, to detect any defect in the evidence, which, from\nbias or negligence, we might otherwise have overlooked. But the\nsyllogistic form, besides being useful (and, when the validity of the\nreasoning is doubtful, even indispensable) for verifying arguments, has\nthe acknowledged merit of all general language, that it enables us to\nmake an induction once for all. We _can_, indeed, and in simple cases\nhabitually _do_, reason straight from particulars; but in cases at all\ncomplicated, all but the most sagacious of men, and they also, unless\ntheir experience readily supplied them with parallel instances, would be\nas helpless as the brutes. The only counterbalancing danger is, that\ngeneral inferences from insufficient premisses may become hardened into\ngeneral maxims, and escape being confronted with the particulars.\n\nThe major premiss is not really part of the argument. Brown saw that\nthere would be a _petitio principii_ if it were. He, therefore,\ncontended that the conclusion in reasoning follows from the minor\npremiss alone, thus suppressing the appeal to experience. He argued,\nthat to reason is merely to analyse our general notions or abstract\nideas, and that, _provided_ that the relation between the two ideas,\ne.g. of _man_ and of _mortal_, has been first perceived, we can evolve\nthe one directly from the other. But (to waive the error that a\nproposition relates to ideas instead of things), besides that this\n_proviso_ is itself a surrender of the doctrine that an argument\nconsists simply of the minor and the conclusion, the perception of the\nrelation between two ideas, one of which is not implied in the name of\nthe other, must obviously be the result, not of analysis, but of\nexperience. In fact, both the minor premiss, and also the expression of\nour former experience, must _both_ be present in our reasonings, or the\nconclusion will not follow. Thus, it appears that the universal type of\nthe reasoning process is: Certain individuals possess (as I or others\nhave observed) a given attribute; An individual resembles the former in\ncertain other attributes: Therefore (the conclusion, however, not being\nconclusive from its form, as is the conclusion in a syllogism, but\nrequiring to be sanctioned by the canons of induction) he resembles them\nalso in the given attribute. But, though this, and not the syllogistic,\nis the universal type of reasoning, yet the syllogistic process is a\nuseful test of inferences. It is expedient, _first_, to ascertain\ngenerally what attributes are marks of a certain other attribute, so as,\nsubsequently, to have to consider, _secondly_, only whether any given\nindividuals have those former marks. Every process, then, by which\nanything is inferred respecting an unobserved case, we will consider to\nconsist of both these last-mentioned processes. Both are equally\ninduction; but the name may be conveniently confined to the process of\nestablishing the general formula, while the interpretation of this will\nbe called 'Deduction.'\n\n\n\n\nCHAPTER IV.\n\nTRAINS OF REASONING, AND DEDUCTIVE SCIENCES.\n\n\nThe minor premiss always asserts a resemblance between a new case and\ncases previously known. When this resemblance is not obvious to the\nsenses, or ascertainable at once by direct observation, but is itself\nmatter of inference, the conclusion is the result of a train of\nreasoning. However, even then the conclusion is really the result of\ninduction, the only difference being that there are two or more\ninductions instead of one. The inference is still from particulars to\nparticulars, though drawn in conformity, not to one, but to several\nformulae. This need of several formulae arises merely from the fact that\nthe marks by which we perceive that an inference can be drawn (and of\nwhich marks the formulae are records) happen to be recognisable, not\ndirectly, but only through the medium of other marks, which were, by a\nprevious induction, collected to be marks of them.\n\nAll reasoning, then, is induction: but the difficulties in sciences\noften lie (as, e.g. in geometry, where the inductions are the simple\nones of which the axioms and a few definitions are the formulae) not at\nall in the inductions, but only in the formation of trains of reasoning\nto prove the minors; that is, in so combining a few simple inductions as\nto bring a new case, by means of one induction within which it evidently\nfalls, within others in which it cannot be directly seen to be included.\nIn proportion as this is more or less completely effected (that is, in\nproportion as we are able to discover marks of marks), a science, though\nalways remaining inductive, tends to become also _deductive_, and, to\nthe same extent, to cease to be one of the _experimental_ sciences, in\nwhich, as still in chemistry, though no longer in mechanics, optics,\nhydrostatics, acoustics, thermology, and astronomy, each generalisation\nrests on a special induction, and the reasonings consist but of one step\neach.\n\nAn experimental science may become deductive by the mere progress of\nexperiment. The mere connecting together of a few detached\ngeneralisations, or even the discovery of a great generalisation working\nonly in a limited sphere, as, e.g. the doctrine of chemical equivalents,\ndoes not make a science deductive as a whole; but a science is thus\ntransformed when some comprehensive induction is discovered connecting\nhosts of formerly isolated inductions, as, e.g. when Newton showed that\nthe motions of all the bodies in the solar system (though each motion\nhad been separately inferred and from separate marks) are all marks of\none like movement. Sciences have become deductive usually through its\nbeing shown, either by deduction or by direct experiment, that the\nvarieties of some phenomenon in them uniformly attend upon those of a\nbetter known phenomenon, e.g. every variety of sound, on a distinct\nvariety of oscillatory motion. The science of number has been the grand\nagent in thus making sciences deductive. The truths of numbers are,\nindeed, affirmable of all things only in respect of their quantity; but\nsince the variations of _quality_ in various classes of phenomena have\n(e.g. in mechanics and in astronomy) been found to correspond regularly\nto variations of _quantity_ in the same or some other phenomena, every\nmathematical formula applicable to quantities so varying becomes a mark\nof a corresponding general truth respecting the accompanying variations\nin quality; and as the science of quantity is, so far as a science can\nbe, quite deductive, the theory of that special kind of qualities\nbecomes so likewise. It was thus that Descartes and Clairaut made\ngeometry, which was already partially deductive, still more so, by\npointing out the correspondence between geometrical and algebraical\nproperties.\n\n\n\n\nCHAPTERS V. AND VI.\n\nDEMONSTRATION AND NECESSARY TRUTHS.\n\n\nAll sciences are based on induction; yet some, e.g. mathematics, and\ncommonly also those branches of natural philosophy which have been made\ndeductive through mathematics, are called Exact Sciences, and systems of\nNecessary Truth. Now, their necessity, and even their alleged certainty,\nare illusions. For the conclusions, e.g. of geometry, flow only\nseemingly from the definitions (since from definitions, as such, only\npropositions about the meaning of words can be deduced): really, they\nflow from an implied assumption of the existence of real things\ncorresponding to the definitions. But, besides that the existence of\nsuch things is not actual or possible consistently with the constitution\nof the earth, neither can they even be _conceived_ as existing. In fact,\ngeometrical points, lines, circles, and squares, are simply copies of\nthose in nature, to a part alone of which we choose to _attend_; and the\ndefinitions are merely some of our first generalisations about these\nnatural objects, which being, though equally true of all, not exactly\ntrue of any one, must, actually, when extended to cases where the error\nwould be appreciable (e.g. to lines of perceptible breadth), be\ncorrected by the joining to them of new propositions about the\naberration. The exact correspondence, then, between the facts and those\nfirst principles of geometry which are involved in the so-called\ndefinitions, is a fiction, and is merely _supposed_. Geometry has,\nindeed (what Dugald Stewart did not perceive), some first principles\nwhich are true without any mixture of hypothesis, viz. the axioms, as\nwell those which are indemonstrable (e.g. Two straight lines cannot\nenclose a space) as also the demonstrable ones; and so have all sciences\nsome exactly true general propositions: e.g. Mechanics has the first law\nof motion. But, generally, the necessity of the conclusions in geometry\nconsists only in their following necessarily from certain _hypotheses_,\nfor which same reason the ancients styled the conclusions of all\ndeductive sciences _necessary_. That the hypotheses, which form part of\nthe premisses of geometry, must, as Dr. Whewell says, not be\narbitrary--that is, that in their positive part they are observed facts,\nand only in their negative part hypothetical--happens simply because our\naim in geometry is to deduce conclusions which may be true of real\nobjects: for, when our object in reasoning is not to investigate, but to\nillustrate truths, arbitrary hypotheses (e.g. the operation of British\npolitical principles in Utopia) are quite legitimate.\n\nThe ground of our belief in axioms is a disputed point, and one which,\nthrough the belief arising too early to be traced by the believer's own\nrecollection, or by other persons' observation, cannot be settled by\nreference to actual dates. The axioms are really only generalisations\nfrom experience. Dr. Whewell, however, and others think that, though\nsuggested, they are not proved by experience, and that their truth is\nrecognised _a priori_ by the constitution of the mind as soon as the\nmeaning of the proposition is understood. But this assumption of an _a\npriori_ recognition is gratuitous. It has never been shown that there is\nanything in the facts inconsistent with the view that the recognition of\nthe truth of the axioms, however exceptionally complete and instant,\noriginates simply in experience, equally with the recognition of\nordinary physical generalisations. Thus, that we see a property of\ngeometrical forms to be true, without inspection of the material forms,\nis fully explained by the capacity of geometrical forms of being painted\nin the imagination with a distinctness equal to reality, and by the fact\nthat experience has informed us of that capacity; so that a conclusion\non the faith of the imaginary forms is really an induction from\nobservation. Then, again, there is nothing inconsistent with the theory\nthat we learn by experience the truth of the axioms, in the fact that\nthey are conceived by the mind as universally and necessarily true, that\nis, that we cannot figure them to ourselves as being false. Our capacity\nor incapacity of conceiving depends on our associations. Educated minds\ncan break up their associations more easily than the uneducated; but\neven the former not entirely at will, even when, as is proved later,\nthey are erroneous. The Greeks, from ignorance of foreign languages,\nbelieved in an inherent connection between names and things. Even Newton\nimagined the existence of a subtle ether between the sun and bodies on\nwhich it acts, because, like his rivals the Cartesians, he could not\nconceive a body acting where it is not. Indeed, inconceivableness\ndepends so completely on the accident of our mental habits, that it is\nthe essence of scientific triumphs to make the contraries of once\ninconceivable views themselves appear inconceivable. For instance,\nsuppositions opposed even to laws so recently discovered as those of\nchemical composition appear to Dr. Whewell himself to be inconceivable.\nWhat wonder, then, that an acquired incapacity should be mistaken for a\nnatural one, when not merely (as in the attempt to conceive space or\ntime as finite) does experience afford no model on which to shape an\nopposed conception, but when, as in geometry, we are unable even to call\nup the geometrical ideas (which, being impressions of form, exactly\nresemble, as has been already remarked, their prototypes), e.g. of two\nstraight lines, in order to try to conceive them inclosing a space,\nwithout, by the very act, repeating the scientific experiment which\nestablishes the contrary.\n\nSince, then, the axioms and the misnamed definitions are but inductions\nfrom experience, and since the definitions are only hypothetically true,\nthe deductive or demonstrative sciences--of which these axioms and\ndefinitions form together the first principles--must really be\nthemselves inductive and hypothetical. Indeed, it is to the fact that\nthe results are thus only conditionally true, that the necessity and\ncertainty ascribed to demonstration are due.\n\nIt is so even with the Science of Number, i.e. arithmetic and algebra.\nBut here the truth has been hidden through the errors of two opposite\nschools; for while many held the truths in this science to be _a\npriori_, others paradoxically considered them to be merely verbal, and\nevery process to be simply a succession of changes in terminology, by\nwhich equivalent expressions are substituted one for another. The excuse\nfor such a theory as this latter was, that in arithmetic and algebra we\ncarry no ideas with us (not even, as in a geometrical demonstration, a\nmental diagram) from the beginning, when the premisses are translated\ninto signs, till the end, when the conclusion is translated back into\nthings. But, though this is so, yet in every step of the calculation,\nthere is a real inference of facts from facts: but it is disguised by\nthe comprehensive nature of the induction, and the consequent generality\nof the language. For numbers, though they must be numbers of something,\nmay be numbers of anything; and therefore, as we need not, when using an\nalgebraical symbol (which represents all numbers without distinction),\nor an arithmetical number, picture to ourselves all that it stands for,\nwe may picture to ourselves (and this not as a sign of things, but as\nbeing itself a thing) the number or symbol itself as conveniently as any\nother single thing. That we are conscious of the numbers or symbols, in\ntheir character of things, and not of mere signs, is shown by the fact\nthat our whole process of reasoning is carried on by predicating of them\nthe properties of things.\n\nAnother reason why the propositions in arithmetic and algebra have been\nthought merely verbal, is that they seem to be _identical_ propositions.\nBut in 'Two pebbles and one pebble are equal to three pebbles,' equality\nbut not identity is affirmed; the subject and predicate, though names of\nthe same objects, being names of them in different states, that is, as\nproducing different impressions on the senses. It is on such inductive\ntruths, resting on the evidence of sense, that the Science of Number is\nbased; and it is, therefore, like the other deductive sciences, an\ninductive science. It is also, like them, hypothetical. Its inductions\nare the definitions (which, as in geometry, assert a fact as well as\nexplain a name) of the numbers, and two axioms, viz. The sums of equals\nare equal; the differences of equals are equal. These axioms, and\nso-called definitions are themselves exactly, and not merely\nhypothetically, true. Yet the conclusions are true only on the\nassumption that, 1 = 1, i.e. that all the numbers are numbers of the\nsame or equal units. Otherwise, the certainty in arithmetical processes,\nas in those of geometry or mechanics, is not _mathematical_, i.e.\nunconditional certainty, but only certainty of inference. It is the\nenquiry (which can be gone through once for all) into the inferences\nwhich can be drawn from assumptions, which properly constitutes all\ndemonstrative science.\n\nNew conclusions may be got as well from fictitious as from real\ninductions; and this is even consciously done, viz. in the _reductio ad\nabsurdum_, in order to show the falsity of an assumption. It has even\nbeen argued that all ratiocination rests, in the last resort, on this\nprocess. But as this is itself syllogistic, it is useless, as a proof of\na syllogism, against a man who denies the validity of this kind of\nreasoning process itself. Such a man cannot in fact be forced to a\ncontradiction in terms, but only to a contradiction, or rather an\ninfringement, of the fundamental maxim of ratiocination, viz. 'Whatever\nhas a mark, has what it is a mark of;' and, since it is only by\nadmitting premisses, and yet rejecting a conclusion from them, that this\naxiom is infringed, consequently nothing is _necessary_ except the\nconnection between a conclusion and premisses.\n\n\n\n\nBOOK III.\n\nINDUCTION.\n\n\n\n\nCHAPTER I.\n\nPRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.\n\n\nAs all knowledge not intuitive comes exclusively from inductions,\ninduction is the main topic of Logic; and yet neither have\nmetaphysicians analysed this operation with a view to practice, nor, on\nthe other hand, have discoverers in physics cared to generalise the\nmethods they employed.\n\nInferences are equally _inductive_, whether, as in science, which needs\nits conclusions for record, not for instant use, they pass through the\nintermediate stage of a general proposition (to which class Dr. Whewell,\nwithout sanction from facts, or from the usage of Reid and Stewart, the\nfounders of modern English metaphysical terminology, limits the term\ninduction), or are drawn direct from particulars to a supposed parallel\ncase. Neither does it make any difference in the _character_ of the\ninduction, whether the process be experiment or ratiocination, and\nwhether the object be to infer a general proposition or an individual\nfact. That, in the latter case, the difficulty of the practical\nenquiries, e.g. of a judge or an advocate, lies chiefly in selecting\nfrom among all approved general propositions those inductions which suit\nhis case (just as, even in deductive sciences, the ascertaining of the\ninductions is easy, their combination to solve a problem hard) is not to\nthe point: the legitimacy of the inductions so selected must at all\nevents be tried by the same test as a new general truth in science.\nInduction, then, may be treated here as though it were the operation of\ndiscovering and proving general propositions; but this is so only\nbecause the evidence which justifies an inference respecting one unknown\ncase, would justify a like inference about a whole class, and is really\nonly another form of the same process: because, in short, the logic of\nscience is the universal logic applicable to all human enquiries.\n\n\n\n\nCHAPTER II.\n\nINDUCTIONS IMPROPERLY SO CALLED.\n\n\nInduction is the process by which what is true at certain times, or of\ncertain individuals, is inferred to be true in like circumstances at all\ntimes, or of a whole class. There must be an inference from the known to\nthe unknown, and not merely from a less to a more general expression.\nConsequently, there is no valid induction, 1, in those cases laid down\nin the common works on Logic as the only perfect instances of induction,\nviz. where what we affirm of the class has already been ascertained to\nbe true of each individual in it, and in which the seemingly general\nproposition in the conclusion is simply a number of singular\npropositions written in an abridged form; or, 2, when, as often in\nmathematics, the conclusion, though really general, is a mere summing up\nof the different propositions from which it is drawn (whether actually\nascertained, or, as in the case of the uncalculated terms of an\narithmetical series, when once its law is known, readily to be\nunderstood); or, 3, when the several parts of a complex phenomenon,\nwhich are only capable of being observed separately, have been pieced\ntogether by one conception, and made, as it were, one fact represented\nin a single proposition.\n\nDr. Whewell sets out this last operation, which he terms the\n_colligation of facts_, as induction, and even as the type of induction\ngenerally. But, though induction is always colligation, or (as we may,\nwith equal accuracy, characterise such a general expression obtained by\nabstraction simply connecting observed facts by means of common\ncharacters) _description_, colligation, or description, as such, though\na necessary preparation for induction, is not induction. Induction\nexplains and predicts (and, as an incident of these powers, describes).\nDifferent explanations collected by real induction from supposed\nparallel cases (e.g. the Newtonian and the _Impact_ doctrines as to the\nmotions of the heavenly bodies), or different predictions, i.e.\ndifferent determinations of the conditions under which similar facts may\nbe expected again to occur (e.g. the stating that the position of one\nplanet or satellite so as to overshadow another, and, on the other hand,\nthat the impending over mankind of some great calamity, is the condition\nof an eclipse), cannot be true together. But, for a colligation to be\ncorrect, it is enough that it enables the mind to represent to itself as\na whole all the separate facts ascertained at a given time, so that\nsuccessive tentative descriptions of a phenomenon, got by guessing till\na guess is found which tallies with the facts, may, though conflicting\n(e.g. the theories respecting the motions of the heavenly bodies), be\n_all_ correct _so far as they go_. Induction is proof, the inferring\nsomething unobserved from something observed; and to provide a proper\ntest of proof is the special purpose of inductive logic. But colligation\nsimply sums up the facts observed, as seen under a new point of view.\nDr. Whewell contends that, besides the sum of the facts, colligation\nintroduces, as a principle of connection, a conception of the mind not\nexisting in the facts. But, in fact, it is only because this conception\nis a copy of something in the facts, although our senses are too weak to\nrecognise it directly, that the facts are rightly classed under the\nconception. The conception is often even got by abstraction from the\nfacts which it colligates; but also when it is a hypothesis, borrowed\nfrom strange phenomena, it still is accepted as true only because found\nactually, and as a fact, whatever the origin of the knowledge of the\nfact, to fit and to describe as a whole the separate observations. Thus,\nthough Kepler's consequent inference that, _because_ the orbit of a\nplanet is an ellipse, the planet would _continue_ to revolve in that\nsame ellipse, was an induction, his previous application of the\nconception of an ellipse, abstracted from other phenomena, to sum up his\ndirect observations of the successive positions occupied by the\ndifferent planets, and thus to describe their orbits, was no induction.\nIt altered only the _predicate_, changing--The successive places of,\ne.g. Mars, are A, B, C, and so forth, into--The successive places of,\ne.g. Mars, are points in an ellipse: whereas induction always widens the\n_subject_.\n\n\n\n\nCHAPTER III.\n\nTHE GROUND OF INDUCTION.\n\n\nInduction is generalisation from experience. It assumes, that whatever\nis true in any one case, is true in all cases of a certain description,\nwhether past, present, or future (and not merely in future cases, as is\nwrongly implied in the statement by Reid's and Stewart's school, that\nthe principle of induction is 'our intuitive conviction that the future\nwill resemble the past'). It assumes, in short, that the course of\nnature is uniform, that is, that all things take place according to\ngeneral laws. But this general axiom of induction, though by it were\ndiscovered the obscure laws of nature, is no explanation of the\ninductive process, but is itself an induction (not, as some think, an\nintuitive principle which experience _verifies_ only), and is arrived at\nafter many separate phenomena have been first observed to take place\naccording to general laws. It does not, then, _prove_ all other\ninductions. But it is a _condition_ of their proof. For any induction\ncan be turned into a syllogism by supplying a major premiss, viz. What\nis true of this, that, &c. is true of the whole class; and the process\nby which we arrive at this immediate major may be itself represented by\nanother syllogism or train of syllogisms, the major of the ultimate\nsyllogism, and which therefore is the warrant for the immediate major,\nbeing this axiom, viz. that there is uniformity, at all events, in the\nclass of phenomena to which the induction relates, and a uniformity\nwhich, if not foreknown, may now be known.\n\nBut though the course of nature is uniform, it is also infinitely\nvarious. Hence there is no certainty in the induction in use with the\nancients, and all non-scientific men, and which Bacon attacked, viz.\n'Inductio per enumerationem simplicem, ubi non reperitur instantia\ncontradictoria'--_unless_, as in a few cases, we must have known of the\ncontradictory instances if existing. The scientific theory of induction\nalone can show why a general law of nature may sometimes, as when the\nchemist first discovers the existence and properties of a before unknown\nsubstance, be inferred from a single instance, and sometimes (e.g. the\nblackness of all crows) not from a million.\n\n\n\n\nCHAPTER IV.\n\nLAWS OF NATURE.\n\n\nThe uniformity of the course of nature is a complex fact made up of all\nthe separate uniformities in respect to single phenomena. Each of these\nseparate uniformities, if it be not a mere case of and result from\nothers, is a law of nature; for, though _law_ is used for any general\nproposition expressing a uniformity, _law of nature_ is restricted to\ncases where it has been thought that a separate act of creative will is\nnecessary to account for the uniformity. Laws of nature, in the\naggregate, are the fewest general propositions from which all the\nuniformities in the universe might be deducted. Science is ever tending\nto resolve one law into a higher. Thus, Kepler's three propositions,\nsince having been resolved by Newton into, and shown to be cases of the\nthree laws of motion, may be indeed called laws, but not laws of nature.\n\nSince every correct inductive generalisation is either a law of nature,\nor a result from one, the problem of inductive logic is to unravel the\nweb of nature, tracing each thread separately, with the view, 1, of\nascertaining what are the _several_ laws of nature, and, 2, of following\nthem into their results. But it is impossible to frame a scientific\nmethod of induction, or test of inductions, unless, unlike Descartes, we\nstart with the hypothesis that some trustworthy inductions have been\nalready ascertained by man's involuntary observation. These spontaneous\ngeneralisations must be revised; and the same principle which common\nsense has employed to revise them, correcting the narrower by the wider\n(for, in the end, experience must be its own test), serves also, only\nmade more precise, as the real type of scientific induction. As\npreliminary to the employment of this test, nature must be surveyed,\nthat we may discover which are respectively the invariable and the\nvariable inductions at which man has already arrived unscientifically.\nThen, by connecting these different ascertained inductions with one\nanother through ratiocination, they become mutually confirmative, the\nstrongest being made still stronger when bound up with the weaker, and\nthe weakest at least as strong as the weakest of those from which they\nare deduced (as in the case of the Torricellian experiment) while those\nleading deductively to incompatible consequences become each other's\ntest, showing that one must be given up (e.g. the old farmers' bad\ninduction that seed never throve if not sown during the increase of the\nmoon). It is because a survey of the uniformities ascertained to exist\nin nature makes it clear that there are certain and universal\nuniformities serving as premisses whence crowds of lower inductions may\nbe deduced, and so be raised to the same degree of certainty, that a\nlogic of induction is possible.\n\n\n\n\nCHAPTER V.\n\nTHE LAW OF UNIVERSAL CAUSATION.\n\n\nPhenomena in nature stand to each other in two relations, that of\nsimultaneity, and that of succession. On a knowledge of the truths\nrespecting the succession of facts depends our power of predicting and\ninfluencing the future. The object, therefore, must be to find some law\nof succession not liable to be defeated or suspended by any change of\ncircumstances, by being tested by, and deduced from which law, all other\nuniformities of succession may be raised to equal certainty. Such a law\nis not to be found in the class of laws of number or of space; for\nthough these are certain and universal, no laws except those of space\nand number can be deduced from them by themselves (however important\n_elements_ they may be in the ascertainment of uniformities of\nsuccession). But causation is such a law; and of this, moreover, all\ncases of succession whatever are examples.\n\nThis _Law of Causation_ implies no particular theory as to the ultimate\nproduction of effects by _efficient_ causes, but simply implies the\nexistence of an invariable order of succession (on our assurance of\nwhich the validity of the canons of inductive logic depends) found by\nobservation, or, when not yet observed, believed, to obtain between an\ninvariable antecedent, i.e. the _physical_ cause, and an invariable\nconsequent, the effect. This sequence is generally between a consequent\nand the _sum_ of several antecedents. The cause is really the sum total\nof the conditions, positive and negative; the negative being stated as\none condition, the same always, viz. the absence of counteracting causes\n(since one cause generally counteracts another by the same law whereby\nit produces its own effects, and, therefore, the particular mode in\nwhich it counteracts another may be classed under the positive causes).\nBut it is usual, even with men of science, to reserve the name _cause_\nfor an antecedent _event_ which completes the assemblage of conditions,\nand begins to exist immediately before the effect (e.g. in the case of\ndeath from a fall, the slipping of the foot, and not the weight of the\nbody), and to style the permanent facts or _states_, which, though\nexisting immediately before, have also existed long previously, the\n_conditions_. But indeed, popularly, any condition which the hearer is\nleast likely to be aware of, or which needs to be dwelt upon with\nreference to the particular occasion, will be selected as the cause,\neven a negative condition (e.g. the sentinel's absence from his post, as\nthe cause of a surprise), though from a mere negation no consequence can\nreally proceed. On the other hand, the object which is popularly\nregarded as standing in the relation of _patient_, and as being the mere\ntheatre of the effect, is never styled _cause_, being included in the\nphrase describing the effect, viz. as the object, of which the effect is\n_a state_. But really these so-called _patients_ are themselves agents,\nand their properties are positive conditions of the effect. Thus, the\ndeath of a man who has taken prussic acid is as directly the effect of\nthe organic properties of the man, i.e. the _patient_, as of the poison,\ni.e. the _agent_.\n\nTo be a cause, it is not enough that the sequence _has been_ invariable.\nOtherwise, night might be called the cause of day; whereas it is not\neven a condition of it. Such relations of succession or coexistence, as\nthe succession of day and night (which Dr. Whewell contrasts as _laws of\nphenomena_ with _causes_, though, indeed, the latter also are laws of\nphenomena, only more universal ones), result from the coexistence of\nreal causes. The causes themselves are followed by their effects, not\nonly invariably, but also _necessarily_, i.e. _unconditionally_, or\nsubject to none but negative conditions. _This_ is material to the\nnotion of a cause. But another question is not material, viz. whether\ncauses _must_ precede, or may, at times, be simultaneous with (they\ncertainly are never preceded by) their effects. In some, though not in\nall cases, the causes do invariably continue _together with_ their\neffects, in accordance with the schools' dogma, _Cessante causa, cessat\net effectus_; and the hypothesis that, in such cases, the effects are\nproduced _afresh_ at each instant by their cause, is only a verbal\nexplanation. But the question does not affect the theory of causation,\nwhich remains intact, even if (in order to take in cases of simultaneity\nof cause and effect) we have to define a cause, as the assemblage of\nphenomena, which occurring, some other phenomenon invariably and\nunconditionally commences, or has its origin.\n\nThere exist certain original natural agents, called permanent causes\n(some being objects, e.g. the earth, air, and sun; others, cycles of\nevents, e.g. the rotation of the earth), which together make up nature.\nAll other phenomena are immediate or remote effects of these causes.\nConsequently, as the state of the universe at one instant is the\nconsequence of its state at the previous instant, a person (but only if\nof more than human powers of calculation, and subject also to the\npossibility of the order being changed by a new volition of a supreme\npower) might predict the whole future order of the universe, if he knew\nthe original distribution of all the permanent causes, with the laws of\nthe succession between each of them and its different mutually\nindependent effects. But, in fact, the distribution of these permanent\ncauses, with the reason for the proportions in which they coexist, has\nnot been reduced to a law; and this is why the sequences or coexistences\namong the effects of several of them together cannot rank as laws of\nnature, though they are invariable while the causes coexist. For this\nsame reason (since the proximate causes are traceable ultimately to\npermanent causes) there are no original and independent uniformities of\ncoexistence between effects of different (proximate) causes, though\nthere may be such between different effects of the same cause.\n\nSome, and particularly Reid, have regarded man's voluntary agency as\nthe true type of causation and the exclusive source of the idea. The\nfacts of inanimate nature, they argue, exhibit only antecedence and\nsequence, while in volition (and this would distinguish it from physical\ncauses) we are conscious, prior to experience, of power to produce\neffects: volition, therefore, whether of men or of God, must be, they\ncontend, an efficient cause, and the only one, of all phenomena. But, in\nfact, they bring no positive evidence to show that we could have known,\napart from experience, that the effect, e.g. the motion of the limbs,\nwould follow from the volition, or that a volition is more than a\nphysical cause. In lieu of positive evidence, they appeal to the\nsupposed conceivableness of the direct action of will on matter, and\ninconceivableness of the direct action of matter on matter. But there is\nno inherent law, to this effect, of the conceptive faculty: it is only\nbecause our voluntary acts are, from the first, the most direct and\nfamiliar to us of all cases of causation, that men, as is seen from the\nstructure of languages (e.g. their active and passive voices, and\nimpersonations of inanimate objects), get the _habit_ of borrowing them\nto explain other phenomena by a sort of original Fetichism. Even Reid\nallows that there is a tendency to assume volition where it does not\nexist, and that the belief in it has its sphere gradually limited, in\nproportion as fixed laws of succession among external objects are\ndiscovered.\n\nThis proneness to require the appearance of some necessary and natural\nconnection between the cause and its effect, i.e. some reason _per se_\nwhy the one should produce the other, has infected most theories of\ncausation. But the selection of the particular agency which is to make\nthe connection between the physical antecedent and its consequent seem\n_conceivable_, has perpetually varied, since it depends on a person's\nspecial habits of thought. Thus, the Greeks, Thales, Anaximenes, and\nPythagoras, thought respectively that water, air, or number is such an\nagency explaining the production of physical effects. Many moderns,\nagain, have been unable to _conceive_ the production of effects by\nvolition itself, without some intervening agency to connect it with\nthem. This medium, Leibnitz thought, was some _per se_ efficient\nphysical antecedent; while the Cartesians imagined for the purpose the\ntheory of Occasional Causes, that is, supposed that God, not _qua_ mind,\nor _qua_ volition, but _qua_ omnipotent, intervenes to connect the\nvolition and the motion: so far is the mind from being forced to think\nthe action of mind on matter more _natural_ than that of matter on\nmatter. Those who believe volition to be an efficient cause are guilty\nof exactly the same error as the Greeks, or Leibnitz or Descartes; that\nis, of requiring an _explanation_ of physical sequences by something\n[Greek: aneu hou to aition ouk an pot' eie aition]. But they are guilty\nof another error also, in inferring that volition, even if it is an\n_efficient_ cause of so peculiar a phenomenon as nervous action, must\ntherefore be the efficient cause of all other phenomena, though having\nscarcely a single circumstance in common with them.\n\n\n\n\nCHAPTER VI.\n\nTHE COMPOSITION OF CAUSES.\n\n\nAn effect is almost always the result of the concurrence of several\ncauses. When all have their full effect, precisely as if they had\noperated _successively_, the joint effect (and it is not inconsistent to\ngive the name of _joint effect_ even to the mutual obliteration of the\nseparate ones) may be _deduced_ from the laws which govern the causes\nwhen acting separately. Sciences in which, as in mechanics, this\nprinciple, viz. the _composition of causes_, prevails, are deductive and\ndemonstrative. Phenomena, in effect, do generally follow this principle.\nBut in some classes, e.g. chemical, vital, and mental phenomena, the\nlaws of the elements when called on to work together, cease and give\nplace to others, so that the joint effect is not the sum of the separate\neffects. Yet even here the more general principle is exemplified. For\nthe new _heteropathic_ laws, besides that they never supersede _all_ the\nold laws (thus, The weight of a chemical compound is equal to the sum of\nthe weight of the elements), have been often found, especially in the\ncase of vital and mental phenomena, to enter _unaltered_ into\ncomposition with one another, so that complex facts may thus be\n_deducible_ from comparatively simple laws. It is even possible that, as\nhas been already partly effected by Dalton's law of definite\nproportions, and the law of isomorphism, chemistry itself, which is now\nthe least deductive of sciences, may be made deductive, through the laws\nof the combinations being ascertained to be, though not compounded of\nthe laws of the separate agencies, yet derived from them according to a\nfixed principle.\n\nThe proposition, that effects are proportional to their causes, is\nsometimes laid down as an independent axiom of causation: it is really\nonly a particular case of the composition of causes; and it fails at the\nsame point as the latter principle, viz. when an addition does not\nbecome compounded with the original cause, but the two together generate\na new phenomenon.\n\n\n\n\nCHAPTER VII.\n\nOBSERVATION AND EXPERIMENT.\n\n\nSince the whole of the present facts are the infallible result of the\nwhole of the past, so that if the prior state of the entire universe\ncould recur it would be followed by the present, the process of\nascertaining the relations of cause and effect is an analysis or\nresolution of this complex uniformity into the simpler uniformities\nwhich make it up. We must first mentally analyse the facts, not making\nthis analysis minuter than is needed for our object at the time, but at\nthe same time not regarding (as did the Greeks their verbal\nclassifications) a mental decomposition of facts as ultimate. When we\nhave thus succeeded in looking at any two successive chaotic masses (for\nsuch nature keeps at each instant presenting to us) as so many distinct\nantecedents and consequents, we must analyse the facts themselves, and\ntry, by varying the circumstances, to discover which of the antecedents\nand consequents (for many are always present together) are related to\neach other.\n\nExperiment and observation are the two instruments for thus varying the\ncircumstances. When the enquiry is, What are the effects of a given\ncause? experiment is far the superior, since it enables us not merely to\nproduce many more and more opportune variations than nature, which is\nnot arranged on the plan of facilitating our studies, offers\nspontaneously, but, what is a greater advantage, though one less\nattended to, also to insulate the phenomenon by placing it among known\ncircumstances, which can be then infinitely varied by introducing a\nsuccession of well-defined new ones.\n\nObservation cannot ascertain the effects of a given cause, because it\ncannot, except in the simplest cases, discover what are the concomitant\ncircumstances; and therefore sciences in which experiment cannot be\nused, either at all, as in astronomy, or commonly, as in mental and\nsocial science, must be mainly deductive, not inductive. When, however,\nthe object is to discover causes by means of their effects, observation\nalone is primarily available, since new effects could be artificially\nproduced only through their causes, and these are, in the supposed case,\nunknown. But even then observation by itself cannot directly discover\ncauses, as appears from the case of zoology, which yet contains many\nrecognised uniformities. We have, indeed, ascertained a real uniformity\nwhen we observe some one antecedent to be invariably found along with\nthe effects presented by nature. But it is only by reversing the\nprocess, and experimentally producing the effects by means of that\nantecedent, that we can prove it to be unconditional, i.e. the cause.\n\n\n\n\nCHAPTER VIII. AND NOTE TO CHAPTER IX.[1]\n\nTHE FOUR METHODS OF EXPERIMENTAL ENQUIRY.\n\n\nFive canons may be laid down as the principles of experimental enquiry.\nThe first is that of the Method of Agreement, viz.: _If two or more\ninstances of the phenomenon under investigation have only one\ncircumstance in common, the circumstance in which alone all the\ncircumstances agree is the cause or the effect of the given phenomenon._\nThe second canon is that of the Method of Difference, viz.: _If an\ninstance in which the phenomenon occurs and an instance in which it does\nnot occur have every circumstance in common, save one, and that one\noccurs only in the former, that one circumstance is the effect, or the\ncause, or a necessary part of the cause, of the phenomenon._\n\nThese two are the simplest modes of singling out from the facts which\nprecede or follow a phenomenon, those with which it is connected by an\ninvariable law. Both are methods of elimination, their basis being, for\nthe method of agreement, that whatever can be eliminated _is not_, and\nfor that of difference, that whatever cannot be eliminated _is_\nconnected with the given phenomenon by a law. It is only, however, by\nthe method of difference, which is a method of artificial experiment\n(and by experiment we can introduce into the pre-existing facts a change\nperfectly definite), that we can, at least by direct experience, arrive\nwith certainty at causes. The method of agreement is chiefly useful as\npreliminary to and suggestive of applications of the method of\ndifference, or as an inferior resource in its stead, when, as in the\ncase of many spontaneous operations of nature, we have no power of\nproducing the phenomenon.\n\nWhen we have power to produce the phenomenon, but only by the agency,\nnot of a single antecedent, but of a combination, the method of\nagreement can be improved (though it is even then inferior to the direct\nmethod of difference) by a double process being used, each proof being\nindependent and corroborative of the other. This may be called the\nIndirect Method of Difference, or the Joint Method of Agreement and\nDifference, and its canon will be: _If two or more instances in which\nthe phenomenon occurs have only one circumstance in common, while two or\nmore instances in which it does not occur have nothing in common save\nthe absence of that circumstance, the circumstance in which alone the\ntwo sets of instances differ, is the effect, or the cause, or a\nnecessary part of the cause, of the phenomenon._\n\nThe fourth canon is that of the Method of Residues, viz.: _Subduct from\nany phenomenon such part as is known by previous inductions to be the\neffect of certain antecedents, and the residue of the phenomenon is the\neffect of the remaining antecedents._ This method is a modification of\nthe method of difference, from which it differs in obtaining, of the\ntwo required instances, only the positive instance, by observation or\nexperiment, but the negative, by deduction. Its certainty, therefore, in\nany given case, is conditional on the previous inductions having been\nobtained by the method of difference, and on there being in reality no\nremaining antecedents _besides_ those given as such.\n\nThe fifth canon is that of the Method of Concomitant Variations, viz.:\n_Whatever phenomenon varies in any manner whenever another phenomenon\nvaries in some particular manner, is either a cause or an effect of that\nphenomenon, or_ (since they may be effects of a common cause) _is\nconnected with it through some fact of causation._ Through this method\nalone can we find the laws of the permanent causes. For, though those of\nthe permanent causes whose influence is local may be escaped from by\nchanging the scene of the observation or experiment, many can neither be\nexcluded nor even kept isolated from each other; and, therefore, in such\ncases, the method of difference, which requires a negative instance, and\nthat of agreement, which requires the different instances to agree only\nin one circumstance, in order to prove causation, are (together with the\nmethods which are merely forms of these) equally inapplicable. But,\nthough many permanent antecedents insist on being always present, and\nnever present alone, yet we have the resource of making or finding\ninstances in which (the accompanying antecedents remaining unchanged)\ntheir influence is _varied_ and _modified_. This method can be used most\neffectually when the variations of the cause are variations of\nquantity; and then, if we know the absolute quantities of the cause and\nthe effect, we may affirm generally that, at least within our limits of\nobservation, the variations of the cause will be attended by similar\nvariations of the effect; it being a corollary from the principle of the\ncomposition of causes, that more of the cause is followed by more of the\neffect. This method is employed usually when the method of difference is\nimpossible; but it is also of use to determine according to what law the\nquantity or different relations of an effect ascertained by the method\nof difference follow those of the cause.\n\nThese four methods are the only possible modes of experimental enquiry.\nDr. Whewell attacks them, first, on the ground (and the canon of\nratiocination was attacked on the same) that they assume the reduction\nof an argument to formulae, which (with the procuring the evidence) is\nitself the chief difficulty. And this is in truth the case: but, to\nreduce an argument to a particular form, we must first know what the\nform is; and in showing us this, Inductive Logic does a service the\nvalue of which is tested by the number of faulty inductions in vogue.\nDr. Whewell next implies a complaint that no discoveries have ever been\nmade by these four methods. But, as the analogous argument against the\nsyllogism was invalidated by applying equally as against all reasoning,\nwhich must be reducible to syllogism, so this also falls by its own\ngenerality, since, if true against these methods, it must be true\nagainst all observation and experiment, since these must ever proceed by\none of the four. And, moreover, even if the four methods were not\nmethods of discovery, as they are, they would yet be subjects for logic,\nas being, at all events, the sole methods of Proof, which (unless Dr.\nWhewell be correct in his view that inductions are simply conceptions\nconsistent with the facts they colligate) is the principal topic of\nlogic.\n\nFOOTNOTE:\n\n[1] Chap. IX. consists of 'Miscellaneous Examples of the Four Methods,'\nwhich cannot be well represented in an abridged form.\n\n\n\n\nCHAPTER X.\n\nPLURALITY OF CAUSES, AND INTERMIXTURE OF EFFECTS.\n\n\nThe difficulty in tracing the laws of nature arises chiefly from the\nIntermixture of Effects, and from the Plurality of Causes. The\npossibility of the latter in any given case--that is, the possibility\nthat the same effect may have been produced by different causes--makes\nthe Method of Agreement (when applied to positive instances)\ninconclusive, if the instances are few; for that Method involves a tacit\nsupposition, that the same effect in different instances, which have\n_one_ common antecedent, must follow in all from the same cause, viz.\nfrom their common antecedent. When the instances are varied and very\nmany (how many, it is for the Theory of Probability to consider), the\nsupposition, that the presence in all of the common antecedent may be\nsimply a coincidence, is rebutted; and this is the sole reason why mere\n_number_ of instances, differing only in immaterial points, is of any\nvalue. As applied, indeed, to negative instances, i.e. to those\nresembling each other in the absence of a certain circumstance, the\nMethod of Agreement is not vitiated by Plurality of Causes. But the\nnegative premiss cannot generally be worked unless an affirmative be\njoined with it: and then the Method is the Joint Method of Agreement and\nDifference. Thus, to find the cause of Transparency, we do not enquire\nin what circumstance the numberless _non_-transparent objects agree; but\nwe enquire, first, in what the few transparent ones agree; and then,\nwhether all the opaque do not agree in the _absence_ of this\ncircumstance.\n\nNot only may there be Plurality of Causes, the whole of the effect being\nproduced now by one, now by another antecedent; but there may also be\nIntermixture of Effects, through the interference of different causes\nwith each other, so that part of the total effect is due to one, and\npart to another cause. This latter contingency, which, more than all\nelse, complicates, the study of nature, does not affect the enquiry into\nthose (the exceptional) cases, where, as in chemistry, the total effect\nis something quite different to the separate effects, and governed by\ndifferent laws. There the great problem is to discover, not the\nproperties, but the cause of the new phenomenon, i.e. the particular\nconjunction of agents whence it results; which could indeed never be\nascertained by specific enquiry, were it not for the peculiarity, not of\nall these cases (e.g. not of mental phenomena), but of many, viz. that\nthe heterogeneous effects of combined causes often reproduce, i.e. are\n_transformed into_ their causes (as, e.g. water into its components,\nhydrogen and oxygen). The great difficulty is _not_ there to discover\nthe properties of the new phenomenon itself, for these can be found by\nexperiment like the _simple_ effects of any other cause; since, in this\nclass of cases the effects of the separate causes give place to a new\neffect, and thereby cease to need consideration as separate effects. But\nin the far larger class of cases, viz. when the total effect is the\nexact sum of the separate effects of all the causes (the case of the\nComposition of Causes), at no point may it be overlooked that the effect\nis not simple but complex, the result of various separate causes, all of\nwhich are always tending to produce the whole of their several natural\neffects; having, it may be, their _effects_ modified, disturbed, or even\nprevented by each other, but always preserving their _action_, since\nlaws of causation cannot have exceptions.\n\nThese complex effects must be investigated by _deducing_ the law of the\neffect from the laws of the separate causes on the combination of which\nit depends. No inductive method is conclusive in such cases (e.g. in\nphysiology, or _a fortiori_, in politics and history), whether it be the\nmethod of simple observation, which compares instances, whether positive\nor negative, to see if they agree in the presence or the absence of one\ncommon antecedent, or the empirical method, which proceeds by directly\ntrying different combinations (either made or found) of causes, and\nwatching what is the effect. Both are inconclusive; the former, because\nan effect may be due to the concurrence of many causes, and the latter,\nbecause we can rarely know what all the coexisting causes are; and still\nmore rarely whether a certain portion (if not all) of the total effect\nis not due to these other causes, and not to the combination of causes\nwhich we are observing.\n\n\n\n\nCHAPTER XI.\n\nTHE DEDUCTIVE METHOD.\n\n\nThe deductive method is the main source of our knowledge of complex\nphenomena, and the sole source of all the theories through which vast\nand complicated facts have been embraced under a few simple laws. It\nconsists of processes of Induction, Ratiocination, and Verification.\nFirst, by one of the four inductive methods, the simple laws (whence may\nbe _deduced_ the complex) of each separate cause which shares in\nproducing the effect, must be first ascertained. This is difficult, when\nthe causes or rather tendencies cannot be observed singly. Such is the\ncase in physiology, since the different agencies which make up an\norganized body cannot be separated without destroying the phenomenon;\nconsequently there our sole resource is to produce experimentally, or\nfind (as in the case of diseases), pathological instances in which only\none organ at a time is affected. Secondly, when the laws of the causes\nhave been found, we calculate the effect of any given combination of\nthem by ratiocination, which may have (though not necessarily) among its\npremisses the theorems of the sciences of number and geometry. Lastly,\nas it might happen that some of the many concurring agencies have been\nunknown or overlooked, the conclusions of ratiocination must be\n_verified_; that is, it must be explained why they do not, or shown that\nthey do, accord with _observed_ cases of at least equal complexity, and\n(which is the most effectual test) that the empirical laws and\nuniformities, if any, arrived at by direct observation, can be deduced\nfrom and so accounted for by them, as, e.g. Kepler's laws of the\ncelestial motions by Newton's theory.\n\n\n\n\nCHAPTERS XII. AND XIII.\n\nTHE EXPLANATION AND EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.\n\n\nThe aim, in the deductive method, is either to discover the law of the\neffect, or to account for it by _explaining_ it, that is, by pointing\nout some more general phenomenon (though often less familiar to us) of\nwhich this is a case and a partial exemplification, or some laws of\ncausation which produce it by their joint or successive action. This\nexplanation may be made, either--1. By resolving the laws of the complex\neffect into its elements, which consist as well of the separate laws of\nthe causes which share in producing it, as also of their collocation,\ni.e. the fact that these separate laws have been so combined; or--2. By\nresolving the law which connects two links, not proximate, in a chain of\ncausation, into the laws which connect each link with the intermediate\nlinks; or--3. By the _subsumption_ or gathering up of several laws under\none which amounts to the sum of them all, and which is the recognition\nof the same sequence in different sets of instances. In the first two of\nthe processes, laws are resolved into others, which both extend to more\ncases, i.e. are more _general_, and also, as being laws of nature, of\nwhich the complex laws are but results, are more _certain_, i.e. more\n_unconditional_ and more _universally true_. In the third process, laws\nare resolved into others which are indeed more _general_, but not more\n_certain_, since they are in fact the same laws, and therefore, subject\nto the same exceptions.\n\nLiebig's researches, e.g. into the Contagious Influence of Chemical\nAction, and his Theory of Respiration, are among the finest examples,\nsince Newton's exposition of the law of gravitation, of the use of the\ndeductive method for _explanation_.[2] But the method is as available\nfor explaining mental as physical facts. It is destined to predominate\nin philosophy. Before Bacon's time deductions were accepted as\nsufficient, when neither had the premisses been established by proper\ncanons of experimental enquiry, nor the results tested by verification\nby specific experience. He therefore changed the method of the sciences\nfrom deductive to experimental. But, now that the principles of\ndeduction are better understood, it is rapidly reverting from\nexperimental to deductive. Only it must not be supposed that the\ninductive part of the process is yet complete. Probably, few of the\ngreat generalisations fitted to be the premisses for future deductions\nwill be found among truths now known. Some, doubtless, are yet unthought\nof; others known only as laws of some limited class of facts, as\nelectricity once was. They will probably appear first in the shape of\nhypotheses, needing to be tested by canons of legitimate induction.\n\nFOOTNOTE:\n\n[2] These, and other illustrations in chap. xiii., cannot be usefully\nrepresented in an abridged form.\n\n\n\n\nCHAPTER XIV.\n\nTHE LIMITS TO THE EXPLANATION OF LAWS OF NATURE. HYPOTHESES.\n\n\nThe constant tendency of science, operating by the Deductive Method, is\nto resolve all laws, even those which once seemed ultimate and not\nderivative, into others still more general. But no process of\n_resolving_ will ever reduce the number of ultimate laws below the\nnumber of those varieties of our feelings which are distinguishable in\nquality, and not merely in quantity or degree. The _ideal_ limit of the\nexplanation of natural phenomena is to show that each of these ultimate\nfacts has (since the differences in the different cases of it affect our\nsensations as differences in degree only, and not in quality) only one\nsort of cause or mode of production; and that all the seemingly\ndifferent modes of production or causes of it are resolvable into one.\nBut _practically_ this limit is never attained. Thus, though various\nlaws of Causes of Motion have been resolved into others (e.g. the fall\nof bodies to the earth, and the motions of the planets, into the one law\nof mutual attraction), many causes of it remain still unresolved and\ndistinct.\n\nHypotheses are made for the sake of this resolving and explaining of\nlaws. When we do not _know_ of any more general laws into which to\nresolve an uniformity, we then (either on no or on insufficient\nevidence) _suppose_ some, imagining either causes (as, e.g. Descartes\ndid the Vortices), or the laws of their operation (as did Newton\nrespecting the planetary central force); but we never feign both cause\nand law. The use of a hypothesis is to enable us to apply the Deductive\nMethod before the laws of the causes have been ascertained by Induction.\nIn those cases where a false law could not have led to a true result (as\nwas the case with Newton's hypothesis as to the law of the Attractive\nforce) the third part of the process in the Deductive Method, viz.\nVerification, which shows that the results deduced are true, amounts to\na complete induction, and one conforming to the canon of the Method of\nDifference. But this is the case only when either the cause is known to\nbe one given agent (and only its law is unknown), or to be one of\nseveral given agents.\n\nAn assumed cause, on the other hand, cannot be accepted as true simply\n_because_ it explains the phenomena (since two conflicting hypotheses\noften do this even originally, or, as Dr. Whewell himself allows, may at\nany rate by modifications be made to do it); nor _because_ it moreover\nleads to the prediction of other results which turn out true (since this\nshows only what was indeed apparent already from its agreement with the\nold facts, viz. that the phenomena are governed by laws partially\nidentical with the laws of other causes); nor _because_ we cannot\nimagine any other hypothesis which will account for the facts (since\nthere may be causes unknown to our present experience which will equally\naccount for them). The utility of such assumptions _of causes_ depends\non their being, in their own nature, _capable_ (as Descartes' Vortices\nwere not, though possibly the Luminiferous Ether may be) of being, at\nsome time or other, proved directly by independent evidence to be the\ncauses. And this was, perhaps, all that Newton meant by his _verae\ncausae_, which alone, he said, may be assigned as causes of phenomena.\nAssumptions of causes, which fulfil this condition, are, in science,\neven indispensable, with a view both to experimental inquiry, and still\nmore to the application of the Deductive Method. They may be accepted,\nnot indeed, as Dr. Whewell thinks they may be, as proof, but as\nsuggesting a line of experiment and observation which may result in\nproof. And this is actually the method used by practical men for\neliciting the truth from involved statements. They first extemporise,\nfrom a few of the particulars, a rude theory of the mode in which the\nevent happened; and then keep altering it to square with the rest of the\nfacts, which they review one by one.\n\nThe attempting, as in Geology, to conjecture, in conformity with known\nlaws, in what former collocations of known agents (though _not_ known to\nhave been formerly present) individual existing facts may have\noriginated, is not Hypothesis but Induction; for then we do not\n_suppose_ causes, but legitimately infer from known effects to unknown\ncauses. Of this nature was Laplace's theory, whether weak or not, as to\nthe origin of the earth and planets.\n\n\n\n\nCHAPTER XV.\n\nPROGRESSIVE EFFECTS, AND CONTINUED ACTION OF CAUSES.\n\n\nSometimes a complex effect results, not (as has been supposed in the\nlast four chapters) from several, but from _one_ law. The following is\nthe way.\n\nSome effects are instantaneous (e.g. some sensations), and are\nprolonged only by the prolongation of the causes; others are in their\nown nature permanent. In some cases of the latter class, the original is\nalso the proximate cause (e.g. Exposure to moist air is both the\noriginal and the proximate cause of iron rust). But in others of the\nsame class, the permanency of the effect is only the permanency of a\nseries of changes. Thus, e.g. in cases of Motion, the original force is\nonly the _remote_ cause of any link (after the very first) in the\nseries; and the motion immediately preceding it, being itself a compound\nof the original force and any retarding agent, is its _proximate_ cause.\nWhen the original cause is permanent as well as the effect (e.g. Suppose\na continuance of the iron's exposure to moist air), we get a progressive\nseries of effects arising from the cause's accumulating influence; and\nthe sum of these effects amounts exactly to what a number of\nsuccessively introduced similar causes would have produced. Such cases\nfall under the head of Composition of Causes, with this peculiarity,\nthat, as the causes (to regard them as plural) do not come into play all\nat once, the effect at each instant is the sum of the effects only of\nthe then acting causes, and the result will appear as an ascending\nseries. Each addition in such case takes place according to a fixed law\n(equal quantities in equal times); and therefore it can be computed\ndeductively. Even when, as is sometimes the case, a cause is at once\npermanent and progressive (as, e.g. the sun, by its position becoming\nmore vertical, increases the heat in summer) so that the quantities\nadded are unequal, the effect is still progressive, resulting from its\ncause's continuance and progressiveness combined.\n\nIn _all_ cases whatever of progressive effects, the succession not\nmerely between the cause and the effect, but also between the first and\nlatter stages of the effect, is uniform. Hence, from the invariable\nsequence of two terms (e.g. Spring and Summer) in a series going through\nany continued and uniform process of variation, we do not presume that\none is the cause and the others the effect, but rather that the whole\nseries is an effect.\n\n\n\n\nCHAPTER XVI.\n\nEMPIRICAL LAWS.\n\n\nEmpirical laws are derivative laws, of which the derivation is not\nknown. They are observed uniformities, which we compare with the result\nof any deduction to verify it; but of which the _why_, and also the\nlimits, are unrevealed, through their being, though resolvable, not yet\nresolved into the simpler laws. They depend usually, not solely on the\nultimate laws into which they are resolvable; but on those, together\nwith an ultimate fact, viz. the mode of coexistence of some of the\ncomponent elements of the universe. Hence their untrustworthiness for\nscientific purposes; for, till they have been resolved (and then a\nderivative law ceases to be empirical), we cannot know whether they\nresult from the different effects of one cause, or from effects of\ndifferent causes; that is, whether they depend on laws, or on laws and a\ncollocation. And if they thus depend on a collocation, they can be\nreceived as true only within the limits of time and space, and also\ncircumstance, in which they have been observed, since the mode of the\ncollocation of the permanent causes is not reducible to a law, there\nbeing no principle known to us as governing the distribution and\nrelative proportions of the primaeval natural agents.\n\nUniformities cannot be proved by the Method of Agreement alone to be\nlaws of causation; they must be tested by the Method of Difference, or\nexplained deductively. But laws of causation themselves are either\nultimate or derivative. Signs, previous to actual proof by _resolution_\nof them, of their being derivative, are, either that we can _surmise_\nthe existence of a link between the known antecedent and the consequent,\nas e.g. in the laws of chemical action; or, that the antecedent is some\nvery complex fact, the effects of which are probably (since most complex\ncases fall under the Composition of Causes) compounded of the effects of\nits different elements. But the laws which, though laws of causation,\nare thus presumably derivative laws only, need, equally with the\nuniformities which are not known to be laws of causation at all, to be\nexplained by deduction (which they then in turn verify), and are less\n_certain_ than when they have been resolved into the ultimate laws.\nConsequently they come under the definition of Empirical Laws, equally\nwith uniformities not known to be laws of causation. However, the latter\nare far more _uncertain_; for as, till they are resolved, we cannot tell\non how many collocations, as well as laws, they may not depend, we must\nnot rely on them beyond the exact limits in which the observations were\nmade. Therefore, the name _Empirical Laws_ will generally be confined\nhere to these.\n\n\n\n\nCHAPTER XVII.\n\nCHANCE, AND ITS ELIMINATION.\n\n\nEmpirical laws are certain only in those limits within which they have\nbeen _observed_ to be true. But, even within those limits, the\nconnection of two phenomena may, as the same effect may be produced by\nseveral different causes, be due to Chance; that is, it may, though\nbeing, as all facts must be, the result of some law, be a coincidence\nwhence, simply because we do not know all the circumstances, _we_ have\nno ground to infer an uniformity. When neither Deduction, nor the Method\nof Difference, can be applied, the only way of inferring that\ncoincidences are not casual, is by observing the frequency of their\noccurrence, not their absolute frequency, but whether they occur _more_\noften than chance would (that is, more often than the positive frequency\nof the phenomena would) account for. If, in such cases, we could ascend\nto the causes of the two phenomena, we should find at some stage some\ncause or causes common to both. Till we can do this, the fact of the\nconnection between them is only an empirical law; but still it is a law.\n\nSometimes an effect is the result partly of chance, and partly of law:\nviz. when the total effect is the result partly of the effects of casual\nconjunctions of causes, and partly of the effects of some constant cause\nwhich they blend with and modify. This is a case of Composition of\nCauses. The object being to find _how much_ of the result is\nattributable to a given constant cause, the only resource, when the\nvariable causes cannot be wholly excluded from the experiment, is to\nascertain what is the effect of all of _them_ taken together, and then\nto eliminate this, which is the casual part of the effect, in reckoning\nup the results. If the results of frequent experiments, in which the\nconstant cause is kept invariable, oscillate round one point, that\naverage or middle point is due to the constant cause, and the variable\nremainder to chance; that is, to causes the coexistence of which with\nthe constant cause was merely casual. The test of the sufficiency of\nsuch an induction is, whether or not an increase in the number of\nexperiments materially alters the average.\n\nWe can thus discover not merely _how much_ of the effect, but even\nwhether _any_ part of it whatever is due to a constant cause, when this\nlatter is so uninfluential as otherwise to escape notice (e.g. the\nloading of dice). This case of the Elimination of Chance is called _The\ndiscovery of a residual phenomenon by eliminating the effects of\nchance._\n\nThe mathematical doctrine of chances, or Theory of Probabilities,\nconsiders what deviation from the average chance by itself can possibly\noccasion in some number of instances smaller than is required for a fair\naverage.\n\n\n\n\nCHAPTER XVIII.\n\nTHE CALCULATION OF CHANCES.\n\n\nIn order to calculate chances, we must know that of several events one,\nand no more, must happen, and also not know, or have any reason to\nsuspect, which of them that one will be. Thus, with the simple knowledge\nthat the issue must be one of a certain number of possibilities, we\n_may_ conclude that one supposition is most probable _to us_. For this\npurpose it is not _necessary_ that specific experience or reason should\nhave also proved the occurrence of each of the several events to be, as\na fact, equally frequent. For, the probability of an event is not a\nquality of the event (since every event is in itself certain), but is\nmerely a name for the degree of ground _we_ have, with our present\nevidence, for expecting it. Thus, if we know that a box contains red,\nwhite, and black balls, though we do not know in what proportions they\nare mingled, we have numerically appreciable grounds for considering the\nprobability to be two to one against any one colour. Our judgment may\nindeed be said in this case to rest on the experience we have of the\nlaws governing the frequency of occurrence of the different cases; but\nsuch experience is universal and axiomatic, and not specific experience\nabout a particular event. Except, however, in games of chance, the\npurpose of which requires ignorance, such specific experience can\ngenerally be, and should be gained. And a slight improvement in the data\nprofits more than the most elaborate application of the calculus of\nprobabilities to the bare original data, e.g. to such data, when we are\ncalculating the credibility of a witness, as the proportion, even if it\ncould be verified, between the number of true and of erroneous\nstatements a man, _qua_ man, may be supposed to make during his life.\nBefore applying the Doctrine of Chance, therefore, we should lay a\nfoundation for an evaluation of the chances by gaining positive\nknowledge of the facts. Hence, though not a _necessary_, yet a most\nusual condition for calculating the probability of a fact is, that we\nshould possess a _specific_ knowledge of the proportion which the cases\nin which facts of the particular sort occur bear to the cases in which\nthey do not occur.\n\nInferences drawn correctly according to the Doctrine of Chances depend\nultimately on causation. This is clearest, when, as sometimes, the\nprobability of an event is deduced from the frequency of the occurrence\nof the causes. When its probability is calculated by merely counting and\ncomparing the number of cases in which it has occurred with those in\nwhich it has not, the law, being arrived at by the Method of Agreement,\nis only empirical. But even when, as indeed generally, the numerical\ndata are obtained in the latter way (since usually we can judge of the\nfrequency of the causes only through the medium of the empirical law,\nwhich is based on the frequency of the effects), still then, too, the\ninference really depends on causation alone. Thus, an actuary infers\nfrom his tables that, of any hundred living persons under like\nconditions, five will reach a given age, not simply because that\nproportion have reached it in times past, but because that fact shows\nthe existence there of a particular proportion between the _causes_\nwhich shorten and the causes which prolong life to the given extent.\n\n\n\n\nCHAPTER XIX.\n\nTHE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.\n\n\nDerivative laws are inferior to ultimate laws, both in the extent of the\npropositions, and in their degree of certainty within that extent. In\nparticular, the uniformities of coexistence and sequence which obtain\nbetween effects depending on different primaeval causes, vary along with\nany variation in the collocation of these causes. Even when the\nderivative uniformity is between different effects of the same cause, it\ncannot be trusted to, since one or more of the effects may be producible\nby another cause also. The effects, even, of derivative laws of\n_causation_ (resulting, i.e. the laws, from the combination of several\ncauses) are not independent of collocations; for, though laws of\ncausation, whether ultimate or derivative, are themselves universal,\nbeing fulfilled even when counteracted, the peculiar probability of the\nlatter kind of laws of causation being counteracted (as compared with\nultimate laws, which are liable to frustration only from one set of\ncounteracting causes) is fatal to the universality of the derivative\nuniformities made up of the sequences or coexistences of their effects;\nand, therefore, such derivative uniformities as the latter are to be\nrelied on only when the collocations are known not to have changed.\n\nDerivative laws, not causative, may certainly be extended beyond the\nlimits of observation, but only to cases _adjacent_ in time. Thus, we\nmay not predict that the sun will rise this day 20,000 years, but we can\npredict that it will rise to-morrow, on the ground that it has risen\nevery day for the last 5,000 years. The latter prediction is lawful,\n_because_, while we know the causes on which its rising depends, we\nknow, also, that there has existed hitherto no perceptible cause to\ncounteract them; and that it is opposed to experience that a cause\nimperceptible for so long should start into immensity in a day. If the\nuniformity is empirical only, that is, if we do not know the causes, and\nif we infer that they remain uncounteracted from their effects alone, we\nstill can extend the law to adjacent cases, but only to cases still more\nclosely adjacent in time; since we can know neither whether changes in\nthese unknown causes may not have occurred, nor whether there may not\nexist now an adverse cause capable after a time of counteracting them.\n\nAn empirical law cannot generally be extended, in reference to _Place_,\neven to adjacent cases (since there is no uniformity in the collocations\nof primaeval causes). Such an extension is lawful only if the new cases\nare _presumably_ within the influence of the same individual causes,\neven though unknown. When, however, the causes are known, and the\nconjunction of the effects is deducible from laws of the causes, the\nderivative uniformity may be extended over a wider space, and with less\nabatement for the chance of counteracting causes.\n\n\n\n\nCHAPTER XX.\n\nANALOGY.\n\n\nOne of the many meanings of _Analogy_ is, Resemblance of Relations. The\nvalue of an analogical argument in this sense depends on the showing\nthat, on the common circumstance which is the _fundamentum relationis_,\nthe rest of the circumstances of the case depend. But, generally, _to\nargue from analogy_ signifies to infer from resemblance in some points\n(not necessarily in _relations_) resemblance in others. Induction does\nthe same: but analogy differs from induction in not requiring the\nprevious proof, by comparison of instances, of the invariable\nconjunction between the known and the unknown properties; though it\nrequires that the latter should not have been ascertained to be\n_unconnected_ with the common properties.\n\nIf a fair proportion of the properties of the two cases are known, every\nresemblance affords ground for expecting an indefinite number of other\nresemblances, among which the property in question may perhaps be found.\nOn the other hand, every dissimilarity will lead us to expect that the\ntwo cases differ in an indefinite number of properties, including,\nperhaps, the one in question. These dissimilarities may even be such as\nwould, in regard to one of the two cases, imply the absence of that\nproperty; and then every resemblance, as showing that the two cases have\na similar nature, is even a reason for presuming against the presence of\nthat property. Hence, the value of an analogical argument depends on\nthe extent of ascertained resemblance as compared, first, with the\namount of ascertained difference, and next, with the extent of the\nunexplored region of unascertained properties.\n\nThe conclusions of analogy are not of direct use, unless when the case\nto which we reason is a case _adjacent_, not, as before, in time or\nplace, but in _circumstances_. Even then a complete induction should be\nsought after. But the great value of analogy, even when faint, in\nscience, is that it may suggest observations and experiments, with a\nview to establishing positive scientific truths, for which, however, the\nhypotheses based on analogies must never be mistaken.\n\n\n\n\nCHAPTER XXI.\n\nTHE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION.\n\n\nThe validity of all the four inductive methods depends on our assuming\nthat there is a cause for every event. The belief in this, i.e. in the\nlaw of universal causation, some affirm, is an instinct which needs no\nwarrant other than all men's disposition to believe it; and they argue\nthat to demand evidence of it is to appeal to the intellect from the\nintellect. But, though there is no appeal from the faculties all\ntogether, there may be from one to another: and, as belief is not proof\n(for it may be generated by association of ideas as well as by\nevidence), a case of belief does require to be proved by an appeal to\nsomething else, viz. to the faculties of sense and consciousness.\n\nThe law of universal causation is, in fact, a generalisation from many\npartial uniformities of sequence. Consequently, like these, which cannot\nhave been arrived at by any strict inductive method (for all such\nmethods presuppose the law of causation itself), it must itself be based\non inductions _per simplicem enumerationem_, that is, generalisations of\nobserved facts, from the mere absence of any known instances to the\ncontrary. This unscientific process is, it is true, usually delusive;\nbut only because, and in proportion as, the subject-matter of the\nobservation is limited in extent. Its results, whenever the number of\ncoincidences is too large for chance to explain, are empirical laws.\nThese are ordinarily true only within certain limits of time, place, and\ncircumstance, since, beyond these, there may be different collocations\nor counteracting agencies. But the subject-matter of the law of\nuniversal causation is so diffused that there is no time, place, or set\nof circumstances, at least within the portion of the universe within our\nobservation, and adjacent cases, but must prove the law to be either\ntrue or false. It has, in fact, never been found to be false, but in\never increasing multitudes of cases to be true; and phenomena, even\nwhen, from their rarity or inaccessibility, or the number of modifying\ncauses, they are not reducible _universally_ to any law, yet _in some\ninstances_ do conform to this. Thus, it may be regarded as coextensive\nwith all human experience, at which point the distinction between\nempirical laws and laws of nature vanishes. Formerly, indeed, it was\nonly a very high probability; but, with our modern experience, it is,\npractically, absolutely certain, and it confirms the particular laws of\ncausation, whence itself was drawn, when there seem to be exceptions to\nthem. All narrower inductions got by simple enumeration are unsafe,\ntill, by the application to them of the four methods, the supposition of\ntheir falsity is shown to contradict _this_ law, though it was itself\narrived at by simple enumeration.\n\n\n\n\nCHAPTER XXII.\n\nUNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION.\n\n\nBesides uniformities of succession, which always depend on causation,\nthere are uniformities of coexistence. These also, whenever the\ncoexisting phenomena are effects of causes, whether of one common cause\nor of several different causes, depend on the laws of their cause or\ncauses; and, till resolved into these laws, are mere empirical laws. But\nthere are some uniformities of coexistence, viz. those between the\nultimate properties of _kinds_, which do not depend on causation, and\ntherefore seem entitled to be classed as a peculiar sort of laws of\nnature. As, however, the presumption always is (except in the case of\nthose _kinds_ which are called _simple substances_ or elementary natural\nagents), that a thing's properties really depend on causes though not\ntraced, and we _never_ can be certain that they do not; we cannot safely\nclaim (though it _may_ be an ultimate truth) higher certainty than that\nof an empirical law for any generalisation about coexistence, that is to\nsay (since _kinds_ are known to us only by their properties, and,\nconsequently, all assertions about them are assertions about the\ncoexistence of something with those properties), about the properties of\n_kinds_.\n\nBesides, no rigorous inductive system can be applied to the uniformities\nof coexistence, since there is no general axiom related to them, as is\nthe law of causation to those of succession, to serve as a basis for\nsuch a system. Thus, Bacon's practical applications of his method\nfailed, from his supposing that we can have previous certainty that a\nproperty must have an invariable coexistent (as it must have an\ninvariable antecedent), which he called its form. He ought to have seen\nthat his great logical instrument, elimination, is inapplicable to\ncoexistences, since things, which agree in having certain apparently\nultimate properties, often agree in nothing else; even the properties\nwhich (e.g. Hotness) are effects of causes, generally being not\nconnected with the ultimate resemblances or diversities in the objects,\nbut depending on some outward circumstance.\n\nOur only substitute for an universal law of coexistence is the ancients'\ninduction _per enumerationem simplicem ubi non reperitur instantia\ncontradictoria_, that is, the improbability that an exception, if any\nexisted, could have hitherto remained unobserved. But the certainty thus\narrived at can be only that of an empirical law, true within the limits\nof the observations. For the coexistent property must be either a\nproperty of the _kind_, or an accident, that is, something due to an\nextrinsic cause, and not to the _kind_ (whose own indigenous properties\nare always the same). And the ancients' class of induction can only\nprove that _within given limits_, either (in the latter case) one\ncommon, though unknown, cause has always been operating, or (in the\nformer case) that no new _kind_ of the object has _as yet_ or _by us_\nbeen discovered.\n\nThe evidence is, of course (with respect both to the derivative and the\nultimate uniformities of coexistence), stronger in proportion as the law\nis more general; for the greater the amount of experience from which it\nis derived, the more probable is it that counteracting causes, or that\nexceptions, if any, would have presented themselves. Consequently, it\nneeds more evidence to establish an exception to a very general, than to\na special, empirical law. And common usage agrees with this principle.\nStill, even the greater generalisations, when not based on connection by\ncausation, are delusive, unless grounded on a separate examination of\n_each_ of the included _infimae species_, though certainly there is a\nprobability (no more) that a sort of parallelism will be found in the\nproperties of different kinds; and that their degree of unlikeness in\none respect bears some proportion to their unlikeness in others.\n\n\n\n\nCHAPTER XXIII.\n\nAPPROXIMATE GENERALISATIONS, AND PROBABLE EVIDENCE.\n\n\nThe inferences called _probable_ rest on approximate generalisations.\nSuch generalisations, besides the inferior assurance with which they\ncan be applied to individual cases, are _generally_ almost useless as\npremisses in a deduction; and therefore in _Science_ they are valuable\nchiefly as steps towards universal truths, the discovery of which is its\nproper end. But in _practice_ we are forced to use them--1, when we have\nno others, in consequence of not knowing what general property\ndistinguishes the portion of the class which have the attribute\npredicated, from the portion which have it not (though it is true that\nwe can, in such a case, usually obtain a collection of exactly true\npropositions by subdividing the class into smaller classes); and, 2,\nwhen we _do_ know this, but cannot examine whether that general property\nis present or not in the individual case; that is, when (as usually in\n_moral_ inquiries) we could get universal majors, but not minors to\ncorrespond to them. In any case an approximate generalisation can never\nbe more than an empirical law. Its authority, however, is less when it\ncomposes the whole of our knowledge of the subject, than when it is\nmerely the most available form of our knowledge for practical guidance,\nand the causes, or some certain mark of the attribute predicated, being\nknown to us as well as the effects, the proposition can be tested by our\ntrying to deduce it from the causes or mark. Thus, our belief that most\nScotchmen can read, rests on our knowledge, not merely that most\nScotchmen that we have known about could read, but also that most have\nbeen at efficient schools.\n\nEither a single approximate generalisation may be applied to an\nindividual instance, or several to the same instance. In the former\ncase, the proposition, as stating a general average, must be applied\nonly to average cases; it is, therefore, generally useless for guidance\nin affairs which do not concern large numbers, and simply supplies, as\nit were, the first term in a series of approximations. In the latter\ncase, when two or more approximations (not connected with each other)\nare _separately_ applicable to the instance, it is said that two (or\nmore) _probabilities are joined by addition_, or, that there is a\n_self-corroborative chain_ of evidence. Its type is: Most A are B; most\nC are B; this is both an A and a C; therefore it is probably a B. On the\nother hand, when the subsequent approximation or approximations is or\nare applicable only by virtue of the application of the first, this is\njoining two (or more) probabilities, _by way of Deduction_, which\nproduces a _self-infirmative chain_; and the type is: Most A are B; most\nC are A; this is a C; therefore it is probably an A; therefore it is\nprobably a B. As, in the former case, the probability increases at each\nstep, so, in the latter, it progressively dwindles. It is measured by\nthe probability arising from the first of the propositions, abated in\nthe ratio of that arising from the subsequent; and the error of the\nconclusion amounts to the aggregate of the errors of all the premisses.\n\nIn two classes of cases (exceptions which prove the rule) approximate\ncan be employed in deduction as usefully as complete generalisations.\nThus, first, we stop at them sometimes, from the inconvenience, not the\nimpossibility, of going further; and, by adding provisos, we might\nchange the approximate into an universal proposition; the sum of the\nprovisos being then the sum of the errors liable to affect the\nconclusion. Secondly, they are used in Social Science with reference to\nmasses with _absolute_ certainty, even without the addition of such\nprovisos. Although the premisses in the Moral and Social Sciences are\nonly probable, these sciences differ from the exact only in that we\ncannot decipher so many of the laws, and not in the conclusions that we\ndo arrive at being less scientific or trustworthy.\n\n\n\n\nCHAPTER XXIV.\n\nTHE REMAINING LAWS OF NATURE.\n\n\nThere are, we have seen, five facts, one of which every proposition must\nassert, viz. Existence, Order in Place, Order in Time, Causation, and\nResemblance. Causation is not fundamentally different from Coexistence\nand Sequence, which are the two modes of Order in Time. They have been\nalready discussed. Of the rest, Existence, if of things in themselves,\nis a topic for Metaphysics, Logic regarding the existence of _phenomena_\nonly; and as this, when it is not perceived directly, is proved by\nproving that the unknown phenomenon is connected by _succession or\ncoexistence_ with some known phenomenon, the fact of Existence is not\namenable to any _peculiar_ inductive principles. There remain\nResemblance and Order in Place.\n\nAs for Resemblance, Locke indeed, and, in a more unqualified way, his\nschool, asserted that all reasoning is simply a comparison of two ideas\nby means of a third, and that knowledge is only the perception of the\nagreement or disagreement, that is, the resemblance or dissimilarity, of\ntwo ideas: they did not perceive, besides erring in supposing ideas, and\nnot the phenomena themselves, to be the subjects of reasoning, that it\nis only sometimes (as, particularly, in the sciences of Quantity and\nExtension) that the agreement or disagreement of two things is the one\nthing to be established. Reasonings, however, about _Resemblances_,\nwhenever the two things cannot be directly compared by the virtually\nsimultaneous application of our faculties to each, do agree with Locke's\naccount of reasoning; being, in fact, simply such a comparison of two\nthings through the medium of a third. There are laws or formulae for\nguiding the comparison; but the only ones which do not come under the\nprinciples of Induction already discussed, are the mathematical axioms\nof Equality, Inequality, and Proportionality, and the theorems based on\nthem. For these, which are true of all phenomena, or, at least, without\ndistinction of origin, have no connection with laws of Causation,\nwhereas all other theorems asserting resemblance have, being true only\nof special phenomena originating in a certain way, and the resemblances\nbetween which phenomena must be derived from, or be identical with, the\nlaws of their causes.\n\nIn respect to Order in Place, as well as in respect to Resemblance, some\nmathematical truths are the only general propositions which, as being\nindependent of Causation, require separate consideration. Such are\ncertain geometrical laws, through which, from the position of certain\npoints, lines, or spaces, we infer the position of others, without any\nreference to their physical causes, or to their special nature, except\nas regards position or magnitude. There is no other peculiarity as\nrespects Order in Place. For, the Order in Place of effects is of course\na mere consequence of the laws of their causes; and, as for primaeval\ncauses, in _their_ Order in Place, called their _collocation_, no\nuniformities are traceable.\n\nHence, only the methods of Mathematics remain to be investigated; and\nthey are partly discussed in the Second Book. The directly inductive\ntruths of Mathematics are few: being, first, certain propositions about\nexistence, tacitly involved in the so-called definitions; and secondly,\nthe axioms, to which latter, though resting only on induction, _per\nsimplicem enumerationem_, there could never have been even any apparent\nexceptions. Thus, every arithmetical calculation rests (and this is what\nmakes Arithmetic the type of a deductive science) on the evidence of the\naxiom: The sums of equals are equals (which is coextensive with nature\nitself)--combined with the definitions of the numbers, which are\nseverally made up of the explanation of the name, which connotes the way\nin which the particular agglomeration is composed, and of the assertion\nof a fact, viz. the physical property so connoted.\n\nThe propositions of Arithmetic affirm the modes of formation of given\nnumbers, and are true of all things under the condition of being divided\nin a particular way. Algebraical propositions, on the other hand, affirm\nthe equivalence of different modes of formation of numbers generally,\nand are true of all things under condition of being divided in _any_\nway.\n\nThough the laws of Extension are not, like those of Number, remote from\nvisual and tactual imagination, Geometry has not commonly been\nrecognised as a strictly physical science. The reason is, first, the\npossibility of collecting its facts as effectually from the ideas as\nfrom the objects; and secondly, the illusion that its ideal data are not\nmere hypotheses, like those in now deductive physical sciences, but a\npeculiar class of realities, and that therefore its conclusions are\n_exceptionally_ demonstrative. Really, all geometrical theorems are laws\nof external nature. They might have been got by generalising from actual\ncomparison and measurement; only, that it was found practicable to\ndeduce them from a few obviously true general laws, viz. The sums of\nequals are equals; things equal to the same thing are equal to one\nanother (which two belong to the Science of Number also); and, thirdly\n(what is no merely verbal definition, though it has been so called):\nLines, surfaces, solid spaces, which can be so applied to one another as\nto coincide, are equal. The rest of the premisses of Geometry consist of\nthe so-called definitions, which assert, together with one or more\nproperties, the real existence of objects corresponding to the names to\nbe defined. The reason why the premisses are so few, and why Geometry is\nthus almost entirely deductive, is, that all questions of position and\nfigure, that is, of quality, may be resolved into questions of quantity\nor magnitude, and so Geometry may be reduced to the one problem of the\nmeasurement of magnitudes; that is, to the finding the equalities\nbetween them.\n\nMathematical principles can be applied to other sciences. All causes\noperate according to mathematical laws; an effect being ever dependent\non the quantity or a function of the agent, and generally on its\nposition too. Mathematical principles cannot, indeed, as M. Comte has\nwell explained, be usefully applied to physical questions, whenever the\ncauses are either too inaccessible for their numerical laws to be\nascertained, or are too complex for _us_ to compute the effect, or are\never fluctuating. And, in proportion as physical questions cease to be\nabstract and hypothetical, mathematical solutions of them become\nimperfect. But the great value of mathematical training is, that we\nlearn to use its _method_ (which is the most perfect type of the\nDeductive Method), that is, we learn to employ the laws of simpler\nphenomena to explain and predict those of the more complex.\n\n\n\n\nCHAPTER XXV.\n\nTHE GROUNDS OF DISBELIEF.\n\n\nThe result of examining evidence is not always belief, or even\nsuspension of judgment, but is sometimes positive disbelief. This can\nensue only when the affirmative evidence does not amount to full proof,\nbut is based on some approximate generalisation. In such cases, if the\nnegative evidence consist of a stronger, though still only an\napproximate, generalisation, we think the fact improbable, and\ndisbelieve it provisionally; but if of a complete generalisation based\non a rigorous induction, it is disbelieved by us totally, and thought\nimpossible. Hence, Hume declared miracles incredible, as being, he\nconsidered, contrary to a complete induction. Now, it is true that _in\nthe absence of any adequate counteracting cause_, a fact contrary to a\ncomplete induction is incredible, whatever evidence it may be grounded\non; unless, indeed, the evidence go to prove the supposed law\ninconsistent with some better established one. But when a miracle is\nasserted, the presence of an adequate counteracting cause _is_ asserted,\nviz. a direct interposition of an act of the will of a Being having\npower over nature. Therefore, all that Hume proved is, that we cannot\nbelieve in a miracle unless we believe in the power, and _the will_, of\nthe Deity to interfere with existing causes by introducing new ones; and\nthat, in default of such belief, not the most satisfactory evidence of\nour senses or of testimony can hinder us from holding a seeming miracle\nto be merely the result of some unknown natural cause. The argument of\nDr. Campbell and others against Hume, however, is untenable, viz. that,\nas we do not disbelieve an alleged fact (which may be something\nconforming to the uniform course of experience) merely because the\nchances are against it, therefore we need never disbelieve any fact\nsupported by credible testimony (even if contrary to the uniform course\nof experience). But this is to confound _improbability before the fact_,\nwhich is _not_ always a ground for disbelief, with _improbability after\nthe fact_, which always is.\n\nFacts which conflict with special laws of causation are only improbable\nbefore the fact; that is, our disbelief depends on the improbability\nthat there could have been present, without our knowledge, at the time\nand place of the event, an adequate counteracting cause. So, too, with\nfacts which conflict with the properties of _kinds_ (which are\nuniformities of mere coexistence not proved to be dependent on\ncausation), that is, facts which assert the existence of a new _kind_;\nsuch facts we disbelieve only if, the generalisation being sufficiently\ncomprehensive, some properties are said to have been found in the\nsupposed new _kind_ disjoined from others which always have been known\nto accompany them. When the assertion would amount, if admitted, only to\nthe existence of an unknown cause or an anomalous _kind_,\n_unconformable_, but, as Hume puts it, _not contrary_ to experience, in\ncircumstances so little explored, that it is credible hitherto unknown\nthings may there be found, and when prejudice cannot have tempted to the\nassertion, one ought neither to admit nor to reject the testimony, but\nto suspend judgment till it be confirmed or disproved from other\nsources. Only facts, then, which are contradictory to the laws of\nNumber, Extension, and Universal Causation (since these know no\ncounteraction or anomaly), or to laws nearly as general, are improbable\nafter, as well as before the fact, and only these we should term\n_absolutely impossible_, calling other facts _improbable_ only, or, at\nmost, _impossible in the circumstances of the case_.\n\nBetween these two species of improbabilities lie _coincidences_; that\nis, combinations of chances presenting some unexpected regularity\nassimilating them in so far to the results of law. It was thought by\nd'Alembert that, though regular combinations are as probable as others\naccording to the mathematical theory, some physical law prevents them\nfrom occurring so often. Now, stronger testimony may indeed be needed\nto support the assertion of such a combination as, e.g. ten successive\nthrows of sixes at dice, because such a regular series is more likely\nthan an irregular series to be the result of design; and because even\nthe desire to excite wonder is likely to tempt men to assert the\noccurrence falsely, though this probability must be estimated afresh in\nevery instance. But though such a series _seems_ peculiarly improbable,\nit is only because the comparison is tacitly made, not between it and\nany one particular previously fixed series of throws, but between all\nregular and all irregular successions taken together. The fact is not in\nitself more improbable; and no stronger evidence is needed to give it\ncredibility, apart from the reasons above mentioned, than in the case of\nordinary events.\n\n\n\n\nBOOK IV.\n\nOPERATIONS SUBSIDIARY TO INDUCTION.\n\n\n\n\nCHAPTER I.\n\nOBSERVATION AND DESCRIPTION.\n\n\nThe mental process which Logic deals with, viz. the investigation of\ntruth by means of evidence, is always a process of Induction. Since\nInduction is simply the extension to a class of something observed to be\ntrue of certain members of it, Observation is the first preliminary to\nit. It is, therefore, right to consider, not indeed how or what to\nobserve (for this belongs to the art of Education), but under what\nconditions observation is to be relied on. The sole condition is, that\nthe supposed observation should really be an observation, and not an\ninference, whereas it is usually a compound of both, there being, in our\npropositions, besides observation which relates only to the sensations,\nan inference from the sensations to the objects themselves. Thus\nso-called errors of sense are only erroneous inferences from sense. The\nsensations themselves must be genuine; but, as they generally arise on a\ncertain arrangement of outward objects being present to the organs, we,\nas though by instinct, infer this arrangement even when not existing.\nThe sole object, then, of the logic of observation, is to separate the\ninferences from observation from the observations themselves, the only\nthing really observed by the mind (to waive the metaphysical problem as\nto the _perception_ of objects) being its own feelings or states of\nconsciousness, outward, viz. Sensations, and inward, viz. Thoughts,\nEmotions, and Volitions.\n\nAs in the simplest observation much is inference, so, in describing an\nobserved fact, we not merely describe the fact, but are always forced to\nclass it, affirming the resemblance, in regard of whatever is the ground\nof the name being given, between it and all other things denoted by the\nname. The resemblance is sometimes perceived by direct comparison of the\nobjects together; sometimes (as, e.g. in the description of the earth's\nfigure as globular and so forth) it is inferred through intermediate\nmarks, i.e. deductively. When a hypothesis is made (e.g. by Kepler, as\nto the figure of the earth's orbit), and then verified by comparison\nwith actual observations, Dr. Whewell calls the process Colligation of\nFacts by appropriate Conceptions, and affirms it to be the whole of\nInduction. But this also is only description, being really the ordinary\nprocess of ascertaining resemblance by a comparison of phenomena; and,\nthough subsidiary to Induction, it is not itself Induction at all.\n\n\n\n\nCHAPTER II.\n\nABSTRACTION, OR THE FORMATION OF CONCEPTIONS.\n\n_This Chapter is a digression._\n\n\nAbstract Ideas, that is, General Conceptions, certainly do exist,\nhowever Metaphysics may decide as to their composition. They\n_represent_ in our minds the whole classes of things called by the\ngeneral names; and, being implied in the mental operation whereby\nclasses are formed, viz. in the comparison of phenomena, to ascertain in\nwhat they agree, cannot be dispensed with in induction, since such a\ncomparison is a necessary preliminary to an induction, and more than two\nobjects cannot well be compared without a type, in which capacity\nconceptions serve.\n\nBut, though implied in the comparison, it does not follow that, as Dr.\nWhewell supposes, they must have existed in the mind prior to\ncomparison. Sometimes, but only sometimes, they are pre-existent to the\ncomparison of the particular facts in question, being, as was Kepler's\nhypothesis of an ellipse, familiar conceptions borrowed from different\nfacts, and _superinduced_, to use Dr. Whewell's expression, on the facts\nin question. But even such conceptions are the results of former\ncomparisons of individual facts. And much more commonly (and these are\nthe more difficult cases in science) conceptions are not pre-existent\neven in this sense; but they have to be got (e.g. the Idea of Polarity)\nby abstraction, that is, by comparison, from among the very phenomena\nwhich they afterwards serve to arrange, or, as Dr. Whewell says, to\n_connect_. They seem to be pre-existent; but this is only because the\nmind keeps ever forming conceptions from the facts, which at the time\nare before it, and then tentatively applies these conceptions (which it\nis always remodelling, dropping some which are found not to suit\nafter-found facts, and generalising others by a further effort of\nabstraction) as types of comparison for phenomena subsequently\npresented to it; so that, being found in these later stages of the\ncomparison already in the mind, they appear in the character simply of\ntypes, and not as being also themselves results of comparison. Really\nthey are always both; and the term _comparison_ expresses as well their\norigin as (and this far more exactly than to _connect_ or to\n_superinduce_) their function.\n\nDr. Whewell says that conceptions must be _appropriate_ and _clear_.\nThey must, indeed, be appropriate relatively to the purpose in view (for\nappropriateness is only relative); but they cannot avoid being\nappropriate (though one may be more so than another) if our comparison\nof the objects has led to a conception corresponding to any real\nagreement in the facts: the ancients' and schoolmen's conceptions were\noften absolutely inappropriate, because grounded on only apparent\nagreement. So, again, they must be _clear_ in the following sense; that\nis to say, a _sufficient number_ of facts must have been _carefully\nobserved_, and accurately _remembered_. It is also a condition (and one\nimplied in the latter qualities) of clearness, that the conception\nshould be _determinate_, that is, that we should know precisely what\nagreements we include in it, and never vary the connotation except\nconsciously.\n\nActivity, carefulness, and accuracy in the observing and comparing\nfaculties are therefore needed; the first quality to produce\nappropriateness, and the latter two, clearness. Moreover, _scientific\nimagination_, i.e. the faculty of mentally arranging known elements into\nnew combinations, is necessary for forming true conceptions; and the\nmind should be stored with previously acquired conceptions, kindred to\nthe subject of inquiry, since a comparison of the facts themselves often\nfails to suggest the principle of their agreement; just as, in seeking\nfor anything lost, we often have to ask ourselves in what places it may\nbe hid, that we may search for it there.\n\n\n\n\nCHAPTER III.\n\nNAMING AS SUBSIDIARY TO INDUCTION.\n\n\nAs reasoning is from particulars to particulars, and consists simply in\nrecognising one fact as a mark of another, or a mark of a mark of\nanother, the only necessary conditions of the exertion of the reasoning\npower are senses, to perceive that two facts are conjoined; and\nassociation, as the law by which one of the two facts raises up the idea\nof the other. The existence of artificial signs is not a third\n_necessary_ condition. It is only, however, the rudest inductions (and\nof such even brutes are capable) that can be made without language or\nother artificial signs. Without such we could avail ourselves but little\nof the experience of others; and (except in cases involving our intenser\nsensations or emotions) of none of our own long past experience. It is\nonly through the medium of such permanent signs that we can register\nuniformities; and the existence of uniformities is necessary to justify\nan inference, even in a single case, and they can be ascertained once\nfor all.\n\nGeneral names are not, as some have argued, a mere contrivance to\neconomise words. For, if there were a name for every individual object,\nbut no general names, we could not record one uniformity, or the result\nof a single comparison. To effect this, all indeed, that are\n_indispensable_, are the abstract names of attributes; but, in fact, men\nhave always given general names to objects also.\n\n\n\n\nCHAPTER IV.\n\nTHE REQUISITES OF A PHILOSOPHICAL LANGUAGE, AND THE PRINCIPLES OF\nDEFINITION.\n\n\nConcrete general names (and the meaning of abstract names depends on the\nconcrete) should have a fixed and knowable connotation. This is easy\nenough when, as in the case of new technical names, we choose the\nconnotation for ourselves; but it is hard when, as generally happens\nwith names in common use, the same name has been applied to different\nobjects, from only a vague feeling of resemblance. For, then, after a\ntime, general propositions are made, in which predicates are applied to\nthose names; and these propositions make up a loose connotation for the\nclass name, which, and the abstract at about this same period formed\nfrom it, are consequently never understood by two people, or by the same\nperson at different times, in the same way. The logician has to fix this\nfluctuating connotation, but so that the name may, if possible, still\n_denote_ the things of which it is currently affirmed. To effect this\ndouble object (which is called, though improperly, defining _not the\nname but the thing_), he must select from the attributes in which the\ndenoted objects agree, choosing, as the common properties are always\nmany, and, in a _kind_, innumerable, those which are familiarly\npredicated of the class, and out of them, if possible, or otherwise,\neven in preference to them, the ones on which depend, or which are the\nbest marks of, those thus familiarly predicated. To do this\nsuccessfully, presumes a knowledge of all the common properties of the\nclass, and the relations between them of causation and dependence. Hence\nthe discussion of non-verbal definitions (which Dr. Whewell calls the\nExplication of Conceptions) is part of the business of discovery. Hence,\ntoo, disputes in science have often assumed the form of a battle of\ndefinitions; such definitions being not arbitrary, but made with a view\nto some tacitly assumed principle needing expression.\n\nWe ought, if possible, to define in consonance with the denotation. But\nsometimes this is impossible, through the name having accumulated\n_transitive_ applications, in its gradual extension from one object, in\nrelation to which it connotes one property, to another which resembles\nthe former, but in quite a different attribute. These _transitive_\napplications, even when found to correspond in different languages, may\nhave arisen, not from any common quality in the objects, but from some\nassociation of ideas founded on the common nature and condition of\nmankind. When the association is so natural and habitual as to become\nvirtually indissoluble, the _transitive_ meanings are apt to coalesce in\none complex conception; and every new transition becomes a more\ncomprehensive generalisation of the term in question. In such cases the\nancients and schoolmen did not suspect, what otherwise they carefully\nwatched for, viz. ambiguities: not Plato, though his Comparisons and\nAbstractions preparatory to Induction are perfect; not even Bacon, in\nhis speculations on Heat. Hence have sprung the various vain attempts to\ntrace a common idea in all the uses of a word, such as _Cause_\n(Efficient, Material, Formal, and Final _Cause_), _the Good_, _the Fit_.\n\nWhen a term is applied to many different objects agreeing _all_ only in\n_one_ quality (e.g. things _beautiful_, in _agreeableness_), though\n_most_ agree in something besides, it is better to exclude part of the\ndenotation than of the connotation, however indistinct: else language\nceases to keep alive old experience, alien perhaps to present\ntendencies. In any case, words are always in danger of losing part of\ntheir connotation. For, just one or two out of a complex cluster of\nideas, and sometimes merely the look or sound of the word itself, is\noften all that is absolutely necessary for the suggesting another set of\nideas to continue the process of thought; and consequently, some\nmetaphysicians have even fancied that all reasoning is but the\nmechanical use of terms according to a certain form. If persons be not\nof active imaginations, the only antidote against the propensity to let\nslip the connotation of names, is the habit of predicating of them the\nproperties connoted; though even the propositions themselves, as may be\nseen from the way in which maxims of Religion, Ethics, and Politics are\nused, are often repeated merely mechanically, not being questioned, but\nalso not being felt. Much of our knowledge recorded in words is ever\noscillating between its tendency, in consequence of different\ngenerations attending exclusively to different properties in names, to\nbecome partially dormant, and the counter-efforts of individuals, at\ntimes, to revive it by tracing the forgotten properties historically in\nthe almost mechanically repeated formulas of propositions; and, when\nthey have been there rediscovered, promulgating them, not as\ndiscoveries, but with authority as what men still profess to believe.\nThe danger is, lest the formula itself be dismissed by clear-headed\nnarrow-minded logicians, and the connotation fixed by them (in order\nthat the denotation may be extended) in accordance with the present use\nof the term. Then, if the truths be at any time rediscovered, the\nprejudice is against them as novelties. The _selfish_ theory of morals\npartly fell because the inconsistency of received formulas with it\nprompted a reconsideration of its basis. What would have been the result\nif the formulas attaching odium to selfishness, praise to\nself-sacrifice, had been dismissed, if this indeed had been possible!\nLanguage, in short, is the depositary of all experience, which, being\nthe inheritance of posterity, we have a right to vary, but none to\ncurtail. We may improve the conclusions of our ancestors; we should not\nlet drop any of their premisses; we may alter a word's connotation; but\nwe must not destroy part of it.\n\n\n\n\nCHAPTER V.\n\nTHE NATURAL HISTORY OF THE VARIATION IN THE MEANING OF TERMS.\n\n\nThe connotation of names shifts not only by reason of gradual\ninattention to some of the common properties, which, if language were\nruled by convention alone, would be in their entirety both the perpetual\nand the sole constituents of the connotation; but also from the\nincorporation in the connotation, in addition to these, and often,\nfinally, to the _exclusion_ of them altogether, of other circumstances\nat first only casually associated with it. These collateral associations\nare the cause why there are so few exact synonymes; and why the\ndictionary meaning, or Definition, is so bad a guide to its uses, as\ncompared with its history, since the latter explains the law of the\nsuccession by showing the causes which determined the successive uses.\n\nTwo counter-movements are always going on in language. One is\ngeneralisation, by which words are ever losing part of their\nconnotation, and becoming more general. This arises, partly from men,\nsuch as historians and travellers, using words, especially those\nexpressing complicated mental and social facts strange to them, in a\nloose sense, in ignorance of the true connotation; partly, from known\nthings multiplying faster than names for them; partly, also, from the\nwish to give people some notion of a new object by reference to a known\nthing resembling it however slightly. The other movement is\nspecialisation; and by it words (even the same words which, as, e.g.\n_pagan_ and _villain_, later get generalised in a new direction) are\never taking a fresh connotation, through their denotation being\ndiminished. Specialisations often occur even in scientific nomenclature,\na word which expressed general characters becoming confined to a\nspecific substance in which these characters are predominant. So it is\nwhen any set of persons has to think of one species oftener than of any\nother contained in the genus: e.g. some sportsmen mean partridges by the\nterm _birds_. But, as ideas of our pleasures and pains and their\nsupposed causes, cling, most of all, by association to what they have\nbeen once connected with, the great source of specialisation is the\naddition of the ideas of agreeableness or painfulness, and approbation\nor censure, to the connotation. And hence arises the fallacy of\n_question-begging_ names referred to later on.\n\nIt is the business of logicians not to ignore, for they cannot prevent,\ntransformations of terms in common use, but to trace and embody them,\nand men's half unconscious reasons for them, in distinct definitions.\n\n\n\n\nCHAPTER VI.\n\nTERMINOLOGY AND NOMENCLATURE.\n\n\nNot only must words have a fixed and knowable meaning; but also, no\nimportant meaning should be without its word: that is, there should be a\nname for everything which we have often to make assertions about. There\nshould be, therefore, first, names suited to describe all the individual\nfacts; secondly, a name for every important common property detected by\ncomparing those facts; and, thirdly, a name for every _kind_.\n\nFirst, it conduces to brevity and clearness to have separate names for\nthe oft-recurring combinations of feelings; but, as these can be defined\nwithout reference back to the feelings themselves, it is _enough_ for a\n_descriptive_ terminology, if there be a name for every variety of\nelementary feeling, since none of these can be defined, or indicated to\na person, except either by his having the sensation itself, or being\nreferred through a known mark to his remembrance of it. The meaning of\nthe name when given to a feeling is fixed, in the first instance, by\nconvention, and must be associated _immediately_, not through the usage\nof ordinary language, with the feeling, so that it may at once recall\nthe latter. But even among the elementary feelings, those purely mental,\nand also sensations, such as those from disease, the identity of which\nin different persons cannot be determined, cannot be exactly\n_described_. It is only the impressions on the outward senses, or those\ninward feelings connected uniformly with outward objects (and,\nconsequently, sciences, such as botany, conversant with outward\nobjects), which are susceptible of an exact descriptive language.\n\nSecondly, there must also be a separate name for every important common\nproperty recognised through that comparison of observed instances which\nis preparatory to induction (including names for the classes which we\nartificially construct in virtue of those properties). For, although a\ndefinition would often convey the meaning, both time and space are\nsaved, perspicuity promoted, and the attention excited and concentrated,\nby giving a brief and compact name to each of the new _general\nconceptions_, as Dr. Whewell calls them, that is, the new results of\nabstraction. Thenceforward the name nails down and clenches the\nunfamiliar combination of ideas, and suggests its own definition.\n\nThirdly, as, besides the artificial classes which are marked out from\nneighbouring classes by definite properties to be arrived at by\nabstraction, there are classes, viz. _kinds_, distinguished severally by\nan unknown multitude of independent properties (and about which classes\ntherefore many assertions will be made), there must be a name for every\n_kind_. That is, besides a terminology, there must be a nomenclature,\ni.e. a collection of the names of all the lowest _kinds_, or _infimae\nspecies_. The Linnaean arrangements of plants and animals, and the French\nof chemistry, are nomenclatures. The peculiarity of a name which belongs\nto a nomenclature is, not that its meaning resides in its denotation\ninstead of its connotation (for it resides in its connotation, like that\nof other concrete general names); but that, besides connoting certain\nattributes which its definition explains, it also connotes that these\nattributes are distinctive of a _kind_; and this fact its definition\ncannot explain.\n\nA philosophical language, then, must possess, first, precision, and next\n(the subject of the present chapter), completeness. Some have argued\nthat, in addition, names are fitted for the purposes of thought in\nproportion as they approximate to mere symbols in compactness, through\nmeaninglessness, and capability of use as counters without reference to\nthe various objects which, though utterly different, they may thus at\ndifferent times equally well represent. Such are, indeed, the qualities\nenabling us to employ the figures of arithmetic and the symbols of\nalgebra perfectly mechanically according to general technical rules.\nBut, in the first place, in our direct inductions, at all events,\ndepending as they do on our perception of the particulars of the\nagreement and difference of the phenomena, we could never dispense with\na distinct mental image of the latter. Further, even in deduction,\nthough a syllogism is conclusive from its mere form, if the terms are\nunambiguous, yet the _practical_ validity of the reasoning depends on\nthe hypothesis that no counteracting cause has interfered with the truth\nof the premisses. We can assure ourselves of this only by studying the\nphenomena at every step. For it is only in geometry and algebra that\nthere is no danger from the Composition of Causes, or the superseding of\none set of laws by another; and that, therefore, the propositions are\ncategorically true. In sciences in general, then, the object should be,\nso far from keeping individualising peculiarities out of sight, to\ncontrive the greatest possible obstacles to a merely mechanical use of\nlanguage: we should carefully keep alive a consciousness of its meaning,\nby referring, by aid of derivation and the analogies between the ideas\nof the roots and the derivatives, to the origin of words; and as words,\nhowever philosophically constructed, are always tending, like coins, to\nhave their inscription worn off, we should be ever stamping them afresh.\nThis we shall effect, if we contemplate habitually, not the _formulas_\nwhich record the laws of the phenomena (for, if so, the formulas will\nthemselves progressively lose their meaning), but the phenomena whence\nthe laws were collected; and we must conceive these phenomena in the\nconcrete, and clothe them in circumstances.\n\n\n\n\nCHAPTER VII.\n\nCLASSIFICATION, AS SUBSIDIARY TO INDUCTION.\n\n\nEvery name which connotes an attribute thereby divides, but only\nincidentally, all things, known and unknown, real and imagined, into two\nclasses, viz. those which have, and those which have not the attribute.\nBut sometimes the naming itself is but the secondary and subsidiary, and\nthe classification, the primary object. The general problem of such\nclassification is, to provide that things shall be thought of in such\ngroups, and the groups in such an order, as will best promote the\nremembrance and ascertainment of their laws. Its subjects are _real\nthings_ exclusively, but _all_ real things, since, to place one object\nin a group, we ought to know the divisions of nature at large.\n\nAny property may be the basis for a classification; but those best\nsuited are properties which are causes, or, next, as the cause of a\nclass's chief peculiarities seldom serves as its diagnostic, any effect\nwhich is a sure mark both of the cause and of the other effects. Only a\nclassification so grounded is scientific; the same also is not technical\nor artificial, but natural, and emphatically _natural_ (as compared with\nclassifications in an inferior degree also _natural_, which are based on\nproperties important with reference to the reasoner's special practical\nobjects), when the classification is based on those properties which\nwould most impress one who knew all the properties, but was not\ninterested particularly in any one. Further, it is a great\nrecommendation of a classification, that it groups together things of\nlike general aspect; but this is not a _sine qua non_: a group may be\n_natural_ even if based on very _unobvious_ properties, provided these\nare marks of many other properties, though certainly then there should\nbe also some more obvious property to act as a mark of the unobvious\nones which form the real basis.\n\nAs the first principle of _natural_ classification is that the classes\nmust be so formed that the objects composing each may have as many\nproperties in common as possible to serve as predicates, all _kinds_\nshould have places among the _natural_ groups, since the common\nproperties of _kinds_, and, therefore, the general assertions that can\nbe made about them, are innumerable. But _kinds_ are too few to make up\nthe whole of a classification: other classes also may be eminently\n_natural_, though marked out from each other only by a definite number\nof properties. Of neither sort of _natural_ groups is Dr. Whewell's\ntheory _strictly_ true, viz. that every _natural_ group is not\ndetermined by definition, that is, by definite characters which can be\nexpressed in words, but is fixed by Type. He explains that a type is an\nexample of any class, for instance, a species of a genus, which\npossesses all the characters and properties of the genus in a marked\nway; that round this type-species are grouped all the other species,\nwhich, though deviating from it in various directions and degrees, yet\nare of closer affinity to it than to the centre of any other group; and\nthat this is the reason why propositions about _natural_ groups so often\nstate matters as being true not in all cases, but only in most. Now,\nthere is a truth, but only a partial truth, in this doctrine. It is\nthis: in forming _natural_ groups, species which want certain of the\nclass-characters, some one, and others another, are classed with those\n(the majority) that have them all, because they are more like (that is,\nin fact, have more of the common characters of) that particular group\nthan of any other. On account of the feeling of vagueness hence\nengendered, we certainly, in deciding if an object belong to the group,\ndo generally (and _must_, when the classification is made expressly with\na view to a special inductive enquiry) refer mentally, not as a\nsubstitute for, but in illustration of the definition of the group, to\nsome standard specimen which has _all_ the characters well developed.\nBut not the less, therefore, are all _natural_, equally with all\nartificial, groups framed with distinct reference to certain definite\ncharacters. In the case of _kinds_, a few characters are chosen as marks\nof the rest. In the case of other _natural_ groups, the formation of the\nlarger groups, into which we collect the _infimae species_, is suggested\nindeed by resemblance to types (since we form each such larger group\nround a selected _kind_ which serves as its exemplar); but the group\nitself, when formed, is determined by definite characters.\n\nClass names should by the mode of their construction help those who have\nlearnt about the thing, to remember it, and those who have not learnt,\nnow to learn, by being merely told the name. This is best effected, in\nthe case of _kinds_, when the word indicates by its very formation the\nproperties it connotes. But this is seldom possible. For, though a\n_kind_-name connotes not all the _kind_-properties, but some only which\nserve as sure marks of the rest, even these have been found too many to\nbe included conveniently in a name (except in Elementary Chemistry,\nwhere every compound substance has one distinctive index-property, viz.\nthe chemical composition). A subsidiary resource is to point out the\n_kind's_ nearest natural affinities. For instance, in the binary\nNomenclature of Botany and of Zoology, the name of every species\nconsists of the name of the _natural_ group next above, with a word\nadded expressive of some quality in the nature or mode of discovery, or\nwhat not, of the particular species itself. By this device (obtaining at\npresent only in Botany and Zoology), as well is the expression, in the\nname, of many of the _kind's characters_ secured, as the use of names\neconomised, and the memory relieved. Except for some such plan, what\nhope of naming the 60,000 known species of Plants?\n\n\n\n\nCHAPTER VIII.\n\nCLASSIFICATION BY SERIES.\n\n\nThe object of Classification generally is to bring our ideas of objects\ninto the order best fitted for prosecuting inductive enquiries into the\nlaws of the phenomena generally. But a Classification which aims at\nfacilitating an inductive enquiry into the laws of some special\nphenomenon, must be based on that phenomenon itself. The requisites of\nsuch a classification are, first, the bringing into one class all\n_kinds_ of things which exhibit the phenomenon; next, the arranging\nthem in a _series_, according to the degrees in which they exhibit it.\nSuch a classification has been largely applied in Comparative Anatomy\nand Physiology (and these alone), since there has been found a\nrecognisable difference in the degree in which animals possess one main\nphenomenon, viz. Animal Life.\n\nThis arrangement of the instances, whence the law is to be collected, in\na series, is that which is always implied in and is a condition of _any_\napplication of the method, viz. that of Concomitant Variations, which\nmust be used when conjoined circumstances cannot easily be separated by\nexperiment. But sometimes (and it is so in Zoology) the law of the\nsubject of the special enquiry (e.g. Animal Life) has such influence\nover the general character of the objects, that all other differences\namong them seem mere modifications of it; and then the classification\nrequired for the special purpose becomes the determining principle of\nthe classification of the same objects for general purposes.\n\nTo recognise the identity of phenomena which thus differ only in degree,\nwe must assume a type-species. This will be that _kind_ which has the\nclass-properties in their greatest intensity (and, therefore, most\neasily studied with all their effects); and we must conceive the other\nvarieties as instances of degeneracy from that type.\n\nThe divisions of the series must be determined by the principles of\n_natural_ grouping in general (that is, in effect, by natural affinity);\nin subordination, however, to the principle of a natural series; that\nis, in the same group must not be placed things which ought to occupy\ndifferent points of the general scale.\n\nZoology affords the only _complete_ example of the true principles of\nrational classification, whether as to the formation of groups or of\nseries. Yet the same principles are applicable to all cases (to art and\nbusiness as well as science) where the various parts of a wide subject\nhave to be brought into mental co-ordination.\n\n\n\n\nBOOK V.\n\nFALLACIES.\n\n\n\n\nCHAPTER I.\n\nFALLACIES IN GENERAL.\n\n\nThe habit of reasoning well is the only complete safeguard against\nreasoning ill, that is, against drawing conclusions with insufficient\nevidence, a practice which the various contradictory opinions,\nparticularly about the phenomena relating to Man, show to be even now\ncommon, and that too among the most enlightened. But, to be able to\nexplain an error is a necessary condition of seeing the truth; for,\n'Contrariorum eadem est Scientia.' Consequently, a work on Logic must\nclassify Fallacies, that is, the varieties of Apparent Evidence; for\nthey _can_ be classified, though not in respect of their negative\nquality of being either not evidence at all, or inconclusive, yet in\nrespect of the positive property they have of _appearing_ to be\nevidence.\n\nAs Logic has been here treated as embracing the whole reasoning process,\nso it must notice the fallacies incident to any part of it (not to\nRatiocination merely), whether arising from faulty Induction, or from\nfaulty Ratiocination, or from dispensing wholly with either or both of\nthem. It does not treat of errors from negligence, or from inexpertness\nin using right methods, nor does it treat of errors from moral causes,\nviz. Indifference to truth, or Bias by our wishes or our fears; for the\nmoral causes are but the _remote_ and _predisposing_, not the _exciting_\ncauses of opinions; and therefore inferences from them, since they must\nalways involve the intellectual operation of admitting insufficient\nevidence as sufficient, really come under a classification of the things\nwhich wrongly _appear_ evidence to the _understanding_.\n\nFallacies may be arranged, with reference either to the cause which\nmakes them (erroneously) appear evidence, or to the particular kind of\nevidence they simulate. The following classification is grounded on both\nthese considerations jointly.\n\n\n\n\nCHAPTER II.\n\nCLASSIFICATION OF FALLACIES.\n\n\nThe business of Logic is, not to enumerate false opinions, but to\nenquire what property in the facts led to them, that is, what\npeculiarity of relation between two facts made us suppose them\nhabitually conjoined or disjoined, and thus regard the presence or\nabsence of the one as evidence of that of the other. For every such\nproperty in the facts, or our mode of considering them, there is a\ncorresponding class of Fallacies.\n\nAs the supposed habitual connexion or repugnance of two facts may be\nadmitted, either as a self-evident and axiomatic truth, or as itself an\ninference, the first great division is into Fallacies of Simple\nInspection or _a priori_ Fallacies, and Fallacies, of Inference. But\nthere is also an intermediate class. For, sometimes an inference is\nerroneous through our not conceiving what our premisses precisely are,\nand from our therefore substituting new premisses for the old, or a new\nconclusion for the one we undertook to prove; and this is called the\nFallacy of Confusion. Under this head, indeed, of Fallacies of\nConfusion, might strictly be brought almost any fallacy, though falling\nalso under some other head: for, some of the links in an argument,\nespecially if sophistical, are sure to be suppressed; and, it being left\ndoubtful which is the proposition to be supplied, we can seldom tell\nwith certainty under _which_ class the fallacy absolutely comes. It is,\nhowever, convenient to reserve the name _Fallacy of Confusion_ for cases\nwhere Confusion is the _sole_ cause of the error.\n\nCases, then, where there is more or less ground for the error in _the\nnature of the apparent evidence itself_, the evidence being assumed to\nbe of a certain sort, and a false conclusion being drawn from it, may be\nclassed as Fallacies of Inference. According as the apparent evidence\nconsists of particular facts, or of foregone generalisations, we call\nthe errors Fallacies of Induction or of Deduction. Each of these\nclasses, again, may be subdivided into two species, according as the\napparent evidence is either false, or, though true, inconclusive. Such\nsubdivisions of the Fallacy of Induction are respectively called, in the\nformer case, Fallacies of Observation (including cases where the facts\nare not directly observed, but inferred), and, in the latter, Fallacies\nof Generalisation. Among Fallacies of Deduction, those which proceed on\nfalse premisses have no specific name, for they must fall under one of\nthe other heads of Fallacies; but those, the premisses of which, though\ntrue, do not support the conclusion, compose a subdivision, which may be\nspecified as Fallacies of Ratiocination.\n\n\n\n\nCHAPTER III.\n\nFALLACIES OF SIMPLE INSPECTION; OR, A PRIORI FALLACIES.\n\n\nThere must be some _a priori_ knowledge, some propositions to be\nreceived without proof; for there cannot be a chain suspended from\nnothing. What these are is disputed, one school recognising as ultimate\npremisses only the facts of our subjective consciousness, e.g.\nSensations, while Ontologists hold that the mind intuitively, and not\nthrough experience, recognises as realities other existences, e.g.\nSubstances, which are suggested by, though not inferrible from, those\nfacts of consciousness. But, as both schools, in fact, allow that the\nmind infers the _reality_ from the _idea_ of a thing, and that it may do\nthis unduly, there results a class of Fallacies resting on the tacit\nassumption that the objects in nature have the same order as our ideas\nof them. Hence not only arose the vulgar belief that facts which make us\nthink of an event are omens foreboding (e.g. lucky or unlucky names), or\neven causing its occurrence; but even men of science both did and do\nfall into this Fallacy. The following dogmas express the different forms\nof this error:--\n\n1. [Greek: a]. _Things which we cannot help thinking of together must\ncoexist_; thus Descartes held that, because existence is involved\n(though really only by the thinker himself) in the idea of a geometrical\nfigure, a thing like the idea must exist. [Greek: b]. _Whatever is\ninconceivable is false._ The latter proposition has been defended by\ndrawing a distinction between the principle, and its possibly wrong\napplication to facts, e.g. to Antipodes; but how can we ever know that\nit has been rightly applied? Coleridge, again, has distinguished between\nthe unimaginable, which he thinks may possibly be true, and the\ninconceivable, which he thinks cannot be; but Antipodes were imaginable\nat the same period when they were inconceivable. In fact, as even to\nNewton it seemed inconceivable, that a thing should act where it is not\n(e.g. that the sun should act upon the earth without the medium of an\nether), simply because his mind was not familiar with the idea, so it\n_may_ be with _our_ incapability (if not, indeed, resulting merely from\nour limited faculties) of _conceiving_, e.g. that matter cannot think;\nthat space is infinite; that _ex nihilo nihil fit_. Leibnitz's tenet\nthat all _natural_ phenomena must be explicable _a priori_, and the\nfurther assumption by some that Nature always acts by the simplest, i.e.\nby the most easily conceivable means (and that, therefore, e.g. the\nheavenly bodies have a circular movement), exhibit vividly this Fallacy\nof Simple Inspection.\n\n2. _Whatever can be thought of apart, or has a separate name, exists\napart as a separate entity_, e.g. Nature, Time, qualities, as e.g.\nWhiteness, and, worst of all, the Substantiae Secundae. Mysticism is this\nhabit of ascribing objective existence to the subjective creations of\nthe mind, and reasoning from them to the things themselves.\n\n3. _A fact must follow a certain law, because we see no reason for its\ndeviating from it in one way rather than in another._ This, which is the\nsame as the Principle of the Sufficient Reason, has been used to prove\nthe Law of Inertia (the very point to be proved, viz. that only external\nforce can be a sufficient reason for motion _in a particular direction_,\nbeing assumed), and also the First Law of Motion, the argument being, in\nthe latter case, that a moving body, if it do _not_ continue of itself\nto move uniformly in a straight line, must deviate right or left, and\nthat there is _no reason_ for its going one way more than the other: to\nwhich the answer is, that, apart from experience, we could not know\nwhether or not there were a reason. Geometers often fall into this\nFallacy.\n\n4. _The differences in nature must correspond to our received\ndistinctions_ (in names and classifications). Thus, the Greeks thought\nthat, by determining the meanings of words, they ascertained facts.\nAristotle usually starts with 'We say thus or thus.' So, with the\n_Doctrine of Contrarieties_, in which the Pythagoreans and others\nassumed that oppositions in language imply similar ones in nature.\nHence, too, the ancient belief in the essential difference between the\nlaws of things terrestrial and things celestial, and in man's\nincapability of imitating nature's works. Bacon's error (which vitiates\nhis inductive system) was analogous, in looking (either through his\neagerness for practical results, or a lingering belief that causes were\nthe sole object of philosophy) for the cause of given effects rather\nthan the effects of a given cause. Hence sprang his tacit assumption\n(and that in enquiries into the causes of a thing's sensible qualities,\nwhere it was especially fatal), that in all cases, e.g. of heat or cold,\nthe _forma_, or set of conditions, is _one_ thing. A similar notion,\nviz. that each property of gold, as of other things, has its one\n_forma_, produced the belief in Alchemy.\n\n5. The conditions of a phenomenon often do resemble the phenomenon\nitself, e.g. in cases of Motion, Contagion, Feelings; but it is a\nFallacy to suppose that _they must or probably will_. By this fancied\nlaw men guided their conjectures. Thus, the _Doctrine of Signatures_\nwas, that substances showed their uses as medicines by external\nresemblance, either to their supposed effect, or to the disease. So, the\nCartesians, and even Leibnitz, argued, that nothing physical but\nprevious motion could account for motion, explaining the human body's\nvoluntary motions by Nervous Vibrations or by Animal Spirits. Hence,\ntoo, the inference that there is a correspondence between the physical\nqualities of the cause, and like or like-named ones, either of the\nphenomenon (e.g. between sharp particles and a sharp taste), or of its\neffects (e.g. between the redness of Mars, and fire and slaughter as\nresults of that planet's influence). In metaphysics, the Epicureans'\ndoctrine of _species sensibiles_, and the moderns' of _perception\nthrough ideas_, arose from this fallacy (combined with another, viz.\nthat a thing cannot act where it is not). Again, the conditions of a\nthing are sometimes spoken of even as though they were the thing itself.\nThus, in the Novum Organon, heat (i.e. really the conditions of the\nfeeling of it) is called a kind of motion; and Darwin, in his Zoonomia,\nafter describing _idea_ as a kind of _notion of external things_,\ndefines it as _a motion of the fibres_. Cousin says: 'Tout ce qui est\nvrai de l'effet est vrai de la cause,' though, the reverse _might_ be\ntrue; and Coleridge affirms, as _an evident truth_, that mind and\nmatter, as having no common property, cannot act on each other. The same\nfallacy led Leibnitz to his _pre-established harmony_, and Malebranche\nto his _occasional causes_. So, Cicero argues that mental pleasures, if\narising from the bodily, could not, as they do, exceed their cause; and\nDescartes, that the Efficient Cause must have all the perfections of the\neffect. Conversely Descartes, too, and persons who assail, e.g. the\nPrinciple of Population by reference to Divine benevolence (thus\nimplying that, because God is perfect, therefore what _they_ think\nperfection must obtain in nature), assume that effects must resemble\ntheir causes.\n\n\n\n\nCHAPTER IV.\n\nFALLACIES OF OBSERVATION.\n\n\nA fallacy of Observation (the first of the three fallacies of Proof) may\nbe either negative or positive.\n\n1. The former, which is called Non-observation, is a case, not of a\npositive mis-estimate of evidence, or of the proper faculties (whether\nthe senses or reason) not having been employed, but simply of the\nnon-employment of any of the faculties. It arises ([Greek: a]) from\nneglect of instances. Sometimes this is when there is a stronger motive\nto remember the instances on the one side, and the observers have\nneglected the principle of the Elimination of Chance. Hence (the mind,\nas Bacon says, being more moved by affirmative than by negative\ninstances) the belief in predictions, e.g. about the weather, because\nthey occasionally turn out correct; and the credit of the proverb, that\n'Fortune favours fools,' since the cases of a wise man's success through\nluck are forgotten in his more numerous successes through genius. But a\npreconceived opinion is the _chief_ cause why opposing instances are\noverlooked. Hence originate the errors about physical facts (e.g. of\nCopernicus's foes, and friends, too, about the falling stone), and _a\nfortiori_, on moral, social, and religious subjects, where yet stronger\nfeelings are involved.\n\nThe fallacy of Non-observation may occur ([Greek: b]) from neglect, not\nof the material instances wholly, but of some material facts in them,\ne.g. in cases of cures by quack remedies (such as Kenelm Digby's\n'sympathetic powder'), of some attendant fact (as exclusion of air from\na wound, rest, regimen, and the like) which really worked the cure.\nSometimes the neglected fact is one ascertainable, not by the senses,\nbut by reasoning, which has been overlooked. Thus, Cousin's argument\nthat, if the sole end of punishment were to prevent crime by\nintimidating intending criminals, the punishment of the innocent,\nindiscriminately with the guilty, would have the same effect, ignores\nthe fact that the innocent would then be equally intimidated, and so the\npunishment would be of no use as an example to criminals. So, in\nPolitical Economy, where the effects of a cause often consist of two\nsets of phenomena, the one obvious, the other deeper under the surface,\nand exactly contrary, the latter is often neglected. This was why the\nrapidly spent capital of the prodigal was supposed formerly to employ\nmore labour than the invested savings of the parsimonious, and the\npurchase of native goods to encourage native industry more than the\npurchase of foreign.\n\n2. The error in Mal-observation, which is the _positive_ kind of\nMis-observation, is not the overlooking facts, but the seeing them\nwrong. It arises from mistaking what is in fact inference (as much\n_must_ be, whenever we try to observe or to describe) for perception,\nwhich is infallible evidence of what is really perceived. The\nAnti-Copernicans, when they appealed to common sense, made this mistake.\nSo do untrained persons generally in describing facts, especially\nnatural phenomena (e.g. apothecaries and nurses in stating symptoms),\nand that, too, in proportion to their ignorance. We might expect this,\nsince usually the actual perceptions of the senses (e.g. the colour and\nextension) are not of interest, except as marks whence to draw\ninferences about something else (e.g. about the body, to which these\nqualities belong). Painters, therefore, to know what the sensation\nactually was, have to go through a special training. But this confusion\nof inference with perception is still more likely in highly abstract\nsubjects; and, consequently, in these, mere, and often false inferences,\nhave continually been regarded as intuitive judgments.\n\n\n\n\nCHAPTER V.\n\nFALLACIES OF GENERALISATION.\n\n\nThis class includes whatever errors of generalisation are not mere\nblunders, but arise from some wrong general conception of the inductive\nprocess. Only a few kinds can be noted. 1. Under this Fallacy come\ngeneralisations which _cannot_ be established by experience, e.g.\ninferences from the order in the Solar System to other and unknown parts\nof the universe; and also, except when a particular effect would\ncontradict either the laws of number and extension, or the universal law\nof causality, all inferences from the fact that _we_ have never known of\na particular effect to its impossibility. 2. Those generalisations also\nare fallacious which resolve, either, as in early Greece, all things\ninto one element, or, as often in modern times, impressions on the\nsenses, differing in quality, and not merely in degree, into the same;\ne.g. heat, light, and (through vibrations) sensation, into motion;\nmental, into nervous states; and vital phenomena, into mechanical or\nchemical processes. In these theories, one fact has its laws applied to\nanother. It may possibly be a condition of that other; but even then the\nmode in which the new fact is actually produced would have to be\nexplained by its own law, and not by that of the condition. 3. Again,\ngeneralisations got by Simple Enumeration, fall under this Fallacy. That\nsort of Induction 'precario concludit,' says Bacon, 'et periculo\nexponitur ab instantia contradictoria, ... ex his tantummodo quae praesto\nsunt pronuncians.' The ancients used it; and in questions relating to\nman and society, it is still employed by _practical_ men. By it men\narrived at the various examples of the formula, _Whatsoever has never\nbeen_ (e.g. a State without artificial distinctions of rank; negroes as\ncivilised as the white race) _will never be_; which, being inductions\nwithout elimination, could at most form the ground only of the lowest\nempirical laws. Higher empirical laws can be got, when a phenomenon\npresents (as no negation can) a series of regular gradations, since\nsomething may then be inferred from the observed as to the unobservable\nterms of the series. Such is the law of man's necessary progression, in\ncontradiction to the above formula. But even this better generalisation\nis similarly, though not as grossly, fallacious as the preceding, when,\nthough not itself a cause, but only a summary expression for the general\nresult of all the causes, it is accepted as _the_ law of human changes,\npast and even future. So, empirical generalisations, from present to\npast time, and from the character of one nation to that of another, are\nsimilarly fallacious when employed as causal laws. 4. This Fallacy\noccurs, not only when an empirical is confounded with a causal law, but\nwhen causation is inferred improperly. The mistake sometimes lies in\ninferring _a posteriori_ that one fact must be the cause of another\n(e.g. the National Debt, or some special institution, of England's\nprosperity), because of their casual conjunction; at other times, in\nassuming _a priori_ that one of several coexisting agents is the sole\ncause, and then deducing the effects from it exclusively. The latter is\nproperly False Theory. It has been exemplified in medicine by the\ntracing of all diseases by one school, to viscidity of the blood, by\nanother, to the presence of some acid or alkali, and, in politics, by\nthe assumption that some special form of government or society is\nabsolutely good. 5. In False Analogies (which fall under this Fallacy)\nthere is no pretence of a conclusive induction. The argument from\nAnalogy is the inferring, in the absence of evidence either way, that an\nobject resembles a second object in one point, because it is seen to\nresemble it in another point, which either is not known to be connected\nwith the first by causation (as, that the planets must be inhabited\nbecause they obey the same astronomical laws with the earth, which is),\nor which is known to be, not, indeed, its cause or its effect, but\neither one of a set of conditions, which together are its cause, or an\noccasional effect of its cause. Now, persons (usually from poverty, not\nfrom luxuriance, of imagination) often overrate the weight of true\nanalogies; but the fallacy specially consists in inferring resemblance\nin one point from resemblance in another, when the evidence is not only\nnot in favour of, but even positively against the connection of the two\nby way of causation. It is so in the argument in favour of absolutism,\non the ground of its resemblance to paternal government in the one point\nof irresponsibility, as though the assumed benefits of paternal rule\nflowed from this quality. Similarly fallacious are the inferences,\nthrough analogies, from the liability to decay of bodies natural to that\nof bodies politic; from the supposed need of a _primum mobile_ in nature\nto that of an irresponsible power in a state; and from the effects of a\ndecrease of a country's corn to the effects of a decrease of its gold\n(the utility of which, but not of corn, depends on its value, and its\nvalue on its scarcity). Such, also, were the Pythagorean inferences that\nthere is a music of the spheres, because the intervals between the\nplanets have the same proportion as the divisions of the monochord; and,\nagain, that the movements of the stars as being _divine_ must be\nregular, because so are those even of orderly _men_. So, Aristotle and\nother ancients supposed perfection to obtain in all natural facts,\nbecause it appeared to exist in some; and so, the Stoics tried to prove\nthe equality of all crimes by reference to various similes and metaphors\n(as, that the man held half an inch below the surface will be drowned as\ncertainly as the man at the bottom of the sea; and that want of skill is\nshown as much in steering a straw-laden boat as a treasure galleon on to\nthe rocks). But, in fact, the connection by causation between the known\nand the inferred resemblance, which is _assumed_ by these metaphors, is\nthe very thing which they are brought to prove. The real use of such\ncases of analogy as metaphors is that they serve, not as an argument,\nbut as an assertion that one exists. Though they cannot prove, they\nsometimes suggest the proof, and point to a case in which the same\ngrounds for a conclusion have been found adequate. Such are d'Alembert's\nclassification of successful politicians as either eagles or serpents;\nand the statement, as an argument for education, that, in waste land\nweeds will spring up; and such is _not_ Bacon's inference from the\nlevity of floating straw to the worthlessness of the _extant_ scientific\nworks of the ancients.\n\nThe great source of fallacious generalisation is bad classification, by\nwhich things with no, or no important, common properties, are grouped\ntogether. Worst is it, when a word which commonly signifies some\ndefinite fact is applied to other facts only slightly similar. Bacon\n(who has himself thus erred in his enquiries into heat) specifies, as\nexamples of this, the various applications (got, by unscientific\nabstraction, from the original sense) of the word 'wet,' to flame, air,\ndust, and glass, as well as to water. The application by Plato,\nAristotle, and other ancients, of the terms Generation, Corruption, and\n[Greek: kinesis] to many heterogeneous phenomena, with a mixture of the\nideas belonging to them severally, caused many perplexities, which may\nbe noticed under Fallacies of Confusion.\n\n\n\n\nCHAPTER VI.\n\nFALLACIES OF RATIOCINATION.\n\n\nThese fallacies (to which the name _Fallacy_ is commonly applied\nexclusively) would generally be detected if the arguments were set out\nformally; and the value of the syllogistic rules is, that they force the\nreasoner to be aware what it is that he is really asserting. The\nfrequent errors in processes such as Conversion and Opposition, which\nare in appearance, though not in reality, inferences from premisses, may\nfor convenience be here referred to. Such are the simple conversion of\nan universal affirmative; the corresponding error in a hypothetical\nproposition of inferring the truth of the antecedent from that of the\nconsequent; and the confusing of a contrary with a contradictory, which\namounts, in practice, to mistaking the reverse of wrong for right. But\nfallacies of Ratiocination properly lie in syllogisms. They commonly\nresolve themselves, when in a single syllogism, into the having more\nthan three terms, whether covertly, as through an undistributed middle,\nor an illicit process, or avowedly. But the most dangerous and the\ncommonest of these fallacies arise in a chain of argument from _changing\nthe premisses_. One of the obscurer forms of this is the fallacy _a\ndicto secundum quid_ (i.e. with a qualification, or condition,\nexpressed, or, more usually, understood) _ad dictum simpliciter_. Thus,\nthe Mercantile Theory was in favour of prohibiting all trade which tends\nto carry out more money than it brings in, on the ground that money is\nriches, though it is so only if the money can be _freely_ spent. Such,\ntoo, was the argument (used to support the doctrine that tithes fall on\nthe landlord) that, because now the rent of tithe-free land exceeds that\nof tithed land, the rent from the latter would be increased by the\nabolition of all tithes. There was a similar fallacy in the use of the\nmaxim, that individuals are the best judges of their pecuniary\ninterests, against Mr. Wakefield's scheme for concentrating settlers.\nCases in which the condition of _time_ is dropped, fall under this same\nparticular fallacy, as, when the maxim that prices always find their\nlevel, is construed as meaning that they are always _at_ their level. It\nis the same with the reasoning (especially in political and social\nsubjects), upon principles, which are true in the absence of all\nmodifying causes, as though no such causes _could_ exist. Other\nanalogous fallacies are those _a dicto simpliciter ad dictum secundum\nquid_ (the converse of the preceding), and _a dicto secundum quid ad\ndictum secundum alterum quid_.\n\n\n\n\nCHAPTER VII.\n\nFALLACIES OF CONFUSION.\n\n\nUnder this head come all fallacies which arise, not so much from a false\nestimate of the probative force of known evidence, as from an indistinct\nconception what the evidence is.\n\n1. Thus, where there is an ambiguous middle, or a term used in different\nsenses in the premisses and in the conclusion, the argument proceeds as\nthough there were evidence to the point, when, in fact, there is none.\nThis error does not occur much in direct inductions, since the things\nthemselves are there present to the senses or memory; but chiefly, in\nRatiocination, where we are deciphering our own or others' notes. The\nambiguity arises very often from assuming that a word corresponds\nprecisely in meaning with the root itself (e.g. _representative_), or\nwith cognate words from the same root, called _paronymous_ words (as,\n_artful_, with _art_). Other examples of ambiguities are; 'Money,'\nwhich, meaning both the currency and also capital seeking investment, is\noften thought to be scarce in the former sense, because scarce in the\nlatter; 'Influence of Property,' which, signifying equally the influence\nof respect for the power for good, and of fear of the power for evil,\nwhich is possessed by the rich, is represented as being assailed under\nits former form when attacked really only under the latter; 'Theory,'\nwhich, because applied popularly to the accounting for an effect apart\nfrom facts, is ridiculed, even when expressing, as it properly does, the\nresult of philosophical induction from experience; 'The Church,' which\nrefers (as in the question of the inviolability of _Church_ property)\nsometimes to the clergy alone, sometimes to all its members; 'Good,' in\nthe Stoic argument that virtue, as alone _good_ (in the Stoic sense),\nmust therefore include freedom and beauty, because these are _good_ (in\nthe popular sense). So, the meaning of 'I' shifts from _the laws of my\nnature_ to _my will_, in Descartes' _a priori_ argument for the being of\na God, viz. that there must be an external archetype whence I got the\nconception, for if _I_ (i.e. _the laws of my nature_) made it, _I_ (i.e.\n_my will_, and not, as it should consistently be, _the laws of my\nnature_) could unmake it; but _I_ (i.e. _my will_) cannot. In the\nFree-Will controversy, 'I' is used ambiguously for volitions, actions,\nand mental dispositions, and 'Necessity' both for _Certainty_ and for\n_Compulsion_. From the application of 'same,' 'one,' 'identical,' which\nprimarily refer to a single object, to several objects because\n_similar_, grew up (for the purpose of accounting for the supposed\n_oneness_ in things said to have the _same_ nature or qualities) both\nthe Platonic _Ideas_, and also the _Substantial Forms_ and _Second\nSubstances_ of the Aristotelians, even though the latter did see the\ndistinction between things differing both _specie_ and _numero_, and\nthose differing _numero_ only. And thence, too, sprang Berkeley's proof\nof the existence of a Universal Mind from the supposed need of such a\nBeing to harbour, in the interval, the idea, which, one and the same\n(really, only two _similar_ ideas), a man's mind has entertained at two\ndistinct times. The difficulty in _Achilles and the Tortoise_ arises\nfrom the use of _infinity_, or, _for ever_, in the premisses, to\nsignify a finite time which is infinitely divisible, and, in the\nconclusion, to signify an infinite time. Thus, again, 'right' is used to\nexpress, both what others have no right to stop a man from doing, and\nalso what it is not against his own duty to do; both what people are\nentitled to expect from, and also what they may enforce from others. The\nFallacy of Composition and Division, i.e. the use of the same term in a\nsyllogism, at one time in a collective, at another in a distributive\nsense, is one of the Fallacies of Ambiguous Terms. Examples of it are\nthe arguments, that _great men_ (collectively) could be dispensed with,\nbecause the place of any particular great man might have been supplied\n(i.e., in fact, by some other great man); and, that a high prize in a\nlottery may be reasonably expected (by _a certain individual_, viz.\noneself), because a high prize is commonly gained (_by some one or\nother_).\n\n2. In Petitio Principii, the premisses are not even verbally sufficient\nfor the conclusion, since one premiss is either clearly the same as the\nconclusion, or actually proved from it, or not susceptible of any other\nproof. Men commonly fall into it, through believing that the premiss\n_was_ verified, though they have forgotten how. But the variety, termed\nReasoning in a Circle, implies a conscious attempt to prove two\npropositions reciprocally from each other. This formal proof is not\noften attempted, except under the pressure of controversy; but, from\nmistaking mutual coherency for truth, propositions, which cannot be\nproved except from each other, are often _admitted_, when expressed in\ndifferent language, without other proof. Frequently a proposition is\npresented in abstract terms as a proof of the same in concrete, as, in\nMoliere's parody, 'L'opium endormit parcequ'il a une vertu soporifique.'\nSo, some qualities of a thing selected arbitrarily are termed its nature\nor essence, and then reasoned from as though not able to be counteracted\nby any of the rest. 'Question-begging appellatives,' particularly, are\ncases of Petitio Principii, e.g. the styling any reform an _innovation_,\nwhich it really is, only that _innovation_ conveys, besides its\ndictionary meaning, a covert sense of something extreme. Thus, in\nCicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to\nexpress certain desires the moral character of which is the point in\nquestion. Again, the infinite divisibility of matter was assumed by the\nargument which was used to prove it, viz. that the least portion of\nmatter must have both an upper and an under surface (which, as every\nother Fallacy of Confusion, when cleared up, appears as a fallacy of a\ndifferent sort, under shelter of which, as indeed in ratiocinative\nfallacies generally, the mere verbal juggle at first escapes detection).\nSuch, again, was Euler's argument, that _minus_ multiplied by _minus_\ngives _plus_, _because_ it could not give the same as _minus_ multiplied\nby _plus_, which gives _minus_. So, some ethical writers begin by\nassuming, that certain general sentiments are the _natural_ sentiments\nof mankind, and thence argue that any which differ are morbid and\n_unnatural_. Thus, lastly, Hobbes and Rousseau rested the existence of\ngovernment and law on a supposed social compact, and not on men's\nperception of the interests of society, which, however, could be the\nonly ground for their abiding by such compact if a fact.\n\n3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the\nerror lies not either in mistaking the import of the premisses, or in\nforgetting what they are, but in mistaking what is the conclusion to be\nproved. Sometimes, a particular is substituted for the universal as the\nproposition needing proof, and sometimes, a proposition with different\nterms. Under this fallacy come the cases, not only of proving what was\nnot denied, but of disproving what was not asserted; e.g. the argument\nused against Malthus (whose own position was, that population increases\nonly _in so far as not kept down_ by prudence, or by poverty and\ndisease), that, at times, population has been nearly stationary; or\nagain, that, in some country or other, population and comfort are\nincreasing together, Malthus himself having asserted that this might be\nso, if capital has increased. Similarly, even Reid, Stewart, and Brown\n(not merely Dr. Johnson) urged that Berkeley ought, if consistent, to\nhave run his head against a post, as though the non-recognition of an\noccult _cause_ of sensations implies disbelief in any _fixed order among\nthem_.\n\n\n\n\nBOOK VI.\n\nON THE LOGIC OF THE MORAL SCIENCES.\n\n\n\n\nCHAPTER I.\n\nINTRODUCTORY REMARKS.\n\n\nMany complex problems have been resolved through the use of the\nScientific Methods, and thus only. The most complex of all problems are\nthe problems relating to Man himself; and of them those concerned with\nthe Mind and Society have never been scientifically resolved. They can\nbe rescued from empiricism, if at all, only by being submitted to some\nof the methods already characterised as applicable to science in\ngeneral. Which of these methods must be selected, and why; what are the\ncauses of previous failures; and what degree of success now is possible\nor probable, will be considered in this book, when a preliminary\nobjection (_based on the theory of free will_), that men's actions are\nnot, like other natural events, subject to invariable laws, has been\nfirst removed.\n\n\n\n\nCHAPTER II.\n\nLIBERTY AND NECESSITY.\n\n\nThe theory of _free will_, viz. that the will is determined by itself,\nand not by antecedents, was invented as being more in accordance with\nthe dignity of human nature and our consciousness of freedom, than\n_philosophical necessity_. The latter doctrine, in laying down simply\nthat our volitions and actions are invariable consequents of our\nantecedent states of mind, and that, given our motives, character, and\ndisposition, other men could predict our conduct as certainly as any\nphysical event, states indeed nothing which is in itself either\ncontradicted by our consciousness, or degrading; yet the doctrine of\ncausation, as applied to volition, is supposed, from the natural\ntendency of the mind to imagine falsely that a mysterious constraint is\nexercised by _any_ antecedent over the consequent, to imply some state\nof dependence which our consciousness does contradict. Moreover, the\nerroneous notion that something more than uniformity of order and\ncapability of being predicted is meant, has been favoured by the use of\nthe ambiguous term _necessity_ (which, it is true, commonly implies\nirresistibleness), to signify simply that the given cause will be\nfollowed by the effect subject to all possibilities of counteraction by\nother causes. Most necessarians have been themselves deceived by the\nexpression: they are apt to be partially fatalists as to their own\nactions, with a weaker spirit of self-culture than the believers in\nfree-will, and to fail to see that the fact of their character being\nformed _for_ them, that is, by their circumstances, including their own\norganisation, is consistent with its being formed _by_ themselves, as\nintermediate agents, moulding it in any particular way which they may\n_wish_. The belief that the _wishing_ is excited by external causes,\ne.g. by education, casual aspirations, and experience of ills resulting\nfrom our previous character, can be of no practical harm, and does not\nconflict with our feeling of moral freedom, that is, of power, _if we\nwish_, to modify or conquer our own character.\n\nThe ambiguity of the word _motive_ has also caused confusion. A motive,\nwhen used to signify that which determines the will, means not always or\nonly the anticipation of a pleasure or a pain, but often the desire of\nthe action itself. The action having finally become by association in\nitself desirable, we may get the habit of willing it (that is, get a\n_purpose_) without reference to its being pleasurable. We are then said\nto have a confirmed character.\n\n\n\n\nCHAPTER III.\n\nTHERE IS, OR MAY BE, A SCIENCE OF HUMAN NATURE.\n\n\nAny facts may be a subject of science, if they follow one another\naccording to constant laws; and this, whether, although the ultimate\nlaws are known, yet, of the derivative laws on which a phenomenon\ndirectly depends, either _none_, as in Meteorology, or, as in Tidology,\n_only_ the laws of the greater causes on which the chief part of a\nphenomenon directly depends, have been ascertained, and not those of all\nthe minor modifying causes; or, as in Astronomy (which is therefore\ncalled an _exact_ science), both the ultimate laws are known, and also\nthe derivative laws as well of the greater as of all the minor causes.\nThe science of Human Nature cannot be exact, the causes of human conduct\nbeing only approximately known. Hence it is impossible to predict _with\nscientific accuracy_ any one man's acts, resulting as they do partly\nfrom his circumstances, which, in the future, cannot be precisely\nforeseen, and, partly, from his character, which can never be exactly\ncalculated, because the causes which have determined it are sure, in the\naggregate, not to be entirely like those which have determined any other\nman's. But approximate generalisations, though only probably true as to\nthe acts and characters of individuals, will be certainly true as to\nthose of masses, whose conduct is determined by general causes chiefly;\nand they are therefore sufficient for political and social science. They\nmust, however, be connected deductively with the universal laws of human\nnature on which they rest, or they will be only low empirical laws. This\nis the text of the next two chapters.\n\n\n\n\nCHAPTER IV.\n\nTHE LAWS OF MIND.\n\n\nBy the laws of mind (i.e. as considered in this treatise, the laws of\nmental phenomena) are meant the laws according to which one state of\nmind is produced by another. If M. Comte and others be right in saying\nthat, in like manner with the mental phenomena called sensations, all\nthe other states of mind have for their proximate causes nervous states,\nthere would be no original laws of mind, and Psychology would be a mere\nbranch of Physiology. But at present, this tenet is not proved, however\nhighly probable; and, at all events, the characteristics of those\nnervous states are quite unknown; consequently the uniformities of\nsuccession among the mental phenomena, which undoubtedly do exist, and\nwhich are not proved to result from more general laws, must be\nconsidered as the subject of a distinct science called Psychology. We\ncan ascertain only by experiment the simple laws of Mind, such as--1.\nThat a state of consciousness can be reproduced in the absence of the\ncause which first excited it (i.e. that every mental impression has its\nidea), and--2. That these secondary mental states themselves are\nproduced according to the three laws of ideas. But the complex laws are\ngot from these simple laws, according either to the Composition of\nCauses, when the complex idea is said to _consist of_ the Simple Ideas,\nor to chemical combination, when it is said to be _generated by_ them.\nHartley and Mr. James Mill indeed hold _all_ the mental phenomena to be\ngenerated by chemical combination from simple ideas of _sensation_,\nhowever unlike to the alleged results; but even though they had proved\ntheir theory, employing the Method of Difference, and not only the\nMethod of Agreement (which latter itself they have used only partially),\nwe should still have to study the complex ideas themselves inductively,\nbefore we could ascertain their sequences.\n\nThe analytical enquiry (neglected alike by the German metaphysical\nschool, and by M. Comte) into the general laws of mind, will show that\nthe mental differences of individuals are not ultimate facts, but may be\nreferred generally to their particular mental history, their education\nand circumstances, but sometimes also to organic differences influencing\nthe mental phenomena, not directly, but through the medium of the\npsychological causes of the latter. Men's animal instincts, however, are\nprobably, equally with the mere sensations, connected directly with\nphysical conditions of the brain and nerves. Whether or not there be any\ndirect relation between organic causes and any other mental phenomena,\nPhysiology is likely in time to show; but at least Phrenology does not\nembody the principles of the relation.\n\n\n\n\nCHAPTER V.\n\nETHOLOGY, OR THE SCIENCE OF THE FORMATION OF CHARACTER.\n\n\nTill the Empirical laws of Mind, i.e. the truths of common experience,\nare _explained_ by being resolved into the causal laws (the subject of\nthe last chapter), they are mere approximate generalisations which\ncannot be safely applied beyond the limits in which they were collected\nby observation. But this does not prove aught against the universality\nand simplicity of the ultimate mental laws; for the same is the case\nwith the empirical laws even in astronomy, where each effect results\nfrom but few causes; _a fortiori_, therefore, will it be so in regard to\nman's character, which is influenced by each of his circumstances, which\ndiffer in the case of each nation, generation, and individual. But\nthough mankind have not one universal character, yet there exist\nuniversal laws of the formation of character. These universal laws\ncannot be discovered experimentally, i.e. either by artificial\nexperiment, since we can seldom vary the experiment sufficiently, and\nexclude all but known circumstances, or by observation, since, even in\nthe most favourable instances for the latter, viz. National acts, only\nthe Method of Agreement can be applied. Observation has its uses in\nrelation to this subject; but only as verification of the results\narrived at by the Deductive Method. The Deductive Method must be\nemployed to obtain the laws of the formation of character. They are got\nby supposing any given circumstances, and then considering how these\nwill, according to the general laws of mind, influence the formation of\ncharacter. So, contrary to Bacon's rule, laid down wrongly as universal,\nfor the discovery of principles, the highest generalisations must be\nfirst ascertained by the experimental science of Psychology; and then\nwill come what is in fact a system of corollaries from the latter\nscience, viz. Ethology, i.e. (as dealing only with tendencies) the\n_exact_ science of human character, or of education both national and\nindividual, and which has for its principles the middle principles\n(_axiomata media_) of mental science. It does not yet, but it will soon,\nexist as a science. Its object must be to determine, from the general\nlaws of mind, combined with man's general position in the universe, what\ncircumstances will aid or check the growth of good or bad qualities, so\nthat the Art of Education will be merely the transformation of these\nmiddle principles into precepts and their adaptation to the special\ncases. But at every step these middle principles, got by deduction, must\nbe verified _a posteriori_ by empirical laws, and by specific experience\nrespecting the assumed circumstances.\n\n\n\n\nCHAPTER VI.\n\nGENERAL CONSIDERATIONS ON THE SOCIAL SCIENCE.\n\n\nPolitical and social phenomena have been thought too complex for\nscientific treatment. Practitioners hitherto have been the only\nstudents; and so, as in medicine, before the rise of Physiology and\nNatural History, _experimenta fructifera_, and not _lucifera_, have been\nsought. The scheme of such a science has even been thought quackery,\nthrough the vain attempts of some theorists to frame universal precepts,\nas though their failure (arising from the variety of human\ncircumstances) proved that the phenomena do not conform to universal\nlaws. Social phenomena, however, being phenomena of human nature in\nmasses, must, as human nature is itself subject to fixed laws, obey\nfixed laws resulting from the fixed laws of human nature. The number and\nchangefulness of the data (unlike those of Astronomy) will prevent our\never predicting the far future of society. But, when general laws have\nbeen ascertained, an application of them to the individual circumstances\nof a given age and country will show us the causes and tendencies of,\nand the means of modifying, its actual condition. A consideration of two\nmethods, erroneously used for this science, viz. the Experimental or\nChemical, and the Abstract or Geometrical, will introduce us to the true\none.\n\n\n\n\nCHAPTER VII.\n\nTHE CHEMICAL, OR EXPERIMENTAL, METHOD IN THE SOCIAL SCIENCE.\n\n\nThe followers of this method do not recognise the laws of social\nphenomena as merely a composition of the laws of individual human\nnature. They demand specific experience in all cases; and they attempt\nto make effects, which depend on the greatest possible complication of\ncauses, the subject of induction by observation and experiment. The\nattempt must fail; for, we can neither get by experiment appropriate\n_artificial_ instances, nor, by observation, _spontaneous_ instances\n(from history), with the circumstances enough varied for a true\ninduction. Neither the _direct_ nor the _indirect_ Method of Difference\ncan be applied, for we cannot find either two single instances differing\nin nothing but the presence or absence of a given circumstance (the\n_direct_), or two classes respectively agreeing in nothing but the\npresence of a circumstance on one side and its absence on the other (the\n_indirect_). Then, again, the Method of Agreement is of small value,\nbecause social phenomena admit the widest plurality of causes; and so\nalso is that of Concomitant Variations, on account of the mutual action\nof the coexisting elements of society being such that what affects one\naffects all. The Method of Residues is better suited to social enquiries\nthan the other three. But _it_ is not a method of pure observation and\nexperiment. It presupposes that we know, by previous deduction from\nprinciples of human nature, the causes of part of the effect. But if\nthus part of the truths are, why may not all be, ascertained by\nDeduction, and the experimental argument be confined to the verifying of\nthe deductions?\n\n\n\n\nCHAPTER VIII.\n\nTHE GEOMETRICAL, OR ABSTRACT, METHOD.\n\n\nThe Methods of Elementary Chemistry are applied to social phenomena from\ncarelessness as to, or ignorance of, any of the higher physical\nsciences: the Geometrical Method, from the belief that Geometry, that\nis, a science of coexistent, not successive facts, where there are no\nconflicting forces, is, and that the now deductive physical sciences of\nCausation, where there are conflicting forces, are _not_, the type of\ndeductive science. Thus, it seems to have been supposed by many\nphilosophers, that each social phenomenon results from only one force,\none single property of human nature. For instance, Hobbes assumed (eking\nout his assumption by the fiction of an original contract), that\ngovernment is founded on fear. Even the scientific Bentham School based\na general theory on one premiss, viz. that men's actions are always\ndetermined by their interests, meaning probably thereby, that the bulk\nof the conduct of any succession, or of the majority of any body of men,\nis determined by their private or worldly interests. They inferred\nthence, that those rulers alone will govern according to the interest of\nthe governed, whose selfish interests are identified with it (forgetting\nthat, apart from the philanthropy and sense of duty of many, the\nconduct of _all_ rulers must be influenced by the habits of mind, both\nof the whole community, and also of their own class in it, and by the\nmaxims of their predecessors). Lastly, they laid down that this sense of\nidentity of interest with the governed is producible only by\nresponsibility (whereas the personal interest of rulers often prompts\nthem to acts, e.g. for the suppression of anarchy, which are also for\nthe interest of the governed). In fact, this school was pleading for\nparliamentary reform, and saw truly, that it is against the selfish\ninterests of rulers that constitutional checks are needed, and that, in\nmodern Europe, a feeling in the governors of identity of interest, when\nnot active enough, can be roused only by responsibility to the governed.\nTheir mistake was, that they based on just these few premisses a general\ntheory of government, in forgetfulness that such should proceed by\ndeduction from _the whole_ of the laws of human nature, since each\neffect is an aggregate result of many causes operating now through the\nsame ones, now through different ones, of these laws.\n\n\n\n\nCHAPTER IX.\n\nTHE PHYSICAL, OR CONCRETE DEDUCTIVE, METHOD.\n\n\nThe complexity in social effects arises from the number, not of the\nlaws, but of the data. Therefore, Sociology, i.e. Social Science, must\nuse the Concrete Deductive Method, compounding with one another the laws\nof all the causes on which any one effect depends, and inferring its law\nfrom them all. As in the easiest case to which the Method of Deduction\napplies, so in this, the most difficult, the conclusions of\nratiocination must be _verified_ by collation with the concrete\nphenomena, or, if possible, with their empirical laws; and then the only\neffect of an increase in the complication of the subject will be a\ntendency to a disturbance, and sometimes even to an inversion (which,\nindeed, M. Comte thinks inseparable from all Sociological enquiries) in\nthe order of the two processes, obliging us, first, to conjecture the\nconclusions by specific experience, and then verify them by _a priori_\nreasonings showing their connection with the principles of human nature.\n\nSociology is a system not of positive predictions, but of tendencies. Of\ntendencies themselves, not many can be laid down as true of all\nsocieties alike. Even in the case of any single feature of society, the\n_consensus_ which exists in the body politic, as in the body natural,\nmakes it uncertain whether a cause with a special tendency in one age or\ncountry will have quite the same in another. General propositions,\ntherefore, in this deductive science, as, to be true, they must be\nhypothetical, and state the operation of a given cause in _given\ncircumstances_, so, to be of any utility, should be limited to those\nclasses of facts, which, though influenced by all sociological agents,\nare yet influenced _immediately_ by a few only, certain fixed\ncombinations of which are likely to recur often. Thus, Political\nEconomy, taking the one psychological law that men prefer a greater gain\nto a smaller, and ignoring every other motive, except what are\nperpetually adverse principles to this, viz. men's aversion to labour\nand desire of present costly pleasures, assumes, in enquiring what acts\nthis desire of gain will produce, that, within the department of human\naffairs, where it is actually the main end, it is the _sole_ end. Yet\nits general propositions are of great practical use, even though it thus\nprovisionally overlooks as well miscellaneous concurrent causes (with\nsome exceptions, as e.g. the principle of population), as also the fact\nof the non-existence elsewhere of the conditions of any one particular\ncountry (e.g. the peculiarly British mode of distribution of the produce\nof industry among three classes). Another hypothetical or abstract\nscience, which can be carved out of Sociology, is the as yet unexplored\nPolitical Ethology, i.e. the theory of the causes which determine a\npeople's, or age's, type of character, which collective character,\nbesides being the most interesting phenomenon in the particular state of\nsociety, is the _main_ cause of the social state which follows, and\nmoulds _entirely_ customs and laws. The neglect of national diversities\nsometimes (as e.g. the assumption by our political economists, that in\ncommercial populations everywhere, equally as in Great Britain and\nAmerica, all motives yield to the desire of gain) vitiates only the\npractical application of a proposition; but when the national character\nis mixed up at every step with the phenomena (as is the case in\nquestions respecting the tendencies of forms of government), the\nphenomena cannot properly be insulated in a separate branch of\nSociology.\n\nAs in Ethology and other deductive sciences, so in Statistics and\nHistory there are empirical laws. The immediate causes of social facts\nare often not open to direct observation; and the deductive science can\ndetermine only what causes produce a given effect, and not the frequency\nand quantities of them; in such cases, the empirical law of the causes\n(which, however, can be applied to new cases only if we know that the\nremoter causes, on which these latter causes depend, remain unchanged)\nmust be found through that of the effects, the Deductive Science relying\nthen for its data on indirect observation. But, in the separate branches\nof Sociology, we cannot obtain empirical laws by specific experience. It\nis so particularly (on account both of the number of the causes, and\nalso the fewness of the instances to be compared with the one in point)\nwhen the effect of any one (e.g. Corn Laws) of many simultaneous social\ncauses has to be determined. We can, however, in such cases, verify\n_indirectly_ a theory as to the influence of a particular cause in given\ncircumstances, by seeing if the same theory accounts for the _existing_\nstate of actual social facts which that cause has a tendency to\ninfluence.\n\n\n\n\nCHAPTER X.\n\nTHE INVERSE DEDUCTIVE, OR HISTORICAL, METHOD.\n\n\nThe _general_ Science of Society, as contrasted with the branches,\nshows, not what effect will follow from a given cause under given\ncircumstances, but what are the causes and characteristic phenomena of\nStates of Society generally. A _State of Society_ is the simultaneous\nstate of all the chief social facts (e.g. employments, beliefs, laws).\nIt is a condition of the whole organism; and, when analysed, it\nexhibits uniformities of coexistence between its different elements.\nBut, as this correlation between the phenomena is itself a law resulting\nfrom the laws which regulate the succession between one state of society\nand another, the fundamental problem of Social Science is to find these\nlatter laws. The form of this succession, by which (on account of the\nexceptionally constant reaction, in social facts, of the effects, i.e.\nhuman character, on their causes, i.e. human circumstances) one social\nstate is ever in process of changing into a different one, is now\nallowed to be, not, as in the solar system, a cycle, but a _progress_\n(by which is not here _necessarily_ meant _improvement_, whatever the\nfact may be). In France it has been thought, that a law of progress, to\nbe found by an analysis of the course of history, would enable us to\npredict the whole future. But such a law would be empirical, and not\ntrue beyond its own facts; for the succession of mental and social\nstates cannot have an independent law. Empirical laws must indeed be\nfound; or a _general_ Science of Society would be impossible: for, the\ncharacter of any one generation is so much the result of the characters\nof all prior ones, that _men_ could not compute so long a series from\nthe elementary laws producing it. But the empirical laws, when found (as\nthey can be, since the series of the effects as a whole is ever growing\nin uniformity), must be shown by deductions to be, if not the only\npossible, or even the most probable, at least possible, consequences of\nthe laws of human nature.\n\nThe empirical laws of society are uniformities, either of coexistence,\nor of succession. The former are ascertained and verified by Social\nStatics (which is the theory of the _consensus_, i.e. the mutual actions\nand reactions, of contemporaneous social elements); the latter, by\nSocial Dynamics (the theory of Society considered as in a state of\nprogress). As to Social Statics--there is, M. Comte thinks, a perpetual\nreciprocity of influence between all aspects of the same organism, and\nto such an extent, that the condition of any one which we cannot\ndirectly observe can be estimated by that of another which we can. There\nis, he considers, such an interdependence, not only between the\ndifferent sciences and arts among themselves, but between the sciences\nin general and the arts in general, even between the condition of\ndifferent nations of the same age, and between a form of government and\nthe civilisation of the period. Social Statics will ascertain for us the\nrequisites of stable political union: it will enquire what special\ncircumstances have always attended on such union, increasing and\ndecreasing in proportion to its completeness; and will then verify these\nfacts as requisites by deducing them from general laws of human nature.\nThus, history indicates as such requisites and conditions of free\npolitical union: 1. A system of educational discipline checking man's\ntendency to anarchy; 2. Loyalty, i.e. a feeling of there being\nsomething, whether persons, institutions, or individual freedom and\npolitical and social equality, which is not to be, at least in practice,\ncalled in question; 3. That which the Roman Empire, notwithstanding all\nits tyranny, established, viz. a strong sense of common interest among\nfellow-citizens (a very different feeling, by the bye, to mere\nantipathy to foreigners).\n\nSocial Dynamics regards sequences. But the _consensus_ in social facts\nprevents our tracing the leading facts in one generation to separate\ncauses in a prior one. Therefore, we must find the law of the\ncorrespondence not only between the simultaneous states, but between the\nsimultaneous changes of the elements of society. To find this law,\nwhich, when duly verified, will be the scientific derivative law of the\ndevelopment of humanity, we must combine the statical view of the\nphenomena with the dynamical. Fortunately, the state of mankind's\nspeculative faculties and beliefs, being the prime agent of the social\nmovement, furnishes a clue in the maze of social elements, since the\norder of human progression in all respects will mainly depend on the\norder of progression of this prime agent. That the other dispositions\nwhich aid in social progress (e.g. the desire for increased material\ncomfort) owe their means of working to this (however relatively weak a\npropensity it may be) is a conclusion from the laws of human nature; and\nthis conclusion is in accordance also with the course of history, in\nwhich internal social changes have ever been preceded by proportionate\nintellectual changes. To determine the law of the successive\ntransformations of opinions all past time must be searched, since such\nchanges appear definitely only at long intervals. M. Comte alone has\nfollowed out this conception of the Historical Method; and his\ngeneralisation, to the effect that speculation has, on all subjects,\nthree successive stages, has high scientific value.\n\nThe Historical Method will trace the derivative laws of social order\nand progress. It will enable us both to predict the future, and (thus\nfounding the noblest part of the Political Art) partly to shape it. At\npresent, both the Science and the Art are in the rudiments; but they are\nprogressing.\n\n\n\n\nCHAPTER XI.\n\nTHE LOGIC OF PRACTICE, OR ART; INCLUDING MORALITY AND POLICY.\n\n\nPractical Ethics, i.e. Morality, is an art; and therefore its Method\nmust be that of Art in general. Now, Art from the major premiss,\nsupplied by itself, viz. that the end is desirable, and from the\ntheorem, lent by Science, of the combinations of circumstances by which\nthe end can be reached, concludes that to secure this combination of\ncircumstances is desirable; if it also appear practicable, it turns the\ntheorem into a rule. Unless Science's report as to the circumstances is\na full one, the rule may fail; and as, in any case, rules of conduct\ncannot comprise more than the ordinary conditions of the effect (or they\nwould be too cumbrous for use), they must, at least in moral subjects,\nbe considered, till confronted with the theorems, which are the reasons\nof them, provisional only. Practical maxims, therefore, till so\nconfronted, are not universally true even for a given end, much less for\nconduct generally, and must not be used, as they are by the\n_geometrical_ school, as ultimate premisses.\n\nAny particular art consists of its rules, _together with_ the theorems\non which they depend; and Art in general consists of the truths of\nScience; only these must be arranged in the order most convenient, not,\nas in Science (which is an enquiry into the course of nature), for\nthought, but for practice. Intermediate scientific truths must be framed\nto serve as first principles of the various arts: and through them the\nend or purpose of an art will be connected with the means for realising\nthe conditions of its attainment. The end itself, however, is defined by\nthe art, not by the science. Each art has one first principle or major\npremiss which does not, as the propositions of Science, assert that a\nthing _is_ or _will be_, but recommends it as what _ought to be_. A\nscientific theory, however complete, of the history and tendencies of\nsociety does not show us (without Teleology, i.e. the Doctrine of Ends)\nwhat are the preferable ends. Art itself has its Philosophia Prima, for\nascertaining the standard of ends. There can be but one such standard or\ngeneral principle to which all rules of practice should conform; for, if\nthere were several, a higher yet would be needed, as umpire when they\ndisagreed. In Morality the felt need of a standard has been sometimes\nsupplied by the hypothesis of intuitive moral principles: but a standard\nwould still be wanted for the other two branches of the Art of Life,\nviz. Prudence or Policy, and Taste; and _their_ standard when found\nwould serve for Morality as well. The true standard, or general\nprinciple, is, _the promotion of the happiness of_ ALL _sentient\nbeings_. This is not the _sole_ end; for instance, ideal nobleness of\nwill or conduct should be pursued in preference to the _specific_\npursuit of happiness; but all ends whatsoever must be justified and\nshould be controlled by it.\n\n\nLONDON\nPRINTED BY SPOTTISWOODE AND CO.\nNEW-STREET SQUARE","title":"Analysis of Mr. Mill's System of Logic","tradition":"philosophy-ethics","translated_text":null,"word_count":43516}