{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_41838/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_41838","id":"gutenberg_41838","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/41838","summary":null,"tags":["Category: Philosophy & Ethics","Logic","Reasoning"],"text":"THE ART OF\n  LOGICAL THINKING\n\n  OR\n\n  THE LAWS OF REASONING\n\n  By WILLIAM WALKER ATKINSON\n\n\n  L.N. FOWLER & COMPANY\n  7, Imperial Arcade, Ludgate Circus\n  London, E.C., England\n\n  1909\n  THE PROGRESS COMPANY\n  CHICAGO, ILL.\n\n\n\n\n  Copyright 1909\n  By\n  THE PROGRESS COMPANY\n  Chicago, Ill., U.S.A.\n\n\n\n\nCONTENTS\n\n\n      I. Reasoning                            9\n\n     II. The Process of Reasoning            17\n\n    III. The Concept                         25\n\n     IV. The Use of Concepts                 37\n\n      V. Concepts and Images                 48\n\n     VI. Terms                               56\n\n    VII. The Meaning of Terms                73\n\n   VIII. Judgments                           82\n\n     IX. Propositions                        90\n\n      X. Immediate Reasoning                 99\n\n     XI. Inductive Reasoning                107\n\n    XII. Reasoning by Induction             116\n\n   XIII. Theory and Hypotheses              125\n\n    XIV. Making and Testing Hypotheses      132\n\n     XV. Deductive Reasoning                144\n\n    XVI. The Syllogism                      156\n\n   XVII. Varieties of Syllogisms            167\n\n  XVIII. Reasoning by Analogy               179\n\n    XIX. Fallacies                          186\n\n\n\n\nCHAPTER I.\n\nREASONING\n\n\n\"Reasoning\" is defined as: \"The act, process or art of exercising the\nfaculty of reason; the act or faculty of employing reason in argument;\nargumentation, ratiocination; reasoning power; disputation, discussion,\nargumentation.\" Stewart says: \"The word _reason_ itself is far from\nbeing precise in its meaning. In common and popular discourse it denotes\nthat power by which we distinguish truth from falsehood, and right from\nwrong, and by which we are enabled to combine means for the attainment\nof particular ends.\"\n\nBy the employment of the reasoning faculties of the mind we compare\nobjects presented to the mind as percepts or concepts, taking up the\n\"raw materials\" of thought and weaving them into more complex and\nelaborate mental fabrics which we call abstract and general ideas of\ntruth. Brooks says: \"It is the thinking power of the mind; the faculty\nwhich gives us what has been called _thought-knowledge_, in distinction\nfrom _sense-knowledge_. It may be regarded as the mental architect among\nthe faculties; it transforms the material furnished by the senses ...\ninto new products, and thus builds up the temples of science and\nphilosophy.\" The last-mentioned authority adds: \"Its products are\ntwofold, _ideas_ and _thoughts_. An _idea_ is a mental product which\nwhen expressed in words does not give a proposition; a _thought_ is a\nmental product which embraces the relation of two or more ideas. The\nideas of the understanding are of two general classes; abstract ideas\nand general ideas. The thoughts are also of two general classes; those\npertaining to contingent truth and those pertaining to necessary truth.\nIn contingent truth, we have _facts_, or immediate judgments, and\n_general truths_ including _laws_ and _causes_, derived from particular\nfacts; in necessary truth we have _axioms_, or self-evident truths, and\nthe truths derived from them by reasoning, called _theorems_.\"\n\nIn inviting you to consider the processes of reasoning, we are\nirresistibly reminded of the old story of one of Moliere's plays in\nwhich one of the characters expresses surprise on learning that he \"had\nbeen talking prose for forty years without knowing it.\" As Jevons says\nin mentioning this: \"Ninety-nine people out of a hundred might be\nequally surprised on hearing that they had been converting propositions,\nsyllogizing, falling into paralogisms, framing hypotheses and making\nclassifications with genera and species. If asked whether they were\nlogicians, they would probably answer, No! They would be partly right;\nfor I believe that a large number even of educated persons have no clear\nidea of what logic is. Yet, in a certain way, every one must have been a\nlogician since he began to speak.\"\n\nSo, in asking you to consider the processes of reasoning we are not\nassuming that you never have reasoned--on the contrary we are fully\naware that you in connection with every other person, have reasoned all\nyour mature life. That is not the question. While everyone reasons, the\nfact is equally true that the majority of persons reason incorrectly.\nMany persons reason along lines far from correct and scientific, and\nsuffer therefor and thereby. Some writers have claimed that the majority\nof persons are incapable of even fairly correct reasoning, pointing to\nthe absurd ideas entertained by the masses of people as a proof of the\nstatement. These writers are probably a little radical in their views\nand statements, but one is often struck with wonder at the evidences of\nincapacity for interpreting facts and impressions on the part of the\ngeneral public. The masses of people accept the most absurd ideas as\ntruth, providing they are gravely asserted by some one claiming\nauthority. The most illogical ideas are accepted without dispute or\nexamination, providing they are stated solemnly and authoritatively.\nParticularly in the respective fields of religion and politics do we\nfind this blind acceptance of illogical ideas by the multitude. Mere\nassertion by the leaders seems sufficient for the multitude of followers\nto acquiesce.\n\nIn order to reason correctly it is not merely necessary to have a good\nintellect. An athlete may have the proper proportions, good framework,\nand symmetrical muscles, but he cannot expect to cope with others of his\nkind unless he has learned to develop those muscles and to use them to\nthe best advantage. And, in the same way, the man who wishes to reason\ncorrectly must develop his intellectual faculties and must also learn\nthe art of using them to the best advantage. Otherwise he will waste his\nmental energy and will be placed at a disadvantage when confronted with\na trained logician in argument or debate. One who has witnessed a debate\nor argument between two men equally strong intellectually, one of whom\nis a trained logician and the other lacking this advantage, will never\nforget the impression produced upon him by the unequal struggle. The\nconflict is like that of a powerful wrestler, untrained in the little\ntricks and turns of the science, in the various principles of applying\nforce in a certain way at a certain time, at a certain place, with a\ntrained and experienced wrestler. Or of a conflict between a muscular\ngiant untrained in the art of boxing, when confronted with a trained and\nexperienced exponent of \"the manly art.\" The result of any such conflict\nis assured in advance. Therefore, everyone should refuse to rest content\nwithout a knowledge of the art of reasoning correctly, for otherwise he\nplaces himself under a heavy handicap in the race for success, and\nallows others, perhaps less well-equipped mentally, to have a decided\nadvantage over him.\n\nJevons says in this connection: \"To be a good logician is, however, far\nmore valuable than to be a good athlete; because logic teaches us to\nreason well, and reasoning gives us knowledge, and knowledge, as Lord\nBacon said, is power. As athletes, men cannot for a moment compare with\nhorses or tigers or monkeys. Yet, with the power of knowledge, men tame\nhorses and shoot tigers and despise monkeys. The weakest framework with\nthe most logical mind will conquer in the end, because it is easy to\nforesee the future, to calculate the result of actions, to avoid\nmistakes which might be fatal, and to discover the means of doing things\nwhich seemed impossible. If such little creatures as ants had better\nbrains than men, they would either destroy men or make them into slaves.\nIt is true that we cannot use our eyes and ears without getting some\nkind of knowledge, and the brute animals can do the same. But what gives\npower is the deeper knowledge called Science. People may see, and hear,\nand feel all their lives without really learning the nature of things\nthey see. But reason is the mind's eye, and enables us to see why things\nare, and when and how events may be made to happen or not to happen. The\nlogician endeavors to learn exactly what this reason is which makes the\npower of men. We all, as I have said, must reason well or ill, but logic\nis the science of reasoning and enables us to distinguish between the\ngood reasoning which leads to truth, and the bad reasoning which every\nday betrays people into error and misfortune.\"\n\nIn this volume we hope to be able to point out the methods and\nprinciples of correctly using the reasoning faculties of the mind, in a\nplain, simple manner, devoid of useless technicalities and academic\ndiscussion. We shall adhere, in the main, to the principles established\nby the best of the authorities of the old school of psychology, blending\nthe same with those advanced by the best authorities of the New\nPsychology. No attempt to make of this book a school text-book shall be\nmade, for our sole object and aim is to bring this important subject\nbefore the general public composed of people who have neither the time\nnor inclination to indulge in technical discussion nor academic\nhair-splitting, but who desire to understand the underlying _working\nprinciples_ of the Laws of Reasoning.\n\n\n\n\nCHAPTER II.\n\nTHE PROCESS OF REASONING\n\n\nThe processes of Reasoning may be said to comprise four general stages\nor steps, as follows:\n\nI. _Abstraction_, by which is meant the process of _drawing off_ and\n_setting aside_ from an object, person or thing, _a quality or\nattribute_, and making of it a distinct object of thought. For instance,\nif I perceive in a _lion_ the quality of _strength_, and am able to\nthink of this quality abstractly and independently of the animal--if the\nterm _strength_ has an actual mental meaning to me, independent of the\nlion--then I have _abstracted_ that quality; the thinking thereof is an\nact of _abstraction_; and the thought-idea itself is an _abstract idea_.\nSome writers hold that these abstract ideas are realities, and \"not mere\nfigments of fancy.\" As Brooks says: \"The rose dies, but my idea of its\ncolor and fragrance remains.\" Other authorities regard Abstraction as\nbut an act of _attention_ concentrated upon but the particular quality\nto the exclusion of others, and that the abstract idea has no existence\napart from the general idea of the object in which it is included. Sir\nWilliam Hamilton says: \"We can rivet our attention on some particular\nmode of a thing, as its smell, its color, its figure, its size, etc.,\nand abstract it from the others. This may be called Modal Abstraction.\nThe abstraction we have now been considering is performed on individual\nobjects, and is consequently particular. There is nothing necessarily\nconnected with generalization in abstraction; generalization is indeed\ndependent on abstraction, which it supposes; but abstraction does not\ninvolve generalization.\"\n\nII. _Generalization_, by which is meant the process of forming Concepts\nor General Ideas. It acts in the direction of apprehending the common\nqualities of objects, persons and things, and combining and uniting them\ninto a single notion or _conception_ which will comprehend and include\nthem all. A General Idea or Concept differs from a particular idea in\nthat it includes within itself the qualities of the particular and other\nparticulars, and accordingly may be applied to any one of these\nparticulars as well as to the general _class_. For instance, one may\nhave a _particular idea_ of some _particular_ horse, which applies only\nto that particular horse. He may also have a General Idea of _horse_, in\nthe generic or _class_ sense, which idea applies not only to the general\nclass of _horse_ but also to each and every _horse_ which is included in\nthat class. _The expression of Generalization or Conception is called a\nConcept._\n\nIII. _Judgment_, by which is meant the process of comparing two objects,\npersons or things, one with another, and thus perceiving their agreement\nor disagreement. Thus we may compare the two concepts _horse_ and\n_animal_, and perceiving a certain agreement between them we form the\njudgment that: \"A _horse_ is an _animal_;\" or comparing _horse_ and\n_cow_, and perceiving their disagreement, we form the judgment: \"A\n_horse_ is not a _cow_.\" _The expression of a judgment is called a\nProposition._\n\nIV. _Reasoning_, by which is meant the process of comparing two objects,\npersons or things, through their relation to a third object, person or\nthing. Thus we may reason (a) that all mammals are animals; (b) that a\nhorse is a mammal; (c) that, _therefore_, a horse is an animal; the\nresult of the reasoning being the statement that: \"A horse is an\nanimal.\" The most fundamental principle of reasoning, therefore,\nconsists in the comparing of two objects of thought through and by means\nof their relation to a third object. _The natural form of expression of\nthis process of Reasoning is called a Syllogism._\n\nIt will be seen that these four processes of reasoning necessitate the\nemployment of the processes of Analysis and Synthesis, respectively.\nAnalysis means a separating of an object of thought into its constituent\nparts, qualities or relations. Synthesis means the combining of the\nqualities, parts or relations of an object of thought into a composite\nwhole. These two processes are found in all processes of Reasoning.\nAbstraction is principally analytic; Generalization or Conception\nchiefly synthetic; Judgment is either or both analytic or synthetic;\nReasoning is either a synthesis of particulars in Induction, or an\nevolution of the particular from the general in Deduction.\n\nThere are two great classes of Reasoning; _viz._, (1) Inductive\nReasoning, or the inference of general truths from particular truths;\nand (2) Deductive Reasoning, or the inference of particular truths from\ngeneral truths.\n\n_Inductive Reasoning_ proceeds by discovering a general truth from\nparticular truths. For instance, from the particular truths that\nindividual men die we discover the general truth that \"All men must\ndie;\" or from observing that in all observed instances ice melts at a\ncertain temperature, we may infer that \"All ice melts at a certain\ntemperature.\" Inductive Reasoning proceeds from the _known to the\nunknown_. It is essentially a synthetic process. It seeks to discover\ngeneral laws from particular facts.\n\n_Deductive Reasoning_ proceeds by discovering particular truths from\ngeneral truths. Thus we reason that as all men die, John Smith, being a\nman, must die; or, that as all ice melts at a certain temperature, it\nfollows that the particular piece of ice under consideration will melt\nat that certain temperature. Deductive Reasoning is therefore seen to be\nessentially an analytical process.\n\nMills says of Inductive Reasoning: \"The inductive method of the ancients\nconsisted in ascribing the character of general truths to all\npropositions which are true in all the instances of which we have\nknowledge. Bacon exposed the insufficiency of this method, and physical\ninvestigation has now far outgrown the Baconian conception....\nInduction, then, is that operation by which we infer that what we know\nto be true in a particular case or cases, will be true in all cases\nwhich resemble the former in certain assignable respects. In other\nwords, induction is the process by which we conclude that what is true\nof certain individuals of a class is true of the whole class, or that\nwhat is true at certain times will be true in similar circumstances at\nall times.\"\n\nRegarding Deductive Reasoning, a writer says: \"Deductive Reasoning is\nthat process of reasoning by which we arrive at the necessary\nconsequences, _starting from admitted or established premises_.\" Brooks\nsays: \"The general truths from which we reason to particulars are\nderived from several distinct sources. Some are intuitive, as the axioms\nof mathematics or logic. Some of them are derived from induction....\nSome of them are merely hypothetical, as in the investigation of the\nphysical sciences. Many of the hypotheses and theories of the physical\nsciences are used as general truth for deductive reasoning; as the\ntheory of gravitation, the theory of light; etc. Reasoning from the\ntheory of universal gravitation, Leverrier discovered the position of a\nnew planet in the heavens before it had been discovered by human eyes.\"\n\nHalleck points out the interdependence of Inductive and Deductive\nReasoning in the following words: \"Man has to find out through his own\nexperience, or that of others, the _major premises_ from which he argues\nor draws his conclusions. By induction we examine what seems to us a\nsufficient number of individual cases. We then conclude that the rest of\nthese cases, which we have not examined, _will obey the same general\nlaws_.... The premise, 'All cows chew the cud,' was laid down after a\ncertain number of cows had been examined. If we were to see a cow twenty\nyears hence, we should expect that she chewed her cud.... After\nInduction has classified certain phenomena and _thus given us a major\npremise_, we proceed deductively to apply the inference to any new\nspecimen that can be shown to belong to that class.\"\n\nThe several steps of Deductive Reasoning shall now be considered in turn\nas we proceed.\n\n\n\n\nCHAPTER III.\n\nTHE CONCEPT\n\n\nIn considering the process of thinking, we must classify the several\nsteps or stages of thought that we may examine each in detail for the\npurpose of comprehending them combined as a whole. In actual thinking\nthese several steps or stages are not clearly separated in\nconsciousness, so that each stands out clear and distinct from the\npreceding and succeeding steps or stages, but, on the contrary, they\nblend and shade into each other so that it is often difficult to draw a\nclear dividing line. The first step or stage in the process of thinking\nis that which is called _a concept_.\n\nA concept is a mental representation of anything. Prof. Wm. James says:\n\"The function by which we mark off, discriminate, draw a line around,\nand identify a numerically distinct subject of discourse is called\n_conception_.\" There are five stages or steps in each concept, as\nfollows:\n\nI. _Presentation._ Before a concept may be formed there must first be a\npresentation of the material from which the concept is to be formed. If\nwe wish to form the concept, _animal_, we must first have perceived an\nanimal, probably several kinds of animals--horses, dogs, cats, cows,\npigs, lions, tigers, etc. We must also have received impressions from\nthe sight of these animals which may be reproduced by the\nmemory--represented to the mind. In order that we may have a full\nconcept of _animal_ we should have perceived every kind of animal, for\notherwise there would be some elements of the full concept lacking.\nAccordingly it is practically impossible to have a _full_ concept of\nanything. The greater the opportunities for perception the greater will\nbe the opportunity for conception. In other books of this series we have\nspoken of the value and importance of the attention and of clear and\nfull perception. Without an active employment of the attention, it is\nimpossible to receive a clear perception of anything; and unless the\nperception has been clear, it is impossible for the mind to form a clear\nconcept of the thing perceived. As Sir Wm. Hamilton has said: \"An act\nof attention, that is an act of concentration, seems thus necessary to\nevery exertion of consciousness, as a certain contraction of the pupil\nis requisite to every exertion of vision.... Attention, then, is to\nconsciousness what the contraction of the pupil is to sight, or to the\neye of the mind what the microscope or telescope is to the bodily\neye.... It constitutes the half of all intellectual power.\" And Sir B.\nBrodie said: \"It is attention, much more than in the abstract power of\nreasoning, which constitutes the vast difference which exists between\nminds of different individuals.\" And as Dr. Beattie says: \"The force\nwith which anything strikes the mind is generally in proportion to the\ndegree of attention bestowed upon it.\"\n\nII. _Comparison._ Following the stage of Presentation is the stage of\nComparison. We separate our general concept of _animal_ into a number of\nsub-concepts, or concepts of various kinds of animals. We compare the\npig with the goat, the cow with the horse, in fact each animal with all\nother animals known to us. By this process we distinguish the points of\nresemblance and the points of difference. We perceive that the wolf\nresembles the dog to a considerable degree; that it has some points of\nresemblance to the fox; and a still less distinct resemblance to the\nbear; also that it differs materially from the horse, the cow or the\nelephant. We also learn that there are various kinds of wolves, all\nbearing a great resemblance to each other, and yet having marked points\nof difference. The closer we observe the various individuals among the\nwolves, the more points of difference do we find. The faculty of\nComparison evidences itself in inductive reasoning; ability and\ndisposition to analyze, classify, compare, etc. Fowler says that those\nin whom it is largely developed \"Reason clearly and correctly from\nconclusions and scientific facts up to the laws which govern them;\ndiscern the known from the unknown; detect error by its incongruity with\nfacts; have an excellent talent for comparing, explaining, expounding,\ncriticising, exposing, etc.\" Prof. William James says: \"Any personal or\npractical interest in the results to be obtained by distinguishing,\nmakes one's wits amazingly sharp to detect differences. And long\ntraining and practice in distinguishing has the same effect as personal\ninterest. Both of these agencies give to small amounts of objective\ndifference the same effectiveness upon the mind that, under other\ncircumstances, only large ones would make.\"\n\nIII. _Abstraction._ Following the stage of Comparison is that of\nAbstraction. The term \"Abstraction\" as used in psychology means: \"The\nact or process of separating from the numerous qualities inherent in any\nobject, the particular one which we wish to make the subject of\nobservation and reflection. Or, the act of withdrawing the consciousness\nfrom a number of objects with a view to concentrate it on some\nparticular one. The negative act of which Attention is the positive.\" To\n_abstract_ is \"to separate or set apart.\" In the process of Abstraction\nin our consideration of _animals_, after having recognized the various\npoints of difference and resemblance between the various species and\nindividuals, we proceed to consider some special quality of animals,\nand, in doing so, we _abstract_, set aside, or separate the particular\nquality which we wish to consider. If we wish to consider the _size_ of\nanimals, we abstract the quality of size from the other qualities, and\nconsider animals with reference to size alone. Thus we consider the\nvarious degrees of size of the various animals, classifying them\naccordingly. In the same way we may abstract the quality of shape, color\nor habits, respectively, setting aside this quality for special\nobservation and classification. If we wish to study, examine or consider\ncertain qualities in a thing we abstract that particular quality from\nthe other qualities of the thing; or we abstract the other qualities\nuntil nothing is left but the particular quality under consideration. In\nexamining or considering a class or number of things, we first abstract\nthe qualities _possessed in common_ by the class or number of things;\nand also abstract or set aside the qualities _not common_ to them.\n\nFor instance; in considering classes of animals, we abstract the\ncombined quality of milk-giving and pouch-possessing which is possessed\nin common by a number of animals; then we group these several animals in\na class which we name the _Marsupialia_, of which the opossum and\nkangaroo are members. In these animals the young are brought forth in an\nimperfect condition, undeveloped in size and condition, and are then\nkept in the pouch and nourished until they are able to care for\nthemselves. Likewise, we may abstract the idea of the _placenta_, the\nappendage which connects the young unborn animal with the mother, and by\nmeans of which the foetus is nourished. The animals distinguished by\nthis quality are grouped together as the Placental Mammals. The\nPlacental Mammals are divided into various groups, by an Abstraction of\nqualities or class resemblance or difference, as follows: The\n_Edentata_, or toothless creatures, such as the sloths, ant-eaters,\narmadillos, etc.; the _Sirenia_, so-named from their fancied resemblance\nto the fabled \"sirens,\" among which class are the sea-cows, manatees,\ndugongs, etc.; the _Cetacea_, or whale family, which although fish-like\nin appearance, are really mammals, giving birth to living young which\nthey nourish with breast-milk, among which are the whales, porpoises,\ndolphins, etc.; the _Ungulata_, or hoofed animals, such as the horse,\nthe tapir, the rhinoceros, the swine, the hippopotamus, the camel, the\ndeer, the sheep, the cow, etc.; the _Hyracoidea_, having teeth\nresembling both the hoofed animals and the gnawing animals, of which the\nconey or rock-rabbit is the principal example; the _Proboscidea_, or\ntrunked animals, which family is represented by the various families of\nelephants; the _Carnivora_, or flesh-eaters, represented by various\nsub-families and species; the _Rodentia_, or gnawers; the _Insectivora_,\nor insect feeders; the _Cheiroptera_, or finger-winged; the\n_Lemuroidea_, or lemurs, having the general appearance of the monkey,\nbut also the long bushy tail of the fox; the _Primates_, including the\nmonkeys, baboons, man-apes, gibbons, gorillas, chimpanzees,\norang-outangs and Man.\n\nIn all of these cases you will see that each class or general family\npossesses a certain _common quality_ which gives it its classification,\nand which quality is the subject of the Abstraction in considering the\nparticular group of animals. Further and closer Abstraction divides\nthese classes into sub-classes; for instance, the family or class of the\n_Carnivora_, or flesh-eaters, may be divided by further Abstraction\ninto the classes of seals, bears, weasels, wolves, dogs, lions, tigers,\nleopards, etc. In this process, we must first make the more general\nAbstraction of the wolf and similar animals into the dog-family; and the\nlion, tiger and similar forms into the cat-family.\n\nHalleck says of Abstraction: \"In the process of Abstraction, we draw our\nattention away from a mass of confusing details, unimportant at the\ntime, and attend only to qualities common to the class. Abstraction is\nlittle else than centering the power of attention on some qualities to\nthe exclusion of others.\"\n\nIV. _Generalization._ Arising from the stage of Abstraction is the stage\nof Generalization. _Generalization_ is: \"The act or process of\ngeneralizing or making general; bringing several objects agreeing in\nsome point under a common or general name, head or class; an extending\nfrom particulars to generals; reducing or arranging in a genus; bringing\na particular fact or series of facts into a relation with a wider circle\nof facts.\" As Bolingbroke says: \"The mind, therefore, makes its utmost\nendeavors to _generalize_ its ideas, beginning early with such as are\nmost familiar and coming in time to those which are less so.\" Under the\nhead of Abstraction we have seen that through Abstraction we may\nGeneralize the various species into the various families, and thus, in\nturn, into the various sub-families. Following the same process we may\nnarrow down the sub-families into species composed of various\nindividuals; or into greater and still greater families or groups.\nGeneralization is really the act of Classification, or forming into\nclasses all things having certain qualities or properties _in common_.\nThe corollary is that _all things in a certain generalized class must\npossess the particular quality or property common to the class_. Thus we\nknow that all animals in the class of the _Carnivora_ must eat flesh;\nand that all _Mammals_ possess breasts from which they feed their young.\nAs Halleck says: \"We put all objects having like qualities into a\ncertain _genus_, or class. When the objects are in that class, _we know\nthat certain qualities will have a general application to them all_.\"\n\nV. _Denomination._ Following closely upon the step of Generalization or\nClassification, is the step of Denomination. By _Denomination_ we mean\n\"the act of naming or designating by a name.\" A name is the symbol by\nwhich we think of a familiar thing without the necessity for making a\ndistinct mental image upon each occasion of thought. Or, it may be\nconsidered as akin to a _label_ affixed to a thing. As in the case of\nthe algebraic symbols, _a_, _b_, _c_, _x_, and _y_, by the use of which\nwe are able to make intricate calculations easily and rapidly, so may we\nuse these word symbols much more readily than we could the lengthy\ndescriptions or even the mental images of the thing symbolized. It is\nmuch easier for us to think \"_horse_\" than it would be to think the full\ndefinition of that animal, or to think of it by recalling a mental\npicture of the horse each time we wished to think of it. Or, it is much\nbetter for us to be able to glance at a label on a package or bottle\nthan to examine the contents in detail. As Hobbes says: \"A word taken at\npleasure to serve for a mark, which may raise in our minds a thought\nlike to some thought we had before, and which being pronounced to\nothers, may be to them a sign of what thought the speaker had or had\nnot, before in his mind.\" Mill says: \"A name is a word (or set of\nwords) serving the double purpose of a mark to recall to ourselves the\nlikeness of a former thought and as a sign to make it known to others.\"\nSome philosophers regard names as symbols of _our ideas of things_,\nrather than of the things themselves; others regard them as symbols of\nthe things themselves. It will be seen that the value of a name depends\nmaterially upon the correct meaning and understanding regarding it\npossessed by the person using it.\n\n\n\n\nCHAPTER IV.\n\nTHE USE OF CONCEPTS\n\n\nHaving observed the several steps or stages of a concept, let us now\nconsider the use and misuse of the latter. At first glance it would\nappear difficult to misuse a concept, but a little consideration will\nshow that people very commonly fall into error regarding their concepts.\n\nFor instance, a child perceives a horse, a cow or a sheep and hears its\nelders apply the term \"_animal_\" to it. This term is perfectly correct,\nalthough symbolizing only a very general classification or\ngeneralization. But, the child knowing nothing of the more limited and\ndetailed classification begins to generalize regarding the animal. To\nit, accordingly, an \"animal\" is identical with the dog or the cow, the\nsheep or the horse, as the case may be, and when the term is used the\nchild thinks that _all animals_ are similar to the particular animal\nseen. Later on, when it hears the term \"animal\" applied to a totally\ndifferent looking creature, it thinks that a mistake has been made and\na state of confusion occurs. Or, even when a term is applied within\nnarrower limits, the same trouble occurs. The child may hear the term\n\"dog\" applied to a mastiff, and it accordingly forms a concept of _dog_\nidentical with the qualities and attributes of the mastiff. Later,\nhearing the same term applied to a toy-terrier, it becomes indignant and\ncries out that the latter is no \"dog\" but is something entirely\ndifferent. It is not until the child becomes acquainted with the fact\nthat there are many kinds of creatures in the general category of \"dog\"\nthat the latter term becomes fully understood and its appropriate\nconcept is intelligently formed. Thus we see the importance of the step\nof Presentation.\n\nIn the same way the child might imagine that because some particular\n\"man\" had red hair and long whiskers, _all men_ were red-haired and\nlong-whiskered. Such a child would always form the concept of \"man\" as a\ncreature possessed of the personal qualities just mentioned. As a writer\nonce said, readers of current French literature might imagine that all\nEnglishmen were short, dumpy, red-cheeked and irascible, and that all\nEnglishwomen had great teeth and enormous feet; also that readers of\nEnglish literature might imagine that all Frenchmen were like monkeys,\nand all Frenchwomen were sad coquettes. In the same way many American\nyoung people believe that all Englishmen say \"Don't you know\" and all\nEnglishwomen constantly ejaculate: \"Fancy!\" Also that every Englishman\nwears a monocle. In the same way, the young English person, from reading\nthe cheap novels of his own country, might well form the concept of all\nAmericans as long-legged, chin-whiskered and big-nosed, saying \"Waal, I\nwant to know;\" \"I reckon;\" and \"Du tell;\" while they tilted themselves\nback in a chair with their feet on the mantelpiece. The concept of a\nWestern man, entertained by the average Eastern person who has never\ntraveled further West than Buffalo, is equally amusing. In the same way,\nwe have known Western people who formed a concept of Boston people as\npartaking of a steady and continuous diet of baked beans and studiously\nreading Browning and Emerson between these meals.\n\nHalleck says: \"A certain Norwegian child ten years old had the quality\n_white_ firmly imbedded in his concept _man_. Happening one day to see a\nnegro for the first time, the child refused to call him a man until the\nnegro's other qualities compelled the child to revise his concept and to\neliminate whiteness. If that child should ever see an Indian or a\nChinaman, the concept would undergo still further revision. A girl of\nsix, reared with an intemperate father and brothers, had the quality of\n_drunkenness_ firmly fixed in her concept of _man_. A certain boy kept,\nuntil the age of eleven, _trustworthiness_ in his concept of man.\nAnother boy, until late in his teens thought that man was a creature who\ndid wrong not from determination but from ignorance, that any man would\nchange his course to the right path if he could but understand that he\nwas going wrong. Happening one day to hear of a wealthy man who was\nneglecting to provide comforts for his aged mother in her last sickness,\nthe boy concluded that the man did not know his mother's condition. When\nhe informed the man, the boy was told to mind his own business. The same\nday he heard of some politicians who had intentionally cheated the city\nin letting a contract and he immediately revised his concept. It must be\nborne in mind that most of our concepts are subject to change during our\nentire life; that at first they are made only in a tentative way; that\nexperience may show us, at any time, that they have been erroneously\nformed, that we have, abstracted too little or too much, made this class\ntoo wide or too narrow, or that here a quality must be added or there\none taken away.\"\n\nLet us now consider the mental processes involved in the formation and\nuse of a concept. We have first, as we have seen, the presentation of\nthe crude material from which the concept must be formed. Our attention\nbeing attracted to or directed toward an object, we notice its qualities\nand properties. Then we begin a process of comparison of the object\nperceived or of our perception of it. We compare the object with other\nobjects or ideas in our mind, noting similarities and differences and\nthereby leading towards classification with similar objects and opposed\ndissimilar ones. The greater the range of other objects previously\nperceived, the greater will be the number of relations established\nbetween the new object or idea and others. As we advance in experience\nand knowledge, the web of related objects and ideas becomes more\nintricate and complex. The relations attaching to the child's concept of\nhorse is very much simpler than the concept of the experienced adult.\nThen we pass on to the step of analysis, in which we separate the\nqualities of the object and consider them in detail. The act of\nabstraction is an analytical process. Then we pass on to the step of\nsynthesis, in which we unite the materials gathered by comparison and\nanalysis, and thus form a general idea or concept regarding the object.\nIn this process we combine the various qualities discerned by comparison\nand analysis, and grouping them together as in a bundle, we tie them\ntogether with the string of synthesis and thus have a true general\nconception. Thus from the first general conception of _horse_ as a\nsimple thing, we notice first that the animal has certain qualities\nlacking in other things and certain others similar to other things; then\nwe analyze the various qualities of the horse, recognized through\ncomparison, until we have a clear and distinct idea of the various\nparts, qualities and properties of the horse; then we synthesize, and\njoining together these various conceptions of the said qualities, we at\nlast form a clear general concept of _the horse as he is_, with all his\nqualities. Of course, if we later discover other qualities attached to\nthe horse, we add these to our general synthesized concept--our concept\nof _horse_ is enlarged.\n\nOf course these various steps in the formation and use of a concept are\nnot realized as distinct acts in the consciousness, for the processes\nare largely instinctive and subconscious, particularly in the case of\nthe experienced individual. The subconscious, or habit mind, usually\nattends to these details for us, except in instances in which we\ndeliberately apply the will to the task, as in cases of close study, in\nwhich we take the process from the region of the involuntary and place\nit in the voluntary category. So closely related and blended are these\nvarious steps of the process, that some authorities have disputed\nvigorously upon the question as to which of the two steps, comparison\nor analysis, precedes the other. Some have claimed that analysis must\nprecede comparison, else how could one compare without having first\nanalyzed the things to be compared. Others hold that comparison must\nprecede analysis, else how could one note a quality unless he had his\nattention drawn to it by its resemblance to or difference from qualities\nin other objects. The truth seems to lie between the two ideas, for in\nsome cases there seems to be a perception of some similarity or\ndifference before any analysis or abstraction takes place; while in\nothers there seems to be an analysis or abstraction before comparison is\npossible. In this book we have followed the arrangement favored by the\nlatest authorities, but the question is still an open one to many minds.\n\nAs we have seen, the general concept once having been formed, the mind\nproceeds to classify the concept with others having general qualities in\ncommon. And, likewise, it proceeds to generalize from the\nclassification, assuming certain qualities in certain classes. Then we\nproceed to make still further generalizations and classifications on an\nascending and widening scale, including seeming resemblances less\nmarked, until finally we embrace the object with other objects in as\nlarge a class as possible as well as in as close and limited a sub-class\nas possible. As Brooks says: \"Generalization is an ascending process.\nThe broader concept is regarded as higher than the narrower concept; a\nconcept is considered higher than a percept; a general idea stands above\na particular idea. We thus go up from particulars to generals; from\npercepts to concepts; from lower concepts to higher concepts. Beginning\ndown with particular objects, we rise from them to the general idea of\ntheir class. Having formed a number of lower classes, we compare them as\nwe did individuals and generalize them into higher classes. We perform\nthe same process with these higher classes, and thus proceed until we\nare at last arrested in the highest class, _Being_. Having reached the\npinnacle of generalization, we may descend the ladder by reversing the\nprocess through which we ascend.\"\n\nFrom this process of generalization, or synthesis, we create from our\nsimple concepts our _general concepts_. Some of the older authorities\ndistinguished between these two classes by terming the former\n\"conceptions,\" and reserving the term \"concepts\" for the general\nconcepts. Brooks says of this: \"The products of generalization are\ngeneral ideas called _concepts_. We have already discussed the method of\nforming conceptions and now consider the nature of the concept\nitself.... A concept is a general idea. It is a general notion which has\nin it all that is common to its own class. It is a general scheme which\nembraces all the individuals of the class while it resembles in all\nrespects none of its class. Thus my conception of a _quadruped_ has in\nit all four-footed animals, but it does not correspond in all respects\nto any particular animals; my conception of a _triangle_ embraces all\ntriangles, but does not agree in details with any particular triangle.\nThe general conception cannot be made to fit exactly any particular\nobject, but it teems with many particulars. These points may be\nillustrated with the concepts _horse_, _bird_, _color_, _animal_, etc.\"\n\nSo we may begin to perceive the distinction and difference between a\n_concept_ and a _mental image_. This distinction, and the fact that _a\nconcept cannot be imaged_, is generally difficult for the beginner. It\nis important that one should have a clear and distinct understanding\nregarding this point, and so we shall consider it further in the\nfollowing chapter.\n\n\n\n\nCHAPTER V.\n\nCONCEPTS AND IMAGES\n\n\nAs we have said, a concept cannot be imaged--cannot be used as the\nsubject of a mental image. This statement is perplexing to the student\nwho has been accustomed to the idea that every conception of the mind is\ncapable of being reproduced in the form of a mental image. But the\napparently paradoxical statement is seen as quite simple when a little\nconsideration is given to it.\n\nFor instance, you have a distinct general concept of _animal_. You know\nwhat you mean when you say or think, _animal_. You recognize an animal\nwhen you see one and you understand what is meant when another uses the\nword in conversation. But you cannot form a mental image of the concept,\n_animal_. Why? Because any mental image you might form would be either a\npicture of _some particular animal_ or else a composite of the qualities\nof several animals. Your concept is too broad and general to allow of a\ncomposite picture of _all animals_. And, in truth, your concept is _not\na picture of anything that actually exists_ in one particular, but an\nabstract idea embracing the qualities of all animals. It is like the\nalgebraic _x_--a symbol for something that exists, but not the thing\nitself.\n\nAs Brooks says: \"A concept cannot be represented by a concrete image.\nThis is evident from its being general rather than particular. If its\ncolor, size or shape is fixed by an image, it is no longer general but\nparticular.\" And Halleck says: \"It is impossible to image anything\nwithout giving that image individual marks. The best mental images are\nso definite that a picture could be painted from them. A being might\ncome under the class _man_ and have a snub nose, blonde hair, scanty\neyebrows, and no scar on his face. The presence of one of these\nindividual peculiarities in the concept _man_ would destroy it. If we\nform an image of an apple, it must be either of a yellow, red, green, or\nrusset apple, either as large as a pippin or as small as a crab-apple. A\nboy was asked what he thought of when '_apple_' was mentioned. He\nreplied that he thought of 'a big, dark-red, apple with a bad spot on\none side, near the top.' That boy could image distinctly, but his power\nof forming concepts was still in its infancy.\"\n\nSo we see that while a mental image must picture the particular and\nindividual qualities, properties and appearances of some particular unit\nof a class, a _concept_ can and must contain only the _class\nqualities_--that is, the qualities belonging to the entire class. The\ngeneral concept is as has been said \"a general idea ... a general notion\nwhich has in it all that is common to its own class.\" And it follows\nthat a \"general idea\" of this kind cannot be pictured. A picture must be\nof some particular thing, while a concept is something above and higher\nthan particular things. We may picture _a man_, but we cannot picture\nMan the concept of the race. A concept is not a reproduction of the\nimage of a _thing_, but on the contrary is _an idea of a class of\nthings_. We trust that the student will consider this point until he\narrives at a clear understanding of the distinction, and the reason\nthereof.\n\nBut, while a concept is incapable of being pictured mentally as an\nimage, it is true that _some particular representative of a class_ may\nbe held in the mind or imagination as _an idealized object_, as a\ngeneral representative of the class, when we speak or think of the\ngeneral term or concept, providing that its real relation to the concept\nis recognized. These idealized objects, however, are not concepts--they\nare _percepts_ reproduced by the memory. It is important, however, to\nall who wish to convey their thought plainly, that they be able to\nconvert their concepts into idealized representative objects. Otherwise,\nthey tend to become too idealistic and abstract for common\ncomprehension. As Halleck well says: \"We should in all cases be ready to\ntranslate our concepts, when occasion requires, into the images of those\nindividuals which the concept represents. A concept means nothing except\nin reference to certain individuals. Without them it could never have\nhad existence and they are entitled to representation. A man who cannot\ntranslate his concepts into definite images of the proper objects, is\nfitted neither to teach, preach, nor practice any profession.... There\nwas, not long ago, a man very fond of talking about _fruit_ in the\nabstract; but he failed to recognize an individual cranberry when it\nwas placed before him. A humorist remarked that a certain metaphysician\nhad such a love for abstractions, and such an intense dislike for\nconcrete things, as to refuse to eat a concrete peach when placed before\nhim.\"\n\nIn the beginning many students are perplexed regarding the difference\nbetween a _percept_ and a _concept_. The distinction is simple when\nproperly considered. A percept is: \"the object of an act of perception;\nthat which is perceived.\" A concept is: \"a mental representation.\"\nBrooks makes the following distinction: \"A _percept_ is the mental\nproduct of a real thing; a _concept_ is a mere idea or notion of the\ncommon attributes of things. A _percept_ represents some particular\nobject; a _concept_ is not particular, but general. A _percept_ can be\ndescribed by particulars; a _concept_ can be described only by generals.\nThe former can usually be represented by an image, the latter cannot be\nimagined, _it can only be thought_.\" Thus one is able to image the\n_percept_ of a particular horse which has been perceived; but he is\nunable to image correctly the concept of _horse_ as a class or generic\nterm.\n\nIn connection with this distinction between _perception_ and\n_conception_, we may as well consider the subject of _apperception_, a\nterm favored by many modern psychologists, although others steadfastly\ndecline to recognize its necessity or meaning and refuse to employ it.\nApperception may be defined as: \"perception accompanied by\ncomprehension; perception accompanied by recognition.\" The thing\nperceived is held to be comprehended or recognized--that is, _perceived\nin a new sense_, by reason of certain previously acquired ideas in the\nmind. Halleck explains it as: \"the perception of things in relation to\nthe ideas which we already possess.\" It follows that all individuals\npossessed of equally active organs of perception, and equally active\nattention, will perceive the same thing in the same way and in the same\ndegree. But the _apperception_ of each individual will differ and vary\naccording to his previous experience and training, temperament and\ntaste, habit and custom. For instance, the familiar story of the boy who\nclimbed a tree and watched the passers-by, noting their comments. The\nfirst passer-by noticing the tree, says aloud: \"That would make a good\nstick of timber.\" \"Good morning, Mr. Carpenter,\" said the boy. The next\nman said: \"That tree has fine bark.\" \"Good morning, Mr. Tanner,\" said\nthe boy. Another said, \"I bet there's a squirrel's nest up in that\ntree.\" \"Good morning, Mr. Hunter,\" said the boy.\n\nThe woman sees in a bird something pretty and \"cunning.\" The hunter sees\nin it something to kill. The ornithologist sees it as something of a\ncertain genus and species, and perhaps also as something appropriate for\nhis collection. The farmer perceives it to be something destructive of\neither insects or crops. A thief sees a jail as something to be dreaded;\nan ordinary citizen, something useful for confining objectionable\npeople; a policeman, something in the line of his business. And so on,\nthe apperception differing upon the previous experience of the\nindividual. In the same way the scientist sees in an animal or rock many\nqualities of which the ordinary person is ignorant. Our training,\nexperience, prejudices, etc., affect our apperception.\n\nAnd so, we see that in a measure our _concepts_ are determined not only\nby our simple perceptions, but also materially by our apperceptions. We\nconceive things not only as they are apparent to our senses, but also as\ncolored and influenced by our previous impressions and ideas. For this\nreason we find widely varying concepts of the same things among\ndifferent individuals. Only an absolute mind could form an absolute\nconcept.\n\n\n\n\nCHAPTER VI.\n\nTERMS\n\n\nIn logic the words _concept_ and _term_ are practically identical, but\nin the popular usage of the terms there is a distinct difference. This\ndifference is warranted, if we depart from the theoretical phase of\nlogic, for the word _concept_ really denotes an _idea_ in the mind,\nwhile the word _term_ really denotes a _word_ or name of an idea or\nconcept--the symbol of the latter. In a previous chapter we have seen\nthat Denomination, or \"the act of naming or designating by a name\" is\nthe final step or stage in forming a concept. And it is a fact that the\nmajority of the words in the languages of civilized people denote\ngeneral ideas or concepts. As Brooks says: \"To give each individual or\nparticular idea a name peculiar to itself would be impracticable and\nindeed impossible; the mind would soon become overwhelmed with its\nburden of names. Nearly all the ordinary words of our language are\ngeneral rather than particular. The individuals distinguished by\nparticular names, excepting persons and places, are comparatively few.\nMost objects are named only by common nouns; nearly all of our verbs\nexpress general actions; our adjectives denote common qualities, and our\nadverbs designate classes of actions and qualities. There are very few\nwords in the language, besides the names of persons and places, that do\nnot express general ideas.\"\n\nIn logic the word _term_ is employed to denote _any word or words which\nconstitute a concept_. The word _concept_ is employed strictly in the\nsense of _a subject of thought_, without reference to the words\nsymbolizing it. The _concept_, or subject of thought, is the important\nelement or fact and the _term_ denoting it is merely a convenient symbol\nof expression. It must be remembered that a _term_ does not necessarily\nconsists of but a single word, for often many words are employed to\ndenote the concept, sometimes even an entire clause or phrase being\nfound necessary for the current _term_. For the purpose of the\nconsideration of the subjects to be treated upon in this book, we may\nagree that: _A term is the outward symbol of a concept_; and that: _The\nconcept is the idea expressed by the term_.\n\nThere are three general parts or phases of Deductive Logic, namely:\nTerms, Propositions and Syllogisms. Therefore, in considering Terms we\nare entering into a consideration of the first phase of Deductive Logic.\nUnless we have a correct understanding of Terms, we cannot expect to\nunderstand the succeeding stages of Deductive Reasoning. As Jevons says:\n\"When we join terms together we make a Proposition; when we join\nPropositions together, we make an argument or piece of reasoning.... We\nshould generally get nothing but nonsense if we were to put together any\nterms and any propositions and to suppose that we were reasoning. To\nproduce a good argument we must be careful to obey certain rules, which\nit is the purpose of Logic to make known. But, in order to understand\nthe matter perfectly, _we ought first to learn exactly what a term is,\nand how many kinds of terms there may be_; we have next to learn the\nnature of a proposition and the different kinds of propositions.\nAfterwards we shall learn how one proposition may by reasoning be drawn\nfrom other propositions in the kind of argument called the syllogism.\"\n\nNow, having seen that terms are the outward symbols or expression of\nconcepts, and are the names of things which we join together in a\nproposition, let us proceed to consider the different kinds of terms,\nfollowing the classifications adopted by the authorities.\n\nA _term_ may contain any number of nouns, substantive or adjective or it\nmay contain but a single noun. Thus in, \"Tigers are ferocious,\" the\nfirst term is the single substantive \"tigers;\" the second term is the\nsingle adjective \"ferocious.\" And in the proposition, \"The King of\nEngland is the Emperor of India,\" there are two terms, each composed of\ntwo nouns, \"King of England\" being the first term and \"Emperor of India\"\nbeing the second term. The proposition, \"The library of the British\nMuseum is the greatest collection of books in the world,\" contains\nfifteen words but _only two terms_; the first term being \"The library of\nthe British Museum,\" in which are two substantives, one adjective, two\ndefinite articles and one preposition; the second term being, \"the\ngreatest collection of books in the world,\" which contains three\nsubstantives, one adjective, two articles, and two prepositions. The\nabove illustration is supplied by Jevons, who adds: \"A logical term,\nthen, may consist of any number of nouns, substantive or adjective, with\nthe articles, prepositions and conjunctions required to join them\ntogether; still _it is only one term if it points out, or makes us think\nof a single object, or collection, or class of objects_.\" (A\nsubstantive, is: \"the part of speech which expresses something that\nexists, either material or immaterial.\")\n\nThe first classification of terms divides them into two general classes,\n_viz._, (1) Singular Terms; and (2) General Terms.\n\nA _Singular Term_ is a term denoting a single object, person or thing.\nAlthough denoting only a single object, person or thing, it may be\ncomposed of several words; or it may be composed of but one word as in\nthe case of a proper name, etc. The following are Singular Terms,\nbecause they are terms denoting but a single object, person or thing:\n\"Europe; Minnesota; Socrates; Shakespeare; the first man; the highest\ngood; the first cause; the King of England; the British Museum; the\nCommissioner of Public Works; the main street of the City of New York.\"\nIt will be noted that in all of the examples given, the Singular Term\ndenotes a particular something, a specific thing, a something of which\nthere is but one, and that one possesses particularity and\nindividuality. As Hyslop says: \"_Oneness of kind_ is not the only or\ndistinctive feature of Singular Terms, but _individuality_, or\nsingularity, as representing a concrete individual whole.\"\n\nA _General Term_ is a term which applies, in the same sense, to each and\nevery individual object, person or thing in a number of objects, persons\nor things of the same kind, or to the entire class composed of such\nobjects persons or things of the same kind. For instance, \"horse; man;\nbiped; mammal; trees; figures; grain of sand; matter,\" etc. Hyslop says,\nregarding General Terms: \"In these instances the terms denote more than\none object, and apply to all of the same kind. Their meaning is\nimportant in the interpretation of what are called universal\npropositions.\"\n\nAnother general classification of Terms divides them into two\nrespective classes, as follows: (1) Collective Terms; and (2)\nDistributive Terms. Hyslop says of this classification: \"This division\nis based upon the distinction between aggregate wholes of the same kind\nand class terms. It partly coincides with the division into Singular and\nGeneral Terms, the latter always being distributive.\"\n\nA _Collective Term_ is one which denotes an aggregate or collected whole\nof objects, persons or things of the same or similar kind, _which\ncollective whole is considered as an individual_, although composed of a\ntotality of separate individual objects, persons or things. Thus the\nfollowing terms: \"regiment; congregation; army; family; crowd; nation;\ncompany; battalion; class; congress; parliament; convention;\" etc. are\nCollective Terms, because they denote collective, aggregate or composite\nwholes, considered as an individual.\n\nA _Distributive Term_ is a term which denotes _each and every individual\nobject, person or thing in a given class_. For example, are the terms:\n\"man; quadruped; biped; mammal; book; diamond; tree.\" As Hyslop says:\n\"General terms are always distributive.\" Also: \"It is important also to\nkeep clear the distinction between _class_ wholes and _collective_\nwholes.... They are often confused so as to call a term denoting a\n_class_ a Collective Term.\"\n\nAnother general classification of Terms divides them into the following\ntwo respective classes; (1) Concrete Terms; and (2) Abstract Terms.\n\nA _Concrete Term_ is a term denoting either a definite object, person or\nthing which is subject to perception and experience, and may be\nconsidered as actually existent concretely, as for instance: horse; man;\nmountain; dollar; knife; table; etc., or else an attribute thought of\nand used solely as an attribute, as for instance: \"beautiful, wise,\nnoble, virtuous, good,\" etc.\n\nAn _Abstract Term_ is a term denoting the attribute, quality or property\n_considered as apart from the object, person or thing_ and as having an\nabstract existence, as for instance: \"beauty; wisdom; nobility;\ngoodness; virtue,\" etc. As we have seen elsewhere, these qualities have\nno real existence _in themselves_, but are known and thought of only in\nconnection with concrete objects, persons and things. Thus we cannot\nknow \"Beauty,\" but may know _beautiful things_; we cannot know \"Virtue,\"\nbut we may know virtuous people, etc.\n\nAn _attribute or quality_ is _concrete_ when expressed as an\n_adjective_; and _abstract_ when expressed as a _noun_; as for instance,\n\"beautiful\" and \"beauty,\" respectively, or \"virtuous\" and \"virtue,\"\nrespectively. The distinction may be summed up as follows: A Concrete\nTerm is _the name of a thing or of a quality of a thing expressed as an\nadjective and as merely a quality_; while an Abstract Term is the name\nof a quality of a thing, _expressed as a noun and as a \"thing\" in\nitself_.\n\nCertain terms may be used as either Concrete Terms or as Abstract Terms,\nand certain authorities have seen fit to classify them as _Mixed Terms_,\nas for instance the terms: \"government; religion; philosophy;\" etc.\n\nAnother general classification of Terms divides them into two respective\nclasses as follows: (1) _Positive Terms_; and (2) _Negative Terms_.\n\nA _Positive Term_ is a term which denotes its own qualities, as for\ninstance: \"good, human, large, square, black, strong,\" etc. These terms\nindicate the presence of the quality denoted by the term itself.\n\nA _Negative Term_ is a term denoting the absence of a quality, as for\ninstance: \"inhuman, inorganic, unwell, unpleasant, non-conducive,\" etc.\nThese terms _deny_ the presence of certain qualities, rather than\n_asserting_ the presence of an opposite quality. They are essentially\nnegative in nature and in form. Jevons says: \"We may usually know a\nNegative Term by its beginning with one of the little syllables un-,\nin-, a-, an-, non-, or by its ending with -less.\" Hyslop says: \"The\nusual symbols of Negative Terms are _in_, _un_, _less_, _dis_, _a_, or\n_an_, _anti_, _mis_, and sometimes _de_, and _non_ and _not_.\" Jevons\nadds: \"If the English language were a perfect one, every term ought to\nhave a Negative Term exactly corresponding to it, so that all adjectives\nand nouns would be in pairs. Just as _convenient_ has its negative\n_inconvenient_; metallic, non-metallic; logical, illogical; and so on;\nso blue should have its negative, non-blue; literary, non-literary;\npaper, non-paper. But many of these Negative Terms would be seldom or\nnever used, and if we happen to want them, we can make them for the\noccasion by putting not-, or non-, before the Positive Term.\nAccordingly, we find in the dictionary only those Negative Terms which\nare much employed.\"\n\nThe last named authority also says: \"Sometimes the same word may seem to\nhave two or even more distinct negatives. There is much difference\nbetween _undressed_ and _not-dressed_, that is 'not in evening dress.'\nBoth seem to be negatives of 'dressed,' but this is because the word has\ntwo distinct meanings.\"\n\nSome authorities insist upon closer and further classification, as for\ninstance, in the case of what they call a _Privative Term_, denoting the\nabsence of qualities once possessed by the object, person or thing, as:\n\"deaf, dead, blind, dark,\" etc. Hyslop says that these terms \"are\nPositive in form and Negative in matter or meaning.\" Also in the case of\nwhat they call a _Nego-positive Term_, denoting \"the presence of a\npositive quality expressed in a negative manner,\" as: disagreeable,\ninhuman, invaluable, etc. These last mentioned classes however are\nregarded by some as the result of \"carrying too far\" the tendency\ntoward classification, and the two general classes, Positive and\nNegative, are thought sufficient for the purpose of the general student.\nThe same objection applies to a classification occasionally made _i.e._,\nthat which is called an _Infinitated Term_, denoting a term the intent\nof which is to place in a distinct category every object, person or\nthing other than that expressed in the corresponding Positive Term. The\nintent of the term is to place the positive idea in one class, and all\nelse into a separate one. Examples of this class of terms are found in:\n\"not-I, not-animal, not-tree, unmoral,\" etc. Hyslop says of these terms:\n\"They are not always, if ever, recognized as rhetorically elegant, but\nare valuable often to make clear the really negative, or infinitatively\nnegative nature of the idea in mind.\"\n\nAnother general classification of Terms divides them into two respective\nclasses, as follows: (1) Absolute Terms; and (2) Relative Terms.\n\nAn _Absolute Term_ is a term denoting the presence of qualities\nintrinsic to the object, and not depending upon any relation to any\nother object, as for instance: \"man; book; horse; gun;\" etc. These\nterms _may be_ related to many other terms, but are _not necessarily_\nrelated to any other.\n\nA _Relative Term_ is a term denoting certain _necessary_ relations to\nother terms, as for instance: \"father; son; mother; daughter; teacher;\npupil; master; servant;\" etc. Thus it is impossible to think of \"child\"\nexcept in relation to \"parent,\" or _vice versa_. The one term implies\nthe existence of its related term.\n\nHyslop says of the above classification: \"Relative Terms suggest the\nthought of other individuals with the relation involved as a part of the\nterm's meaning, while Absolute Terms suggest only the qualities in the\nsubject without a relation to others being necessarily involved.\"\n\nSome authorities also classify terms as _higher and lower_; also as\n_broad and narrow_. This classification is meant to indicate the content\nand extent of the term. For instance, when we classify, we begin with\nthe individuals which we then group into a small class. These classes we\nthen group into a larger class, according to their resemblances. These\nlarger classes then go to form a part of still larger classes, and so\non. As these classes advance they form _broader_ terms; and as we\nretreat from the general class into the less general and more\nparticular, the term becomes _narrower_. By some, the _broader_ term\nwhich includes the narrower is called the _higher term_, and the\nnarrower are called the _lower terms_. Thus _animal_ would be a higher\nand broader term than dog, cat or tiger because it includes the latter.\nBrooks says: \"Since a concept is formed by the union of the common\nattributes of individuals, it thus embraces both attributes and\nindividuals. The attributes of a concept constitute what is called its\n_content_; the individuals it embraces constitute its _extent_.\"\n\nAccordingly, the feature of including objects in a concept or term is\ncalled its _extension_; while the feature of including attributes or\nqualities is called its intension. It follows as a natural consequence\nthat the greater the _extension_ of a term, the less its _intension_;\nthe greater its _intension_, the less its _extension_. We will\nunderstand this more clearly when we consider that the more individuals\ncontained in a term, the fewer _common_ properties or qualities it can\ncontain; and the more common properties, the fewer individuals. As\nBrooks says: \"The concept _man_ has more _extension_ than _poet_,\n_orator_ or _statesman_, since it embraces more individuals; and less\n_intension_, since we must lay aside the distinctive attributes of poet,\norator and statesman in order to unite them in a common class _man_.\" In\nthe same way the general term _animal_ is quite extended for it includes\na large number of individual varieties of very different and varied\ncharacteristics and qualities; as for instance, the lion, camel, dog,\noyster, elephant, snail, worm, snake, etc. Accordingly its intension\nmust be small for it can include only the qualities common to all\nanimals, which are very few indeed. The definition of the term shows how\nsmall is its _intension_, as: \"_Animal._ An organic being, rising above\na vegetable in various respects, especially in possessing sensibility,\nwill and the power of voluntary motion.\" Another narrows the intension\nstill further when he defines _animal_ as: \"a creature which possesses,\nor has possessed, life.\" Halleck says: \"_Animal_ is very narrow in\nintension, very broad in extension. There are few qualities common to\nall animals, but there is a vast number of animals. To give the full\nmeaning of the term in _extension_, we should have to name every animal,\nfrom the microscopic infusoria to the tiger, from the angleworm to the\nwhale. When we decrease the extension to one species of animal, _horse_,\nthe individuals are fewer, the qualities more numerous.\"\n\nThe importance of forming clear and distinct concepts and of grouping,\nclassifying and generalizing these into larger and broader concepts and\nterms is recognized by all authorities and is generally regarded as\nforming the real basis of all constructive thought. As Brooks says:\n\"Generalization lies at the basis of language: only as man can form\ngeneral conceptions is it possible for him to form a language.... Nearly\nall the ordinary words in our language are general rather than\nparticular.... This power of generalization lies also at the basis of\nscience. Had we no power of forming general ideas, each particular\nobject would be a study by itself, and we should thus never pass beyond\nthe very alphabet of knowledge. Judgments, except in the simplest form,\nwould be impossible; and it is difficult to see how even the simplest\nform of the syllogism could be constructed. No general conclusion could\nbe drawn from particulars, nor particular conclusions from generals; and\nthus neither inductive nor deductive reasoning would be possible. The\nclassifications of science could not be made; and knowledge would end at\nthe very threshold of science.\"\n\n\n\n\nCHAPTER VII.\n\nTHE MEANING OF TERMS\n\n\nEvery term has its _meaning_, or _content_, as some authorities prefer\nto call it. The word or words of which the term is composed are merely\nvocal sounds, serving as a symbol for the real _meaning_ of the term,\nwhich _meaning_ exists only in the mind of the person understanding it.\nTo one not understanding the meaning of the term, the latter is but as a\nmeaningless sound, but to one understanding it the sound awakens mental\nassociations and representation and thus serves its purpose as a symbol\nof thought.\n\nEach concrete general term has two _meanings_, (1) the actual concrete\nthing, person or object to which the term is applied; and (2) the\nqualities, attributes or properties of those objects, persons or things\nin consequence of which the term is applied. For instance, in the case\nof the concrete term _book_, the first meaning consists of the general\nidea of the thing which we think of as _a book_, and the second meaning\nconsists of the various qualities which go to make that thing a book, as\nthe printed pages, the binding, the form, the cover, etc. Not only is\nthat particular thing _a book_, but every other thing having the same or\nsimilar properties also must be _a book_. And so, whenever I call a\nthing _a book_ it must possess the said qualities. And, whenever I\ncombine the ideas of these qualities in thought, I must think of _a\nbook_. As Jevons says: \"In reality, every ordinary general term has a\ndouble meaning: it means the things to which it is applied, ... it also\nmeans, in a totally different way, the qualities and peculiarities\n_implied_ as being in the things. Logicians say that the number of\nthings to which a term applies is the _extension_ of the term; while the\nnumber of qualities or peculiarities implied is the _intension_.\"\n\nThe extension and intension of terms has been referred to in the\nprevious chapter. The general classification of the degrees of\n_extension_ of a general term is expressed by the two terms, _Genus_ and\n_Species_, respectively. The classification of the character of the\n_intension_ of a term is expressed by the term, _Difference_,\n_Property_ and _Accident_, respectively.\n\n_Genus_ is a term indicating: \"a class of objects containing several\nspecies; a class more extensive than a species; a universal which is\npredicable of several things of different species.\"\n\n_Species_ is a term denoting: \"a smaller class of objects than a genus,\nand of two or more of which a genus is composed; a predicable that\nexpresses the whole essence of its subject in so far as any common term\ncan express it.\"\n\nAn authority says: \"The names _species_ and _genus_ are merely relative\nand the same common term may, in one case, be the species which is\npredicated of an individual, and in another case the individual of which\na species is predicated. Thus the individual, George, belongs to the\nlogical species Man, while Man is an individual of the logical species\nAnimal.\" Jevons says: \"It is desirable to have names by which to show\nthat one class is contained in another, and accordingly we call the\nclass which is divided into two or more smaller ones, the _genus_, and\nthe smaller ones into which it is divided, the _species_.\" _Animal_ is\na _genus_ of which _man_ is a _species_; while _man_, in turn, is a\n_genus_ of which _Caucasian_ is a _species_; and _Caucasian_, in turn,\nbecomes a _genus_ of which _Socrates_ becomes a species. The student\nmust avoid confusing the _logical_ meaning of the terms _genus_ and\n_species_ with the use of the same terms in Natural History. _Each class\nis a \"genus\" to the class below it in extension; and each class is a\n\"species\" to the class above it in extension._ At the lowest extreme of\nthe scale we reach what is called the _infima species_, which cannot be\nfurther subdivided, as for instance \"Socrates\"--this lowest species must\nalways be an individual object, person or thing. At the highest extreme\nof the scale we reach what is _summum genus_, or highest genus, which is\nnever a species of anything, for there is no class higher than it, as\nfor instance, \"being, existence, reality, truth, the absolute, the\ninfinite, the ultimate,\" etc. Hyslop says: \"In reality there is but one\n_summum genus_, while there may be an indefinite number of _infimae\nspecies_. All intermediate terms between these extremes are sometimes\ncalled _subalterns_, as being either genera or species, according to\nthe relation in which they are viewed.\"\n\nPassing on to the classification of the character of the _intension_ of\nterms, we find:\n\n_Difference_, a term denoting: \"The mark or marks by which the species\nis distinguished from the rest of the genus; the specific\ncharacteristic.\" Thus the color of the skin is a _difference_ between\nthe Negro and the Caucasian; the number of feet the _difference_ between\nthe biped and the quadruped; the form and shape of leaves the\n_difference_ between the oak and the elm trees, etc. Hyslop says:\n\"Whatever distinguishes one object from another can be called the\n_differentia_. It is some characteristic in addition to the common\nqualities and determines the species or individual under the genus.\"\n\n_Property_, a term denoting: \"A peculiar quality of anything; that which\nis inherent in or naturally essential to anything.\" Thus a _property_ is\na distinguishing mark of a class. Thus black skin is a _property_ of the\nNegro race; four feet a _property_ of quadrupeds; a certain form of leaf\na _property_ of the oak tree. Thus a _difference_ between two species\nmay be a _property_ of one of the species.\n\n_Accident_, a term denoting: \"Any quality or circumstance which may or\nmay not belong to a class, accidentally as it were; or, whatever does\nnot really constitute an essential part of an object, person or thing.\"\nAs, for instance, the redness of a rose, for a rose might part with its\nredness and still be a rose--the color is the _accident_ of the rose.\nOr, a brick may be white and still be a brick, although the majority of\nbricks are red--the redness or whiteness of the brick are its\n_accidents_ and not its essential _properties_. Whately says:\n\"_Accidents_ in Logic are of two kinds--separable and inseparable. If\nwalking be the _accident_ of a particular man, it is a separable one,\nfor he would not cease to be that man though he stood still; while, on\nthe contrary, if Spaniard is the _accident_ connected with him, it is an\ninseparable one, since he never can cease to be, ethnologically\nconsidered, what he was born.\"\n\nArising from the classification of the meaning or content of terms, we\nfind the process termed \"Definition.\"\n\n_Definition_ is a term denoting: \"An explanation of a word or term.\" In\nLogic the term is used to denote the process of analysis in which the\n_properties_ and _differences_ of a term are clearly stated. There are\nof course several kinds of definitions. For instance, there is what is\ncalled a _Real Definition_, which Whately defines as: \"A definition\nwhich explains the nature of the thing by a particular name.\" There is\nalso what is called a _Physical Definition_, which is: \"A definition\nmade by enumerating such parts as are actually separable, such as the\nhull, masts, etc., of a ship.\" Also a _Logical Definition_, which is: \"A\ndefinition consisting of the genus and the difference. Thus if a planet\nbe defined as 'a wandering star,' _star_ is the genus, and _wandering_\npoints out the difference between a planet and an ordinary star.\" An\n_Accidental Definition_ is: \"A definition of the _accidental_ qualities\nof a thing.\" An _Essential Definition_ is: \"a definition of the\nessential _properties_ and _differences_ of an object, person or thing.\"\n\nCrabbe discriminates between a Definition and an Explanation, as\nfollows: \"A _definition_ is correct or precise; an _explanation_ is\ngeneral or ample. The _definition_ of a word defines or limits the\nextent of its signification; it is the rule for the scholar in the use\nof any word; the _explanation_ of a word may include both definition and\nillustration; the former admits of no more words than will include the\nleading features in the meaning of any term; the latter admits of an\nunlimited scope for diffuseness on the part of the explainer.\"\n\nHyslop gives the following excellent explanation of the _Logical\nDefinition_, which as he states is the proper meaning of the term in\nLogic. He states:\n\n\"The rules which regulate Logical Definition are as follows:\n\n1. A definition should state the essential attributes of the species\ndefined.\n\n2. A definition must not contain the name of word defined. Otherwise the\ndefinition is called _a circulus in definiendo_.\n\n3. The definition must be exactly equivalent to the species defined.\n\n4. A definition should not be expressed in obscure, figurative, or\nambiguous language.\n\n5. A definition must not be negative when it can be affirmative.\"\n\nA correct definition necessarily requires the manifestation of the two\nrespective processes of Analysis and Synthesis.\n\n_Analysis_ is a term denoting: \"The separation of anything into its\nconstituent elements, qualities, properties and attributes.\" It is seen\nat once that in order to correctly define an object, person or thing, it\nis first necessary to analyze the latter in order to perceive its\nessential and accidental properties or differences. Unless the\nqualities, properties and attributes are clearly and fully perceived, we\ncannot properly define the object itself.\n\n_Synthesis_ is a term denoting: \"The act of joining or putting two or\nmore things together; in Logic: the method by composition, in opposition\nto the method of resolution or analysis.\" In stating a definition we\nmust necessarily join together the various essential qualities,\nproperties and attributes, which we have discovered by the process of\nanalysis; and the synthesized combination, considered as a whole, is the\ndefinition of the object expressed by the term.\n\n\n\n\nCHAPTER VIII.\n\nJUDGMENTS\n\n\nThe first step in the process of reasoning is that of Conception or the\nforming of Concepts. The second step is that of Judgment, or the process\nof perceiving the agreement or disagreement of two conceptions.\n\n_Judgment_ in Logic is defined as: \"The comparing together in the mind\nof two notions, concepts or ideas, which are the objects of\napprehension, whether complex or incomplex, and pronouncing that they\nagree or disagree with each other, or that one of them belongs or does\nnot belong to the other. Judgment is therefore affirmative or negative.\"\n\nWhen we have in our mind two concepts, we are likely to compare them one\nwith the other, and to thus arrive at a conclusion regarding their\nagreement or disagreement. This process of comparison and decision is\nwhat, in Logic, is called _Judgment_.\n\nIn every act of Judgment there must be at least two concepts to be\nexamined and compared. This comparison must lead to a Judgment\nregarding their agreement or disagreement. For instance, we have the two\nconcepts, _horse_ and _animal_. We examine and compare the two concepts,\nand find that there is an agreement between them. We find that the\nconcept _horse_ is included in the higher concept of _animal_ and\ntherefore, we assert that: \"_The horse is an animal._\" This is a\nstatement of _agreement_ and is, therefore, a _Positive Judgment_. We\nthen compare the concepts _horse_ and _cow_ and find a disagreement\nbetween them, which we express in the statement of the Judgment that:\n\"_The horse is not a cow._\" This Judgment, stating a disagreement is\nwhat is called a _Negative Judgment_.\n\nIn the above illustration of the comparison between the concepts _horse_\nand _animal_ we find that the second concept _animal_ is broader than\nthe first, _horse_, so broad in fact that it includes the latter. The\nterms are not equal, for we cannot say, in truth, that \"an animal is the\nhorse.\" We may, however, include a _part_ of the broader conception with\nthe narrower and say: \"some animals are horses.\" Sometimes both\nconcepts are of equal rank, as when we state that: \"Man is a rational\nanimal.\"\n\nIn the process of Judgment there is always the necessity of the choice\nbetween the Positive and the Negative. When we compare the concepts\n_horse_ and _animal_, we must of necessity decide either that the horse\n_is_ an animal, or else that it is _not_ an animal.\n\nThe importance of the process of Judgment is ably stated by Halleck, as\nfollows: \"Were isolated concepts possible, they would be of very little\nuse. Isolated facts are of no more service than unspun wool. We might\nhave a concept of a certain class of three-leaved ivy, as we might also\nof poisons. Unless judgment linked these two concepts and decided that\nthis species of ivy is poisonous, we might take hold of it and be\npoisoned. We might have a concept of bread and also one of meat, fruit\nand vegetables. If we also had a concept of food, unrelated to these, we\nshould starve to death, for we should not think of them as foods. A\nvessel, supposing itself to be far out at sea, signaled another vessel\nthat the crew were dying of thirst. That crew certainly had a concept of\ndrinkable things and also of water. To the surprise of the first, the\nsecond vessel signaled back, 'Draw from the sea and drink. You are at\nthe mouth of the Amazon.' The thirsty crew had not joined the concept\n_drinkable_ to the concept of water over the ship's side. A man having\ntaken an overdose of laudanum, his wife lost much valuable time in\nsending out for antidotes, because certain of her concepts had not been\nconnected by judgment. She had good concepts of coffee and of mustard;\nshe also knew that an antidote to opium was needed; but she had never\nlinked these concepts and judged that coffee and mustard were antidotes\nto opium. The moment she formed that judgment she was a wiser woman for\nher knowledge was related and usable.... Judgment is the power\nrevolutionizing the world. The revolution is slow because nature's\nforces are so complex, so hard to be reduced to their simplest forms and\nso disguised and neutralized by the presence of other forces....\nFortunately judgment is ever silently working and comparing things that,\nto past ages, have seemed dissimilar; and it is continually abstracting\nand leaving out of the field of view those qualities which have simply\nserved to obscure the point at issue.\"\n\nJudgment may be both analytic or synthetic in its processes; and it may\nbe neither. When we compare a narrow concept with a broader one, as a\npart with a whole, the process is synthetic or an act of combination.\nWhen we compare a part of a concept with another concept, the process is\nanalytic. When we compare concepts equal in rank or extent, the process\nis neither synthetic nor analytic. Thus in the statement that: \"A horse\nis an animal,\" the judgment is synthetic; in the statement that: \"some\nanimals are horses,\" the judgement is analytic; in the statement that:\n\"a man is a rational animal,\" the judgment is neither analytic nor\nsynthetic.\n\nBrooks says: \"In one sense all judgments are synthetic. A judgment\nconsists of the union of two ideas and this uniting is a process of\nsynthesis. This, however, is a superficial view of the process. Such a\nsynthesis is a mere mechanical synthesis; below this is a\nthought-process which is sometimes analytic, sometimes synthetic and\nsometimes neither analytic nor synthetic.\"\n\nThe same authority states: \"The act of mind described is what is known\nas _logical judgment_. Strictly speaking, however, every intelligent act\nof the mind is accompanied with a _judgment_. To know is to discriminate\nand, therefore, to judge. Every sensation or cognition involves a\nknowledge and so a judgment that it exists. The mind cannot think at all\nwithout judging; to think is to judge. _Even in forming the notions\nwhich judgment compares, the mind judges._ Every notion or concept\nimplies a previous act of judgment to form it: in forming a concept, we\ncompare the common attributes before we unite them; and comparison is\njudgment. It is thus true that 'Every concept is a contracted judgment;\nevery judgment an expanded concept.' This kind of judgment, by which we\naffirm the existence of states of consciousness, discriminate qualities,\ndistinguish percepts and form concepts, is called _primitive or\npsychological judgment_.\"\n\nIn Logical Judgment there are two aspects; _i.e._, Judgment by Extension\nand Judgment by Intension. When we compare the two concepts _horse_ and\n_animal_ we find that the concept _horse_ is contained in the concept\n_animal_ and the judgment that \"_a horse is an animal_\" may be\nconsidered as a Judgment by Extension. In the same comparison we see\nthat the concept _horse_ contains the _quality of animality_, and in\nattributing this quality to the _horse_, we may also say \"_the horse is\nan animal_,\" which judgment may be considered as a Judgment by\nIntension. Brooks says: \"Both views of Judgment are correct; the mind\nmay reach its judgment either by extension or by intension. The method\nby extension is usually the more natural.\"\n\nWhen a Judgment is expressed in words it is called a Proposition. There\nis some confusion regarding the two terms, some holding that a Judgment\nand a proposition are identical, and that the term \"proposition\" may be\nproperly used to indicate the judgment itself. But the authorities who\nseek for clearness of expression and thought now generally hold that:\n\"_A Proposition is a Judgment expressed in words._\" In the next chapter,\nin which we consider Propositions, we shall enter into a more extended\nconsideration of the subject of Judgments as expressed in Propositions,\nwhich consideration we omit at this point in order to avoid repetition.\nJust as the respective subjects of Concepts and Terms necessarily blend\ninto each other, so do the respective subjects of Judgments and\nPropositions. In each case, too, there is the element of the mental\nprocess on the one hand and the verbal expression of it on the other\nhand. It will be well to keep this fact in mind.\n\n\n\n\nCHAPTER IX.\n\nPROPOSITIONS\n\n\nWe have seen that the first step of Deductive Reasoning is that which we\ncall Concepts. The second step is that which we call Propositions.\n\nIn Logic, a _Proposition_ is: \"A sentence, or part of a sentence,\naffirming or denying a connection between the terms; limited to express\nassertions rather than extended to questions and commands.\" Hyslop\ndefines a Proposition as: \"any affirmation or denial of an agreement\nbetween two conceptions.\"\n\n_Examples of Propositions_ are found in the following sentences: \"The\nrose is a flower;\" \"a horse is an animal;\" \"Chicago is a city;\" all of\nwhich are affirmations of agreement between the two terms involved; also\nin: \"A horse is not a zebra;\" \"pinks are not roses;\" \"the whale is not a\nfish;\" etc., which are denials of agreement between the terms.\n\nThe _Parts of a Proposition_ are: (1) the _Subject_, or that of which\nsomething is affirmed or denied; (2) the _Predicate_, or _the\nsomething_ which is affirmed or denied regarding the _Subject_; and (3)\nthe _Copula_, or the verb serving as a link between the Subject and the\nPredicate.\n\n       *       *       *       *       *\n\nIn the Proposition: \"Man is an animal,\" the term _man_ is the Subject;\nthe term _an animal_ is the Predicate; and the word _is_, is the Copula.\nThe Copula is always some form of the verb _to be_, in the present tense\nindicative, in an affirmative Proposition; and the same with the\nnegative particle affixed, in a negative Proposition. The Copula is not\nalways directly expressed by the word _is_ or _is not_, etc., but is\ninstead expressed in some phrase which implies them. For instance, we\nsay \"he runs,\" which implies \"he is running.\" In the same way, it may\nappear at times as if the Predicate was missing, as in: \"God is,\" by\nwhich is meant \"God is existing.\" In some cases, the Proposition is\ninverted, the Predicate appearing first in order, and the Subject last,\nas in: \"Blessed are the peacemakers;\" or \"Strong is Truth.\" In such\ncases judgment must be used in determining the matter, in accordance\nwith the character and meaning of the terms.\n\nAn _Affirmative Proposition_ is one in which the Predicate is _affirmed_\nto agree with the Subject. A _Negative Proposition_ is one in which the\nagreement of the Predicate and Subject is _denied_. Examples of both of\nthese classes have been given in this chapter.\n\nAnother classification of Propositions divides them in three classes, as\nfollows (1) Categorical; (2) Hypothetical; (3) Disjunctive.\n\nA _Categorical Proposition_ is one in which the affirmation or denial is\nmade without reservation or qualification, as for instance: \"Man is an\nanimal;\" \"the rose is a flower,\" etc. The fact asserted may not be\n_true_, but the statement is made positively as a statement of reality.\n\nA _Hypothetical Proposition_ is one in which the affirmation or denial\nis made to depend upon certain conditions, circumstances or\nsuppositions, as for instance: \"If the water is boiling-hot, it will\nscald;\" or \"if the powder be damp, it will not explode,\" etc. Jevons\nsays: \"Hypothetical Propositions may generally be recognized by\ncontaining the little word 'if;' but it is doubtful whether they really\ndiffer much from the ordinary propositions.... We may easily say that\n'boiling water will scald,' and 'damp gunpowder will not explode,' thus\navoiding the use of the word 'if.'\"\n\nA _Disjunctive Proposition_ is one \"implying or asserting an\nalternative,\" and usually containing the conjunction \"or,\" sometimes\ntogether with \"either,\" as for instance: \"Lightning is sheet or forked;\"\n\"Arches are either round or pointed;\" \"Angles are either obtuse, right\nangled or acute.\"\n\nAnother classification of Propositions divides them in two classes as\nfollows: (1) Universal; (2) Particular.\n\nA _Universal Proposition_ is one in which the _whole quantity_ of the\nSubject is involved in the assertion or denial of the Predicate. For\ninstance: \"All men are liars,\" by which is affirmed that _all_ of the\nentire race of men are in the category of liars, not _some_ men but\n_all_ the men that are in existence. In the same way the Proposition:\n\"No men are immortal\" is Universal, for it is a _universal denial_.\n\nA _Particular Proposition_ is one in which the affirmation or denial of\nthe Predicate involves only a _part or portion_ of the whole of the\nSubject, as for instance: \"_Some_ men are atheists,\" or \"_Some_ women\nare not vain,\" in which cases the affirmation or denial does not involve\n_all_ or the _whole_ of the Subject. Other examples are: \"A _few_ men,\"\netc.; \"_many_ people,\" etc.; \"_certain_ books,\" etc.; \"_most_ people,\"\netc.\n\nHyslop says: \"The signs of the Universal Proposition, when formally\nexpressed, are _all_, _every_, _each_, _any_, _and whole_ or words with\nequivalent import.\" The signs of Particular Propositions are also\ncertain adjectives of quantity, such as _some_, _certain_, _a few_,\n_many_, _most_ or such others as denote _at least a part_ of a class.\n\nThe subject of the Distribution of Terms in Propositions is considered\nvery important by Logicians, and as Hyslop says: \"has much importance in\ndetermining the legitimacy, or at least the intelligibility, of our\nreasoning and the assurance that it will be accepted by others.\" Some\nauthorities favor the term, \"Qualification of the Terms of\nPropositions,\" but the established usage favors the term\n\"Distribution.\"\n\nThe definition of the Logical term, \"Distribution,\" is: \"The\ndistinguishing of a universal whole into its several kinds of species;\nthe employment of a term to its fullest extent; the application of a\nterm to its fullest extent, so as to include all significations or\napplications.\" A Term of a Proposition is _distributed_ when it is\nemployed in its fullest sense; that is to say, _when it is employed so\nas to apply to each and every object, person or thing included under\nit_. Thus in the proposition, \"All horses are animals,\" the term\n_horses_ is distributed; and in the proposition, \"Some horses are\nthoroughbreds,\" the term _horses_ is not distributed. Both of these\nexamples relate to the distribution of the _subject_ of the proposition.\nBut the predicate of a proposition also may or may not be distributed.\nFor instance, in the proposition, \"All horses are animals,\" the\npredicate, _animals_, is not distributed, that is, _not used in its\nfullest sense_, for all _animals_ are not _horses_--there are _some_\nanimals which are not horses and, therefore, the predicate, _animals_,\nnot being used in its fullest sense is said to be \"_not distributed_.\"\nThe proposition really means: \"All horses are _some_ animals.\"\n\nThere is however another point to be remembered in the consideration of\nDistribution of Terms of Propositions, which Brooks expresses as\nfollows: \"Distribution generally shows itself in the form of the\nexpression, but sometimes it may be determined by the thought. Thus if\nwe say, 'Men are mortal,' we mean _all men_, and the term men is\ndistributed. But if we say 'Books are necessary to a library,' we mean,\nnot 'all books' but 'some books.' The _test of distribution_ is whether\nthe term applies to '_each and every_.' Thus when we say 'men are\nmortal,' it is true of each and every man that he is mortal.\"\n\nThe Rules of Distribution of the Terms of Proposition are as follows:\n\n1. All _universals_ distribute the _subject_.\n\n2. All _particulars_ do not distribute the _subject_.\n\n3. All _negatives_ distribute the _predicate_.\n\n4. All _affirmatives_ do not distribute the _predicate_.\n\nThe above rules are based upon logical reasoning. The reason for the\nfirst two rules is quite obvious, for when the subject is _universal_,\nit follows that the _whole subject_ is involved; when the subject is\n_particular_ it follows that _only a part_ of the subject is involved.\nIn the case of the third rule, it will be seen that in every _negative_\nproposition the _whole of the predicate_ must be denied the subject, as\nfor instance, when we say: \"Some _animals_ are _not horses_,\" the whole\nclass of _horses_ is cut off from the subject, and is thus\n_distributed_. In the case of the fourth rule, we may readily see that\nin the affirmative proposition the whole of the predicate _is not\ndenied_ the subject, as for instance, when we say that: \"Horses are\nanimals,\" we do not mean that horses are _all the animals_, but that\nthey are merely a _part or portion_ of the class animal--therefore, the\npredicate, _animals_, is not distributed.\n\nIn addition to the forms of Propositions given there is another class of\nPropositions known as _Definitive or Substitutive Propositions_, in\nwhich the Subject and the Predicate are exactly alike in extent and\nrank. For instance, in the proposition, \"A _triangle_ is a _polygon of\nthree sides_\" the two terms are interchangeable; that is, may be\nsubstituted for each other. Hence the term \"substitutive.\" The term\n\"definitive\" arises from the fact that the respective terms of this kind\nof a proposition necessarily _define_ each other. All logical\ndefinitions are expressed in this last mentioned form of proposition,\nfor in such cases the subject and the predicate are precisely equal to\neach other.\n\n\n\n\nCHAPTER X.\n\nIMMEDIATE REASONING\n\n\nIn the process of Judgment we must compare two concepts and ascertain\ntheir agreement of disagreement. In the process of Reasoning we follow a\nsimilar method and compare two judgments, the result of such comparison\nbeing the deduction of a third judgment.\n\nThe simplest form of reasoning is that known as Immediate Reasoning, by\nwhich is meant the deduction of one proposition from another which\n_implies_ it. Some have defined it as: \"_reasoning without a middle\nterm_.\" In this form of reasoning _only one proposition is required for\nthe premise_, and from that premise the conclusion is deduced directly\nand without the necessity of comparison with any other term of\nproposition.\n\nThe two principal methods employed in this form of Reasoning are; (1)\nOpposition; (2) Conversion.\n\n_Opposition_ exists between propositions having the same subject and\npredicate, but differing in quality or quantity, or both. The Laws of\nOpposition are as follows:\n\nI. (1) If the universal is true, the particular is true. (2) If the\nparticular is false, the universal is false. (3) If the universal is\nfalse, nothing follows. (4) If the particular is true, nothing follows.\n\nII. (1) If one of two contraries is true, the other is false. (2) If one\nof two contraries is false, nothing can be inferred. (3) Contraries are\nnever both true, but both may be false.\n\nIII. (1) If one of two sub-contraries is false, the other is true. (2)\nIf one of two sub-contraries is true, nothing can be inferred concerning\nthe other. (3) Sub-contraries can never be both false, but both may be\ntrue.\n\nIV. (1) If one of two contradictories is true, the other is false. (2)\nIf one of two contradictories is false, the other is true. (3)\nContradictories can never be both true or both false, but always one is\ntrue and the other is false.\n\nIn order to comprehend the above laws, the student should familiarize\nhimself with the following arrangement, adopted by logicians as a\nconvenience:\n\n                 {Universal  {Affirmative (A)\n                 {           {Negative    (E)\n  Propositions   {\n                 {           {Affirmative (I)\n                 {Particular {Negative    (O)\n\nExamples of the above: Universal Affirmative (A): \"All men are mortal;\"\nUniversal Negative (E): \"No man is mortal;\" Particular Affirmative (I):\n\"Some men are mortal;\" Particular Negative (O): \"Some men are not\nmortal.\"\n\nThe following examples of abstract propositions are often used by\nlogicians as tending toward a clearer conception than examples such as\ngiven above:\n\n(A) \"All A is B.\"\n\n(I) \"Some A is B.\"\n\n(E) \"No A is B.\"\n\n(O) \"Some A is not B.\"\n\nThese four forms of propositions bear certain logical relations to each\nother, as follows:\n\nA and E are styled _contraries_. I and O are _sub-contraries_; A and I\nand also E and O are called _subalterns_; A and O and also I and E are\nstyled _contradictories_.\n\nA close study of these relations, and the symbols expressing them, is\nnecessary for a clear comprehension of the Laws of Opposition stated a\nlittle further back, as well as the principles of Conversion which we\nshall mention a little further on. The following chart, called the\nSquare of Opposition, is also employed by logicians to illustrate the\nrelations between the four classes of propositions:\n\n   A       CONTRARIES       E\n   +------------------------+\n   |\\                     / |\n   | \\                   /S |\n   | C\\                 /E  |\n   |  O\\               /I   |\n   |   N\\             /R    |\n   |    T\\           /O     |\n  S|     R\\         /T      |S\n  U|      A\\       /C       |U\n  B|        \\     /I        |B\n  A|         \\   /D         |A\n  L|          \\ /           |L\n  T|          / \\           |T\n  E|         /  D\\          |E\n  R|        /    I\\         |R\n  N|       /A     C\\        |N\n  S|      /R       T\\       |S\n   |     /T         O\\      |\n   |    /N           R\\     |\n   |   /O             I\\    |\n   |  /C               E\\   |\n   | /                  S\\  |\n   |/                     \\ |\n   +------------------------+\n   I    SUB-CONTRARIES      O\n\n_Conversion_ is the process of immediate reasoning by which we infer\nfrom a given proposition another proposition having the predicate of\nthe original for its subject and the subject of the original for its\npredicate; or stated in a few words: _Conversion is the transposition of\nthe subject and predicate of a proposition_. As Brooks states it:\n\"Propositions or judgments are _converted_ when the subject and\npredicate change places in such a manner that the resulting judgment is\nan inference from the given judgment.\" The new proposition, resulting\nfrom the operation or Conversion, is called the Converse; the original\nproposition is called the Convertend.\n\n_The Law of Conversion_ is that: \"No term must be distributed in the\nConverse that is not distributed in the Convertend.\" This arises from\nthe obvious fact that nothing should be affirmed in the derived\nproposition than there is in the original proposition.\n\nThere are three kinds of Conversion; _viz_: (1) Simple Conversion; (2)\nConversion by Limitation; (3) Conversion by Contraposition.\n\nIn _Simple Conversion_ there is no change in either quality or quantity.\nIn _Conversion by Limitation_ the quality is changed from universal to\nparticular. In Conversion by Negation the quality is changed but not\nthe quantity. Referring to the classification tables and symbols given\nin the preceding pages of this chapter, we may now proceed to consider\nthe application of these methods of Conversion to each of the four kinds\nof propositions; as follows:\n\n_The Universal Affirmative_ (symbol A) proposition is converted by\nLimitation, or by a change of quality from universal to particular. The\npredicate not being \"distributed\" in the convertend, we must not\ndistribute it in the converse by saying \"_all_.\" Thus in this case we\nmust convert the proposition, \"all men are mortal\" (A), into \"some\nmortals are men\" (I).\n\n_The Universal Negative_ (symbol E) is converted by Simple Conversion,\nin which there is no change in either quality or quantity. For since\nboth terms of \"E\" are distributed, they may both be distributed in the\nconverse without violating the law of conversion. Thus \"No man is\nmortal\" is converted into: \"No mortals are men.\" \"E\" is converted into\n\"E.\"\n\n_The Particular Affirmative_ (symbol I) is also converted by Simple\nConversion in which there is no change in either quality or quantity.\nFor since neither term is distributed in \"I,\" neither term may be\ndistributed in the converse, and the latter must remain \"I.\" For\ninstance; the proposition: \"Some men are mortal\" is converted into the\nproposition, \"Some mortals are men.\"\n\n_The Particular Negative_ (symbol O) is converted by Conversion by\nNegation, in which the quality is changed but not the quantity. Thus in\nconverting the proposition: \"Some men are not mortal,\" we must _not_ say\n\"some mortals are not men,\" for in so doing we would distribute _men_ in\nthe predicate, where it is not distributed in the convertend. Avoiding\nthis, _we transfer the negative particle from the copula to the\npredicate_ so that the convertend becomes \"I\" which is converted by\nSimple Conversion. Thus we transfer \"Some men are not mortal\" into \"Some\nmen are not-mortal\" from which we easily convert (by simple Conversion)\nthe proposition: \"Some not-mortals are men.\"\n\nIt will be well for students, at this point, to consider the three\nfollowing Fundamental Laws of Thought as laid down by the authorities,\nwhich are as follows:\n\n_The Law of Identity_, which states that: \"The same quality or thing is\nalways the same quality or thing, no matter how different the conditions\nin which it occurs.\"\n\n_The Law of Contradiction_, which states that: \"No thing can at the same\ntime and place both be and not be.\"\n\n_The Law of Excluded Middle_, which states that: \"Everything must either\nbe or not be; there is no other alternative or middle course.\"\n\nOf these laws, Prof. Jevons, a noted authority, says: \"Students are\nseldom able to see at first their full meaning and importance. All\narguments may be explained when these self-evident laws are granted; and\nit is not too much to say that the whole of logic will be plain to those\nwho will constantly use these laws as the key.\"\n\n\n\n\nCHAPTER XI.\n\nINDUCTIVE REASONING\n\n\nInductive Reasoning, as we have said, is the process of discovering\ngeneral truth from particular truths, or inferring general laws from\nparticular facts. Thus, from the experience of the individual and the\nrace regarding the particular truth that each and every man under\nobservation has been observed to die sooner or later, it is inferred\nthat _all_ men die, and hence, the induction of the general truth that\n\"All men must die.\" Or, as from experience we know that the various\nkinds of metals expand when subjected to heat, we infer that _all_\nmetals are subject to this law, and that consequently we may arrive by\ninductive reasoning at the conclusion that: \"All metals expand when\nsubjected to heat.\" It will be noticed that the conclusion arrived at in\nthis way by Inductive Reasoning forms the fundamental premise in the\nprocess of Deductive Reasoning. As we have seen elsewhere, the two\nprocesses, Inductive and Deductive Reasoning, respectively are\ninterdependent--resting upon one another.\n\nJevons says of Inductive Reasoning: \"In Deductive Reasoning we inquire\nhow we may gather the truth contained in some propositions called\nPremises, and put into another proposition called the Conclusion. We\nhave not yet undertaken to find out how we can learn what propositions\nreally are true, but only _what propositions are true when other ones\nare true_. All the acts of reasoning yet considered would be called\n_deductive because we deduce, or lead down the truth from premises to\nconclusion_. It is an exceedingly important thing to understand\ndeductive inference correctly, but it might seem to be still more\nimportant to understand _inductive inference_, by which we gather the\ntruth of general propositions from facts observed as happening in the\nworld around us.\" Halleck says: \"Man has to find out through his own\nexperience, or that of others, the major premises from which he argues\nor draws his conclusions. By induction we examine what seems to us a\nsufficient number of individual cases. We then conclude that the rest of\nthese cases, which we have not examined, will obey the same general\nlaw.... Only after general laws have been laid down, after objects have\nbeen classified, after major premises have been formed, can deduction be\nemployed.\"\n\nStrange as may now appear, it is a fact that until a comparatively\nrecent period in the history of man, it was held by philosophers that\nthe only way to arrive at all knowledge was by means of Deductive\nReasoning, by the use of the Syllogism. The influence of Aristotle was\ngreat and men preferred to pursue artificial and complicated methods of\nDeductive Reasoning, rather than to reach the truth by obtaining the\nfacts from Nature herself, at first hand, and then inferring general\nprinciple from the facts so gathered. The rise of modern scientific\nmethods of reasoning, along the lines of Inductive Inference, dates from\nabout 1225-1300. Roger Bacon was one of the first to teach that we must\narrive at scientific truth by a process of observation and\nexperimentation on the natural objects to be found on all sides. He made\nmany discoveries by following this process. He was ably seconded by\nGalileo who lived some three hundred years later, and who also taught\nthat many great general truths might be gained by careful observation\nand intelligent inference. Lord Francis Bacon, who lived about the same\ntime as Galileo, presented in his _Novum Organum_ many excellent\nobservations and facts regarding the process of Inductive Reasoning and\nscientific thought. As Jevons says: \"Inductive logic inquires by what\nmanner of reasoning we can gather the laws of nature from the facts and\nevents observed. Such reasoning is called induction, or inductive\ninquiry, and, as it has actually been practiced by all the great\ndiscoverers in science, it consists in four steps.\"\n\nThe _Four Steps in Inductive Reasoning_, as stated by Jevons, are as\nfollows:\n\n_First Step._--Preliminary observation.\n\n_Second Step._--The making of hypotheses.\n\n_Third Step._--Deductive reasoning.\n\n_Fourth Step._--Verification.\n\nIt will be seen that the process of Inductive Reasoning is essentially\n_a synthetic process_, because it operates in the direction of combining\nand uniting particular facts or truths into general truths or laws which\ncomprehend, embrace and include them all. As Brooks says: \"The\nparticular facts are united by the mind into the general law; the\ngeneral law embraces the particular facts and binds them together into a\nunity of principle and thought. Induction is thus a process of thought\nfrom the parts to the whole--a synthetic process.\" It will also be seen\nthat the process of Inductive Reasoning is essentially _an ascending\nprocess_, because it ascends from particular facts to general laws;\nparticular truths to universal truths; from the lower to the higher, the\nnarrower to the broader, the smaller to the greater.\n\nBrooks says of Inductive Reasoning: \"The relation of induction to\ndeduction will be clearly seen. Induction and Deduction are the\nconverse, the opposites of each other. Deduction derives a particular\ntruth from a general truth; Induction derives a general truth from\nparticular truths. This antithesis appears in every particular.\nDeduction goes from generals to particulars; Induction goes from\nparticulars to generals. Deduction is an analytic process; Induction is\na synthetic process. Deduction is a descending process--it goes from\nthe higher truth to the lower truth; Induction is an ascending\nprocess--it goes from the lower truth to the higher. They differ also in\nthat Deduction may be applied to necessary truths, while Induction is\nmainly restricted to contingent truths.\" Hyslop says: \"There have been\nseveral ways of defining this process. It has been usual to contrast it\nwith Deduction. Now, deduction is often said to be reasoning from\ngeneral to particular truths, from the containing to the contained\ntruth, or from cause to effect. Induction, therefore, by contrast is\ndefined as reasoning from the particular to the general, from the\ncontained to the containing, or from effect to cause. Sometimes\ninduction is said to be reasoning from the known to the unknown. This\nwould make deduction, by contrast, reasoning from the unknown to the\nknown, which is absurd. The former ways of representing it are much the\nbetter. But there is still a better way of comparing them. Deduction _is\nreasoning in which the conclusion is contained in the premises_. This is\na ground for its certitude and we commit a fallacy whenever we go beyond\nthe premises as shown by the laws of the distribution of terms. In\ncontrast with this, then, we may call inductive reasoning _the process\nby which we go beyond the premises in the conclusion_.... The process\nhere is to start from given facts and to infer some other probable facts\nmore general or connected with them. In this we see the process of going\nbeyond the premises. There are, of course, certain conditions which\nregulate the legitimacy of the procedure, just as there are conditions\ndetermining deduction. They are _that the conclusion shall represent the\nsame general kind as the premises_, with a possibility of accidental\ndifferences. But it goes beyond the premises in so far as _known_ facts\nare concerned.\"\n\nThe following example may give you a clearer idea of the processes of\nInductive Reasoning:\n\n_First Step._ Preliminary Observation. _Example_: We notice that all the\nparticular _magnets_ which have come under our observation _attract\niron_. Our mental record of the phenomena may be stated as: \"A, B, C, D,\nE, F, G, etc., and also X, Y, and Z, all of which are _magnets_, in all\nobserved instances, and at all observed times, _attract iron_.\"\n\n_Second Step._ The Making of Hypotheses. _Example_: Upon the basis of\nthe observations and experiments, as above stated, and applying the\naxiom of Inductive Reasoning, that: \"What is true of the many, is true\nof the whole,\" we feel justified in forming a hypothesis or inference of\na general law or truth, applying the facts of the particulars to the\ngeneral, whole or universal, thus: \"_All_ magnets attract iron.\"\n\n_Third Step._ Deductive Reasoning. _Example_: Picking up a magnet\nregarding which we have had no experience and upon which we have made no\nexperiments, we reason by the syllogism, as follows: (1) _All_ magnets\nattract iron; (2) _This thing_ is a magnet; therefore (3) _This thing_\nwill attract iron. In this we apply the axiom of Deductive Reasoning:\n\"Whatever is true of the whole is true of the parts.\"\n\n_Fourth Step._ Verification. _Example_: We then proceed to test the\nhypothesis upon the particular magnet, so as to ascertain whether or not\nit agrees with the particular facts. If the magnet does not attract\niron we know that either our hypothesis is wrong and that _some_ magnets\ndo _not_ attract iron; or else that our _judgment_ regarding that\nparticular \"thing\" being a magnet is at fault and that it is _not_ a\nmagnet. In either case, further examination, observation and experiment\nis necessary. In case the particular magnet _does_ attract iron, we feel\nthat we have verified our hypothesis and our judgment.\n\n\n\n\nCHAPTER XII.\n\nREASONING BY INDUCTION\n\n\nThe term \"Induction,\" in its logical usage, is defined as follows: \"(a)\nThe process of investigating and collecting facts; and (b) the deducing\nof an inference from these facts; also (c) sometimes loosely used in the\nsense of an inference from observed facts.\" Mill says: \"_Induction_,\nthen, is that operation of the mind, by which we infer that what we know\nto be true in a particular case or cases, will be true in all cases\nwhich resemble the former in certain assignable respects. In other\nwords, _Induction_ is the process by which we conclude that what is true\nof certain individuals of a class, is true of the whole class, or that\nwhat is true at certain times will be true in similar circumstances at\nall times.\"\n\nThe _Basis of Induction_ is the axiom that: \"_What is true of the many\nis true of the whole_.\" Esser, a well known authority, states this axiom\nin rather more complicated form, as follows: \"That which belongs or does\nnot belong to many things of the same kind, belongs or does not belong\nto all things of the same kind.\"\n\nThis basic axiom of Induction rests upon the conviction that Nature's\nlaws and manifestations are regular, orderly and _uniform_. If we assume\nthat Nature does not manifest these qualities, then the axiom must fall,\nand all inductive reason must be fallacious. As Brooks well says:\n\"Induction has been compared to a ladder upon which we ascend from facts\nto laws. This ladder cannot stand unless it has something to rest upon;\nand this something is our faith in the constancy of Nature's laws.\" Some\nauthorities have held that this perception of the uniformity of Nature's\nlaws is in the nature of an _intuitive_ truth, or an inherent law of our\nintelligence. Others hold that it is in itself an _inductive_ truth,\narrived at by experience and observation at a very early age. We are\nheld to have noticed the uniformity in natural phenomena, and almost\ninstinctively infer that this uniformity is continuous and universal.\n\nThe authorities assume the existence of two kinds of Induction, namely:\n(1) Perfect Induction; and (2) Imperfect Induction. Other, but similar,\nterms are employed by different authorities to designate these two\nclasses.\n\n_Perfect Induction_ necessitates a knowledge of _all_ the particulars\nforming a class; that is, _all_ the individual objects, persons, things\nor facts comprising a class must be known and enumerated in this form of\nInduction. For instance, if we _knew positively_ all of Brown's\nchildren, and that their names were John, Peter, Mark, Luke, Charles,\nWilliam, Mary and Susan, respectively; and that each and every one of\nthem were freckled and had red hair; then, in that case, instead of\nsimply _generalizing_ and stating that: \"John, Peter, Mark, Luke,\nCharles, William, Mary and Susan, who are _all_ of Brown's children, are\nfreckled and have red hair,\" we would save words, and state the\ninductive conclusion: \"All Brown's children are freckled and have red\nhair.\" It will be noticed that in this case _we include in the process\nonly what is stated in the premise itself_, and we do not extend our\ninductive process beyond the actual data upon which it is based. This\nform of Induction is sometimes called \"Logical Induction,\" because the\ninference is a logical necessity, without the possibility of error or\nexception. By some authorities it is held not to be Induction at all, in\nthe strict sense, but little more than a simplified form of enumeration.\nIn actual practice it is seldom available, for it is almost impossible\nfor us to know all the particulars in inferring a general law or truth.\nIn view of this difficulty, we fall back upon the more practical form of\ninduction known as:\n\n_Imperfect Induction_, or as it is sometimes called \"Practical\nInduction,\" by which is meant the inductive process of reasoning in\nwhich we assume that the particulars or facts actually known to us\ncorrectly represent those which are not actually known, and hence the\nwhole class to which they belong. In this process it will be seen that\n_the conclusion extends_ beyond the data upon which it is based. In this\nform of Induction we must actually employ the principle of the axiom:\n\"What is true of the many is true of the whole\"--that is, must _assume_\nit to be a fact, not because we _know_ it by actual experience, but\nbecause we infer it from the axiom which also agrees with past\nexperience. The conclusion arrived at may not always be true in its\nfullest sense, as in the case of the conclusion of Perfect Induction,\nbut is the result of an inference based upon a principle which gives us\na reasonable right to assume its truth in absence of better knowledge.\n\nIn considering the actual steps in the process of Inductive Reasoning we\ncan do no better than to follow the classification of Jevons, mentioned\nin the preceding chapter, the same being simple and readily\ncomprehended, and therefore preferable in this case to the more\ntechnical classification favored by some other authorities. Let us now\nconsider these four steps.\n\n_First Step._ Preliminary observation. It follows that without the\nexperience of oneself or of others in the direction of observing and\nremembering particular facts, objects, persons and things, we cannot\nhope to acquire the preliminary facts for the generalization and\ninductive inference necessary in Inductive Reasoning. It is necessary\nfor us to form a variety of clear Concepts or ideas of facts, objects,\npersons and things, before we may hope to generalize from these\nparticulars. In the chapters of this book devoted to the consideration\nof Concepts, we may see the fundamental importance of the formation and\nacquirement of correct Concepts. Concepts are the fundamental material\nfor correct reasoning. In order to produce a perfect finished product,\nwe must have perfect materials, and a sufficient quantity of them. The\ngreater the knowledge one possesses of the facts and objects of the\noutside world, the better able is he to reason therefrom. Concepts are\nthe raw material which must feed the machinery of reasoning, and from\nwhich the final product of perfected thought is produced. As Halleck\nsays: \"There must first be a presentation of materials. Suppose that we\nwish to form the concept _fruit_. We must first perceive the different\nkinds of fruit--cherry, pear, quince, plum, currant, apple, fig, orange,\netc. Before we can take the next step, we must be able to form distinct\nand accurate images of the various kinds of fruit. If the concept is to\nbe absolutely accurate, not one kind of fruit must be overlooked.\nPractically this is impossible; but many kinds should be examined. Where\nperception is inaccurate and stinted, the products of thought cannot be\ntrustworthy. No building is firm if reared on insecure foundations.\"\n\nIn the process of Preliminary Observation, we find that there are two\nways of obtaining a knowledge of the facts and things around us. These\ntwo ways are as follows:\n\nI. By _Simple Observation_, or the perception of the happenings which\nare manifested without our interference. In this way we perceive the\nmotion of the tides; the movement of the planets; the phenomena of the\nweather; the passing of animals, etc.\n\nII. By the _Observation of Experiment_, or the perception of happenings\nin which we interfere with things and then observe the result. An\n_experiment_ is: \"A trial, proof, or test of anything; an act,\noperation, or process designed to discover some unknown truth, principle\nor effect, or to test some received or reputed truth or principle.\"\nHobbes says: \"To have had many _experiments_ is what we call\n_experience_.\" Jevons says: \"Experimentation is observation with\nsomething more; namely, regulation of the things whose behavior is to be\nobserved. The advantages of experiment over mere observation are of two\nkinds. In the first place, we shall generally know much more certainly\nand accurately with what we are dealing, when we make experiments than\nwhen we simply observe natural events.... It is a further advantage of\nartificial experiments, that they enable us to discover entirely new\nsubstances and to learn their properties.... It would be a mistake to\nsuppose that the making of an experiment is inductive reasoning, and\ngives us without further trouble the laws of nature. _Experiments only\ngive us the facts upon which we may afterward reason...._ Experiments\nthen merely give facts, and it is only by careful reasoning that we can\nlearn when the same facts will be observed again. _The general rule is\nthat the same causes will produce the same effects._ Whatever happens in\none case will happen in all like cases, provided that they are really\nlike, and not merely apparently so.... When we have by repeated\nexperiments tried the effect which all the surrounding things might have\non the result, we can then reason with much confidence as to similar\nresults in similar circumstances.... In order that we may, from our\nobservations and experiments, learn the law of nature and become able to\nforesee the future, we must perform the process of generalization. To\ngeneralize is to draw a general law from particular cases, and to infer\nthat what we see to be true of a few things is true of the whole genus\nor class to which these things belong. It requires much judgment and\nskill to generalize correctly, because everything depends upon the\nnumber and character of the instances about which we reason.\"\n\nHaving seen that the first step in Inductive Reasoning is Preliminary\nObservation, let us now consider the next steps in which we may see what\nwe do with the facts and ideas which we have acquired by this\nObservation and Experiment.\n\n\n\n\nCHAPTER XIII.\n\nTHEORY AND HYPOTHESES\n\n\nFollowing Jevons' classification, we find that the Second Step in\nInductive Reasoning is that called \"The Making of Hypotheses.\"\n\nA _Hypothesis_ is: \"A supposition, proposition or principle _assumed or\ntaken for granted_ in order to draw a conclusion or inference in proof\nof the point or question; a proposition assumed or taken for granted,\nthough not proved, for the purpose of deducing proof of a point in\nquestion.\" It will be seen that a Hypothesis is merely held to be\n_possibly or probably true_, and _not certainly true_; it is in the\nnature of a _working assumption_, whose truth must be tested by observed\nfacts. The assumption may apply either to the _cause_ of things, or to\nthe _laws_ which govern things. Akin to a hypothesis, and by many people\nconfused in meaning with the latter, is what is called a Theory.\n\nA _Theory_ is: \"A verified hypothesis; a hypothesis which has been\nestablished as, apparently, the true one.\" An authority says \"_Theory_\nis a stronger word than _hypothesis_. A _theory_ is founded on\nprinciples which have been established on independent evidence. A\n_hypothesis_ merely assumes the operation of a cause which would account\nfor the phenomena, but has not evidence that such cause was actually at\nwork. Metaphysically, a theory is nothing but a hypothesis supported by\na large amount of probable evidence.\" Brooks says: \"When a hypothesis is\nshown to explain all the facts that are known, these facts being varied\nand extensive, it is said to be verified, and becomes a theory. Thus we\nhave the theory of universal gravitation, the Copernican theory of the\nsolar system, the undulatory theory of light, etc., all of which were\noriginally mere hypotheses. This is the manner in which the term is\nusually employed in the inductive philosophy; though it must be admitted\nthat it is not always used in this strict sense. Discarded hypotheses\nare often referred to as theories; and that which is actually a theory\nis sometimes called a hypothesis.\"\n\nThe steps by which we build up a hypothesis are numerous and varied. In\nthe first place we may erect a hypothesis by the methods of what we have\ndescribed as Perfect Induction, or Logical Induction. In this case we\nproceed by simple generalization or simple enumeration. The example of\nthe freckled, red-haired children of Brown, mentioned in a previous\nchapter, explains this method. It requires the examination and knowledge\nof every object or fact of which the statement or hypothesis is made.\nHamilton states that it is the only induction which is absolutely\nnecessitated by the laws of thought. It does not extend further than the\nplane of experience. It is akin to mathematical reasoning.\n\nFar more important is the process by which hypotheses are erected by\nmeans of inferences from Imperfect Induction, by which we reason from\nthe known to the unknown, transcending experience, and making true\ninductive inferences from the axiom of Inductive Reasoning. This process\ninvolves the subject of Causes. Jevons says: \"The cause of an event is\nthat antecedent, or set of antecedents, from which the event always\nfollows. People often make much difficulty about understanding what the\ncause of an event means, but it really means nothing beyond _the things\nthat must exist before in order that the event shall happen afterward_.\"\n\nCauses are often obscure and difficult to determine. The following five\ndifficulties are likely to arise: I. The cause may be out of our\nexperience, and is therefore not to be understood; II. Causes often act\nconjointly, so that it is difficult to discover the one predominant\ncause by reason of its associated causes; III. Often the presence of a\ncounteracting, or modifying cause may confuse us; IV. Often a certain\neffect may be caused by either of several possible causes; V. That which\nappears as a _cause_ of a certain effect may be but a co-effect of an\noriginal cause.\n\nMill formulated several tests for ascertaining the causal agency in\nparticular cases, in view of the above-stated difficulties. These tests\nare as follows: (1) The Method of Agreement; (2) The Method of\nDifference; (3) The Method of Residues; and (4) The Method of\nConcomitant Variations. The following definitions of these various tests\nare given by Atwater as follows:\n\n_Method of Agreement_: \"If, whenever a given object or agency is present\nwithout counteracting forces, a given effect is produced, there is a\nstrong evidence that the object or agency is the cause of the effect.\"\n\n_Method of Difference_: \"If, when the supposed cause is present the\neffect is present, and when the supposed cause is absent the effect is\nwanting, there being in neither case any other agents present to effect\nthe result, we may reasonably infer that the supposed cause is the real\none.\"\n\n_Method of Residue_: \"When in any phenomena we find a result remaining\nafter the effects of all known causes are estimated, we may attribute it\nto a residual agent not yet reckoned.\"\n\n_Method of Concomitant Variations_: \"When a variation in a given\nantecedent is accompanied by a variation of a given consequent, they are\nin some manner related as cause and effect.\"\n\nAtwater adds: \"Whenever either of these criteria is found free from\nconflicting evidence, and especially when several of them concur, the\nevidence is clear that the cases observed are fair representatives of\nthe whole class, and warrant a valid inductive conclusion.\"\n\nJevons gives us the following valuable rules:\n\nI. \"Whenever we can alter the quantity of the things experimented on, we\ncan apply _a rule for discovering which are causes and which are\neffects_, as follows: We must vary the quantity of one thing, making it\nat one time greater and at another time less, and if we observe any\nother thing which varies just at the same times, it will in all\nprobability be an _effect_.\"\n\nII. \"When things vary regularly and frequently, there is _a simple rule,\nby following which we can judge whether changes are connected together\nas causes and effects_, as follows: Those things which change in exactly\nequal times are in all likelihood connected together.\"\n\nIII. \"It is very difficult to explain how it is that we can ever reason\nfrom one thing to a class of things by generalization, _when we cannot\nbe sure that the things resemble each other in the important points_....\nUpon what grounds do we argue? We have to get a general law from\nparticular facts. This can only be done by going through all the steps\nof inductive reasoning. Having made certain observations, we must frame\nhypotheses as to the circumstances, or laws from which they proceed.\nThen we must reason deductively; and after verifying the deductions in\nas many cases as possible, we shall know how far we can trust similar\ndeductions concerning future events.... It is difficult to judge when we\nmay, and when we may not, safely infer from some things to others in\nthis simple way, without making a complete theory of the matter. _The\nonly rule_ that can be given to assist us is that _if things resemble\neach other in a few properties only, we must observe many instances\nbefore inferring that these properties will always be joined together in\nother cases_.\"\n\n\n\n\nCHAPTER XIV.\n\nMAKING AND TESTING HYPOTHESES\n\n\nThe older philosophers and logicians were often at a loss how to\nreasonably account for the origin of hypotheses. It will be seen, after\ngiving the matter a little thought, that the actual formation of the\nhypothesis is more than a mere grouping together or synthesis of facts\nor ideas--there is another mental process which actually evolves the\nhypothesis or theory--which gives _a possible reason_. What is this\nmental process? Let us consider the matter. Brooks well says: \"The\nhypotheses of science originate in what is called anticipation. They are\nnot the result of a mere synthesis of facts, for no combination of facts\ncan give the law or cause. We do not see the law; we see the facts and\n_the mind thinks the law_. By the power of anticipation, the mind often\nleaps from a few facts to the cause which produces them or the law which\ngoverns them. Many hypotheses were but _a happy intuition of the mind_.\nThey were the result of what La Place calls 'a great guess,' or what\nPlato so beautifully designates as 'a sacred suspicion of truth.' The\nforming of hypotheses requires a suggestive mind, a lively fancy, a\nphilosophic imagination, that catches a glimpse of the idea through the\nform, or sees the law standing behind the fact.\"\n\nThe student of The New Psychology sees in the mental operation of the\nforming of the hypothesis--\"the mind thinking the law\"--but an instance\nof the operation of the activities of the Subconscious Mind, or even the\nSuperconscious Mind. (See the volume on the Subconscious Mind in this\nseries.) Not only does this hypothesis give the explanation which the\nold psychology has failed to do, but it agrees with the ideas of others\non the subject as stated in the above quotation from Brooks; and\nmoreover agrees with many recorded instances of the formation of great\nhypotheses. Sir Wm. Hamilton discovered the very important mathematical\nlaw of quaternions while walking one day in the Dublin Observatory. He\nhad pondered long on the subject, but without result. But, finally, on\nthat eventful day he suddenly \"felt the galvanic circle of thought\"\nclose, and the result was the realization of the fundamental\nmathematical relations of the problem. Berthelot, the founder of\nSynthetic Chemistry, has testified that the celebrated experiments which\nled to his remarkable discoveries were seldom the result of carefully\nfollowed lines of conscious thought or pure reasoning processes; but,\ninstead, came to him \"of their own accord,\" so to speak, \"as from a\nclear sky.\" In these and many other similar instances, the mental\noperation was undoubtedly purely subjective and subconscious. Dr. Hudson\nhas claimed that the \"Subjective Mind\" cannot reason inductively, and\nthat its operations are purely and distinctly deductive, but the\ntestimony of many eminent scientists, inventors and philosophers is\ndirectly to the contrary.\n\nIn this connection the following quotation from Thomson is interesting:\n\"The system of anatomy which has immortalized the name of Oken is the\nconsequence of a flash of anticipation which glanced through his mind\nwhen he picked up in a chance walk the skull of a deer, bleached and\ndisintegrated by the weather, and exclaimed after a glance, 'It is part\nof a vertebral column!' When Newton saw the apple fall, the anticipatory\nquestion flashed through his mind, 'Why do not the heavenly bodies fall\nlike this apple?' In neither case had accident any important share;\nNewton and Oken were prepared by the deepest previous study to seize\nupon the unimportant fact offered to them, and to show how important it\nmight become; and if the apple and the deer-skull had been wanting, some\nother falling body, or some other skull, would have touched the string\nso ready to vibrate. But in each case there was a great step of\nanticipation; Oken thought he saw a type of the whole skeleton in a\nsingle vertebra, while Newton conceived at once that the whole universe\nwas full of bodies tending to fall.... The discovery of Goethe, which\ndid for the vegetable kingdom what Oken did for the animal, that the\nparts of a plant are to be regarded as metamorphosed leaves, is an\napparent exception to the necessity of discipline for invention, since it\nwas the discovery of a poet in a region to which he seemed to have paid\nno especial or laborious attention. But Goethe was himself most anxious\nto rest the basis of this discovery upon his observation rather than his\nimagination, and doubtless with good reason.... As with other great\ndiscoveries, hints had been given already, though not pursued, both of\nGoethe's and Oken's principles. Goethe left his to be followed up by\nothers, and but for his great fame, perhaps his name would never have\nbeen connected with it. Oken had amassed all the materials necessary for\nthe establishment of his theory; he was able at once to discover and\nconquer the new territory.\"\n\nIt must not be supposed, however, that all hypotheses flashing into the\nfield of consciousness from the Subconsciousness, are necessarily true\nor correct. On the contrary many of them are incorrect, or at least only\npartially correct. The Subconsciousness is not infallible or\nomniscient--it merely produces results according to the material\nfurnished it. But even these faulty hypotheses are often of value in the\nlater formation of a correct one. As Whewell says: \"To try wrong guesses\nis with most persons the only way to hit upon right ones.\" Kepler is\nsaid to have erected at least twenty hypotheses regarding the shape of\nthe earth's orbit before he finally evolved the correct one. As Brooks\nsays: \"Even incorrect hypotheses may be of use in scientific research,\nsince they may lead to more correct suppositions.\" The supposition of\nthe circular motions of the heavenly bodies around the _earth_ as a\ncenter, which lead to the conception of epicycles, etc., and at last to\nthe true theory is an illustration of this. So the 'theory of\nphlogiston' in chemistry, made many facts intelligible, before the true\none of 'oxidation' superseded it. And so, as Thomson says, \"with the\ntheory that 'Nature abhors a vacuum,' which served to bring together so\nmany cognate facts not previously considered as related. Even an\nincorrect conception of this kind has its place in science, so long as\nit is applicable to the facts; when facts occur which it cannot explain,\nwe either correct it or replace it with a new one. The pathway of\nscience, some one remarks, is strewn with the remains of discarded\nhypotheses.\"\n\nHalleck says regarding the danger of hasty inference: \"Men must\nconstantly employ imperfect induction in order to advance; but great\ndangers attend inductive inferences made from too narrow experience. A\nchild has experience with one or two dogs at his home. Because of their\ngentleness, he argues that all dogs are gentle. He does not, perhaps,\nfind out the contrary until he has been severely bitten. His induction\nwas too hasty. He had not tested a sufficiently large number of dogs to\nform such a conclusion. From one or two experiences with a large crop in\na certain latitude, a farmer may argue that the crop will generally be\nprofitable, whereas it may not again prove so for years. A man may have\ntrusted a number of people and found them honest. He concludes that\npeople as a rule are honest, trusts a certain dishonest man, and is\nruined. The older people grow, the more cautious they generally become\nin forming inductive conclusions. Many instances are noted and compared;\nbut even the wisest sometimes make mistakes. It once was a generally\naccepted fact that all swans were white. Nobody had ever seen a dark\nswan, and the inference that all swans were white was regarded as\ncertainly true. Black swans were, however, found in Australia.\"\n\nBrooks says regarding the probability of hypotheses: \"The probability of\na hypothesis is in proportion to the number of facts and phenomena it\nwill explain. The larger the number of facts and phenomena that it will\nsatisfactorily account for, the greater our faith in the correctness of\nour supposition.... If there is more than one hypothesis in respect to\nthe facts under consideration, that one which accounts for the greatest\nnumber of facts is the most probable.... In order to verify a hypothesis\nit must be shown that it will account for all the facts and phenomena.\nIf these facts are numerous and varied, and the subject is so thoroughly\ninvestigated that it is quite certain that no important class of facts\nhas been overlooked, the supposition is regarded as true, and the\nhypothesis is said to be verified. Thus the hypothesis of the 'daily\nrotation' of the earth on its axis to account for the succession of day\nand night is accepted as absolutely true. This is the view taken by Dr.\nWhewell and many other thinkers in respect to the verification of a\nhypothesis. Some writers, however, as Mill and his school, maintain that\nin order to verify a hypothesis, we must show not only that it explains\nall the facts and phenomena, but that there is no other possible\nhypothesis which will account for them.... The former view of\nverification is regarded as the correct one. By the latter view, it is\nevident that a hypothesis could never be verified.\"\n\nJevons says: \"In the fourth step (verification), we proceed to compare\nthese deductions with the facts already collected, or when necessary and\npracticable, we make new observations and plan new experiments, so as to\nfind out whether the hypothesis agrees with nature. If we meet with\nseveral distinct disagreements between our deductions and our\nobservations, it will become likely that the hypothesis is wrong, and we\nmust then invent a new one. In order to produce agreement it will\nsometimes be enough to change the hypothesis in a small degree. When we\nget hold of a hypothesis which seems to give results agreeing with a few\nfacts, we must not at once assume that it is certainly correct. We must\ngo on making other deductions from it under various circumstances, and,\nwhenever it is possible, we ought to verify these results, that is,\ncompare them with facts observed through the senses. When a hypothesis\nis shown in this way to be true in a great many of its results,\nespecially when it enables us to predict what we should never otherwise\nhave believed or discovered, it becomes certain that the hypothesis\nitself is a true one.... Sometimes it will happen that two or even three\nquite different hypotheses all seem to agree with certain facts, so that\nwe are puzzled which to select.... When there are thus two hypotheses,\none as good as the other, we need to discover some fact or thing which\nwill agree with one hypothesis and not with the other, because this\nimmediately enables us to decide that the former hypothesis is true and\nthe latter false.\"\n\nIn the above statements regarding the _verification_ of hypotheses we\nsee references made to the testing of the latter upon the \"facts\" of the\ncase. These _facts_ may be either the observed phenomena or facts\napparent to the perception, or else _facts_ obtained by deductive\nreasoning. The latter may be said to be facts which are held to be true\nif the hypothesis be true. Thus if we erect the hypothesis that \"All men\nare mortal,\" we may reason deductively that it will follow that each and\nevery thing that is a _man_ must die sooner or later. Then we test our\nhypotheses upon _each and every man_ whom we may subject to observation\nand experiment. If we find a single man who does not die, then the test\ndisproves our hypotheses; if on the contrary all men (the \"facts\" in the\ncase) prove to be mortal, then is our hypotheses proven or established.\nThe deductive reasoning in this case is as follows: \"_If_ so-and-so is\ntrue regarding such-and-such a class; and if this particular thing\nbelongs to that class; then it will follow that so-and-so is true\nregarding this particular thing.\" This argument is expressed in what is\ncalled a Hypothetical Proposition (see Chapter IX), the consideration of\nwhich forms a part of the general subject of Deductive Reasoning.\nTherefore as Jevons has said, \"Deductive Reasoning is the Third Step in\nInductive Reasoning, and precedes Verification\", which we have already\nconsidered. Halleck says: \"After Induction has classified certain\nphenomena and thus given us a major premise, we may proceed\n_deductively_ to apply the inference to any new specimen that can be\nshown to belong to that class. Induction hands over to deduction a\nready-made major premise.... Deduction takes that as a fact, making no\ninquiry about its truth.... Only after general laws have been laid down,\nafter objects have been classified, after major premises have been\nformed, can _deduction_ be employed.\"\n\nIn view of the above facts, we shall now proceed to a consideration of\nthat great class of Reasoning known under the term--Deductive\nReasoning.\n\n\n\n\nCHAPTER XV.\n\nDEDUCTIVE REASONING\n\n\nWe have seen that there are two great classes of reasoning, known\nrespectively, as (1) Inductive Reasoning, or the discovery of general\ntruth from particular truths; and (2) Deductive Reasoning, or the\ndiscovery of particular truths from general truths.\n\nAs we have said, Deductive Reasoning is the process of discovering\nparticular truths from a general truth. Thus from the general truth\nembodied in the proposition \"All horses are animals,\" when it is\nconsidered in connection with the secondary proposition that \"Dobbin is\na horse,\" we are able to deduce the particular truth that: \"Dobbin is an\nanimal.\" Or, in the following case we deduce a particular truth from a\ngeneral truth, as follows: \"All mushrooms are good to eat; this fungus\nis a mushroom; therefore, this fungus is good to eat.\" A deductive\nargument is expressed in a deductive syllogism.\n\nJevons says regarding the last stated illustration: \"Here are three\nsentences which state three different facts; but when we know the two\nfirst facts, we learn or gather the third fact from the other two. When\nwe thus learn one fact from other facts, we _infer or reason_, and we do\nthis in the mind. Reasoning thus enables us to ascertain the nature of a\nthing without actual trial. If we always needed to taste a thing before\nwe could know whether it was good to eat or not, cases of poisoning\nwould be alarmingly frequent. But the appearance and peculiarities of a\nmushroom may be safely learned by the eye or the nose, and reasoning\nupon this information and the fact already well known, that mushrooms\nare good to eat, we arrive without any danger or trouble at the\nconclusion that the particular fungus before us is good to eat. _To\nreason, then, is to get some knowledge from other knowledge._\"\n\nThe student will recognize that Deductive Reasoning is essentially _an\nanalytic process_, because it operates in the direction of analyzing a\nuniversal or general truth into its particulars--into the particular\nparts which are included within it--and asserting of them that \"what is\ntrue of the general is true of the particular.\" Thus in the general\ntruth that \"All men are mortal,\" we see included the particular truth\nthat \"John Smith is mortal\"--John Smith having been discovered to be a\nman. We deduce the particular truth about John Smith from the general\ntruth about \"all men.\" We analyze \"all men\" and find John Smith to be\none of its particular parts. Therefore, \"Deduction is an inference from\nthe whole to its parts; that is, an analytic process.\"\n\nThe student will also recognize that Deductive Reasoning is essentially\n_a descending process_, because it operates in the direction of a\ndescent from the universal to the particular; from the higher to the\nlower; from the broader to the narrower. As Brooks says: \"Deduction\ndescends from higher truths to lower truths, from laws to facts, from\ncauses to phenomena, etc. Given the law, we can by deduction descend to\nthe facts that fall under the law, even if we have never before seen the\nfacts; and so from the cause we may pass down to observed and even\nunknown phenomena.\"\n\nThe general truths which are used as the basis of Deductive Reasoning\nare discovered in several ways. The majority arise from Inductive\nReasoning, based upon experience, observation and experiment. For\ninstance in the examples given above, we could not truthfully assert our\nbelief that: \"All horses are animals\" unless we had previously studied\nboth the horse and animals in general. Nor without this study could we\nstate that \"Dobbin is a horse.\" Nor could we, without previous study,\nexperience and experiment truthfully assert that: \"All mushrooms are\ngood to eat;\" or that \"this fungus is a mushroom;\" and that \"therefore,\nthis fungus is good to eat.\" Even as it is, we must be sure that the\nfungus really is a mushroom, else we run a risk of poisoning ourselves.\nGeneral truths of this kind are _not intuitive_, by any means, but are\nbased upon our own experience or the experience of others.\n\nThere is a class of general truths which are called _intuitive_ by some\nauthorities. Halleck says of these: \"Some psychologists claim that we\nhave knowledge obtained neither through induction nor deduction; that\nwe recognize certain truths the moment we perceive certain objects,\nwithout any process of inference. Under the head of intuitive knowledge\nare classified such cases as the following: We perceive an object and\nimmediately know that it is a time relation, as existing now and then.\nWe are said to have an intuitive concept of time. When we are told that\nthe whole is greater than a part; that things equal to the same thing\nare equal to each other; that a straight line cannot enclose space, we\n_immediately_, or intuitively, recognize the truth of these statements.\nAttempts at proof do not make us feel surer of their truth.... We say\nthat it is self-evident, or that we know the fact intuitively. The\naxioms of mathematics and logic are said to be intuitive.\"\n\nAnother class of authorities, however, deny the nature of intuitive\nknowledge of truth, or intuitive truths. They claim that all our ideas\narise from sensation and reflection, and that what we call \"intuition\"\nis merely the result of sensation and reflection _reproduced by memory\nor heredity_. They hold that the _intuitions_ of animals and men are\nsimply the representation of experiences of the race, or individual,\narising from the impressions stored away in the subconsciousness of the\nindividual. Halleck states regarding this: \"This school likens intuition\nto instinct. It grants that the young duck knows water instinctively,\nplunges into it, and swims without learning. These psychologists believe\nthat there was a time when this was not the case with the progenitors of\nthe duck. They had to gain this knowledge slowly through experience.\nThose that learned the proper aquatic lesson survived and transmitted\nthis knowledge through a modified structure, to their progeny. Those\nthat failed in the lesson perished in the struggle for existence....\nThis school claims that the intuition of cause and effect arose in the\nsame way. Generations of human beings have seen the cause invariably\njoined to the effect; hence, through inseparable association came the\nrecognition of their necessary sequence. The tendency to regard all\nphenomena in these relations was with steadily increasing force\ntransmitted by the laws of heredity to posterity, until the recognition\nof the relationship has become an intuition.\"\n\nAnother class of general truths is merely hypothetical. Hypothetical\nmeans \"Founded on or including a hypothesis or supposition; assumed or\ntaken for granted, though not proved, for the purpose of deducing proofs\nof a point in question.\" The hypotheses and theories of physical science\nare used as general truths for deductive reasoning. Hypothetical general\ntruths are in the nature of premises assumed in order to proceed with\nthe process of Deductive Reasoning, and without which such reasoning\nwould be impossible. They are, however, as a rule not mere assumptions,\nbut are rather in the nature of assumptions rendered plausible by\nexperience, experiment and Inductive Reasoning. The Law of Gravitation\nmay be considered hypothetical, and yet it is the result of Inductive\nReasoning based upon a vast multitude of facts and phenomena.\n\nThe _Primary Basis of Deductive Reasoning_ may be said to rest upon the\nlogical axiom, which has come down to us from the ancients, and which is\nstated as follows: \"_Whatever is true of the whole is true of its\nparts_.\" Or, as later authorities have expressed it: \"Whatever is true\nof the general is true of the particular.\" This axiom is the basis upon\nwhich we build our Deductive Reasoning. It furnishes us with the\nvalidity of the deductive inference or argument. If we are challenged\nfor proof of the statement that \"This fungus is good to eat,\" we are\nable to answer that we are justified in making the statement by the\nself-evident proposition, or axiom, that \"Whatever is true of the\ngeneral is true of the particular.\" If the general \"mushroom\" is good to\neat, then the particular, \"this fungus\" being a mushroom, must also be\ngood to eat. All horses (general) being animals, then according to the\naxiom, Dobbin (particular horse) must also be an animal.\n\nThis axiom has been stated in various terms other than those stated\nabove. For instance: \"Whatever may be affirmed or denied of the whole,\nmay be denied or affirmed of the parts;\" which form is evidently derived\nfrom that used by Hamilton who said: \"What belongs, or does not belong,\nto the containing whole, belongs or does not belong, to each of the\ncontained parts.\" Aristotle formulated his celebrated Dictum as follows:\n\"Whatever can be predicated affirmatively or negatively of any class or\nterm distributed, can be predicated in like manner of all and singular\nthe classes or individuals contained under it.\"\n\nThere is another form of Deductive Reasoning, that is a form based upon\nanother axiom than that of: \"Whatever is true of the whole is true of\nthe parts.\" This form of reasoning is sometimes called Mathematical\nReasoning, because it is the form of reasoning employed in mathematics.\nIts axiom is stated as follows: \"Things which are equal to the same\nthing, are equal to one another.\" It will be seen that this is the\nprinciple employed in mathematics. Thus: \"x equals y; and y equals 5;\ntherefore, x equals 5.\" Or stated in logical terms: \"A equals B; B\nequals C; therefore, A equals C.\" Thus it is seen that this form of\nreasoning, as well as the ordinary form of Deductive Reasoning, is\nstrictly _mediate_, that is, made through the medium of a third thing,\nor \"two things being compared through their relation to a third.\"\n\nBrooks states: \"The real reason for the certainty of mathematical\nreasoning may be stated as follows: First, its ideas are definite,\nnecessary, and exact conceptions of quantity. Second, its definitions,\nas the description of these ideas are necessary, exact, and indisputable\ntruths. Third, the axioms from which we derive conclusions by comparison\nare all self-evident and necessary truths. Comparing these exact ideas\nby the necessary laws of inference, the result must be absolutely true.\nOr, stated in another way, using these definitions and axioms as the\npremises of a syllogism, the conclusion follows inevitably. There is no\nplace or opportunity for error to creep in to mar or vitiate our derived\ntruths.\"\n\nIn conclusion, we wish to call your attention to a passage from Jevons\nwhich is worthy of consideration and recollection. Jevons says: \"There\nis a simple rule which will enable us to test the truth of a great many\narguments, even of many which do not come under any of the rules\ncommonly given in books on logic. This rule is that _whatever is true of\none term is true of any term which is stated to be the same in meaning\nas that term_. In other words, we may always _substitute one term for\nanother if we know that they refer to exactly the same thing_. There is\nno doubt that a horse is some animal, and therefore the head of a horse\nis the head of some animal. This argument cannot be brought under the\nrules of the syllogism, because it contains four distinct logical terms\nin two propositions; namely, horse, some animal; head of horse, head of\nsome animal. But it easily comes under the rule which I have given,\nbecause we have simply to put 'some animal' instead of 'a horse'. A\ngreat many arguments may be explained in this way. Gold is a metal;\ntherefore a piece of gold is a piece of metal. A negro is a fellow\ncreature; therefore, he who strikes a negro, strikes a fellow creature.\"\n\nThe same eminent authority says: \"When we examine carefully enough the\nway in which we reason, it will be found _in every case to consist in\nputting one thing or term in place of another, to which we know it to\nhave an exact resemblance in some respect_. We use the likeness as a\nkind of bridge, which leads us from a knowledge of one thing to a\nknowledge of another; thus _the true principle of reasoning may be\ncalled the substitution of similars, or the passing from like to like_.\nWe infer the character of one thing from the character of something\nwhich acts as a go-between, or third term. When we are certain there is\nan exact likeness, our inference is certain; when we only believe that\nthere probably is, or guess that there is, then our inferences are only\nprobable, not certain.\"\n\n\n\n\nCHAPTER XVI.\n\nTHE SYLLOGISM\n\n\nThe third and highest phase or step in reasoning--the step which follows\nafter those styled Conception and Judgment--is generally known by the\ngeneral term \"Reasoning,\" which term, however, is used to include the\ntwo precedent steps as well as the final step itself. This step or\nprocess consists of the comparing of two objects, persons or things,\nthrough their relation to a third object, person or thing. As, for\ninstance, we reason (a) that all mammals are animals; (b) that a horse\nis a mammal; and (c) that, _therefore_, a horse is an animal. The most\nfundamental principle of this step or reasoning consists in the\ncomparing of two objects of thought through and by means of their\nrelation to a third object. The natural form of expression of this\nprocess of reasoning is called a \"Syllogism.\"\n\nThe process of reasoning which gives rise to the expression of the\nargument in the form of a Syllogism must be understood if one wishes to\nform a clear conception of the Syllogism. The process itself is very\nsimple when plainly stated, although the beginner is sometimes puzzled\nby the complicated definitions and statements of the authorities. Let us\nsuppose that we have three objects, A, B and C, respectively. We wish to\ncompare C and B, but fail to establish a relation between them at first.\nWe however are able to establish a relation between A and B; and between\nC and A. We thus have the two propositions (1) \"A equals B; and (2) C\nequals A\". The next step is that of inferring that \"if A equals B, and C\nequals A, then it must follow, logically, _that C equals B_.\" This\nprocess is that of indirect or mediate comparison, rather than\n_immediate_. C and B are not compared directly or immediately, but\nindirectly and through the medium of A. A is thus said to _mediate_\nbetween B and C.\n\nThis process of reasoning embraces three ideas or objects of thought, in\ntheir expression of propositions. It comprises the fundamental or\nelemental form of reasoning. As Brooks says: \"The simplest movement of\nthe reasoning process is the comparing of two objects through their\nrelation to a third.\" The result of this process is an argument\nexpressed in what is called a Syllogism. Whately says that: \"A Syllogism\nis an argument expressed in strict logical form so that its\nconclusiveness is manifest from the structure of the expression alone,\nwithout any regard to the meaning of the terms.\" Brooks says: \"All\nreasoning can be and naturally is expressed in the form of the\nsyllogism. It applies to both inductive and deductive reasoning, and is\nthe form in which these processes are presented. Its importance as an\ninstrument of thought requires that it receive special notice.\"\n\nIn order that the nature and use of the Syllogism may be clearly\nunderstood, we can do no better than to at once present for your\nconsideration the well-known \"Rules of the Syllogism,\" an understanding\nof which carries with it a perfect comprehension of the Syllogism\nitself.\n\nThe Rules of the Syllogism state that in order for a Syllogism to be a\n_perfect_ Syllogism, it is necessary:\n\nI. _That there should be three, and no more than three, Propositions._\nThese three propositions are: (1) the _Conclusion_, or thing to be\nproved; and (2 and 3) the Premises, or the means of proving the\nConclusion, and which are called the Major Premise and Minor Premise,\nrespectively. We may understand this more clearly if we will examine the\nfollowing example:\n\n_Major Premise_: \"Man is mortal;\" (or \"A is B\").\n\n_Minor Premise_: \"Socrates is a man;\" (or \"C is A\"). Therefore:\n\n_Conclusion_: \"Socrates is mortal\" (or \"C is B\").\n\nIt will be seen that the above Syllogism, whether expressed in words or\nsymbols, is logically valid, because the conclusion must logically\nfollow the premises. And, in this case, the premises being true, it must\nfollow that the conclusion is true. Whately says: \"A Syllogism is said\nto be valid when the conclusion logically follows from the premises; if\nthe conclusion does not so follow, the Syllogism is invalid and\nconstitutes a Fallacy, if the error deceives the reasoner himself; but\nif it is advanced with the idea of deceiving others it constitutes a\nSophism.\"\n\nThe reason for Rule I is that only three propositions--a Major Premise,\na Minor Premise, and a Conclusion--are needed to form a Syllogism. If we\nhave more than _three_ propositions, then we must have more than two\npremises from which to draw one conclusion. The presence of more than\ntwo premises would result in the formation of two or more Syllogisms, or\nelse in the failure to form a Syllogism.\n\nII. _That there should be three and no more than three Terms._ These\nTerms are (1) The Predicate of the Conclusion; (2) the Subject of the\nConclusion; and (3) the Middle Term which must occur in both premises,\nbeing the connecting link in bringing the two other Terms together in\nthe Conclusion.\n\nThe _Predicate of the Conclusion_ is called the _Major_ Term, because it\nis the greatest in extension compared with its fellow terms. The\n_Subject of the Conclusion_ is called the _Minor_ Term because it is the\nsmallest in extension compared with its fellow terms. The Major and\nMinor Terms are called the _Extremes_. The Middle Term operates between\nthe two Extremes.\n\nThe _Major Term_ and the _Middle Term_ must appear in the _Major\nPremise_.\n\nThe _Minor Term_ and the _Middle Term_ must appear in the _Minor\nPremise_.\n\nThe _Minor Term_ and the _Major Term_ must appear in the _Conclusion_.\n\nThus we see that _The Major Term_ must be the Predicate of the\nConclusion; the _Minor Term_ the Subject of the Conclusion; the _Middle\nTerm_ may be the Subject or Predicate _of either of the premises_, but\n_must always be found once in both premises_.\n\nThe following example will show this arrangement more clearly:\n\nIn the Syllogism: \"Man is mortal; Socrates is a man; therefore Socrates\nis mortal,\" we have the following arrangement: \"Mortal,\" the Major Term;\n\"Socrates,\" the Minor Term; and \"Man,\" the Middle Term; as follows:\n\n_Major Premise_: \"Man\" (_middle term_) is mortal (_major term_).\n\n_Minor Premise_: \"Socrates\" (_minor term_) is a man (_major term_).\n\n_Conclusion_: \"Socrates\" (_minor term_) is mortal (_major term_).\n\nThe reason for the rule that there shall be \"_only three_\" terms is that\nreasoning consists in comparing _two terms_ with each other through the\nmedium of a _third term_. There _must be_ three terms; if there are\n_more_ than three terms, we form two syllogisms instead of one.\n\nIII. _That one premise, at least, must be affirmative._ This, because\n\"from two negative propositions nothing can be inferred.\" A negative\nproposition asserts that two things differ, and if we have two\npropositions so asserting difference, we can infer nothing from them. If\nour Syllogism stated that: (1) \"Man is _not_ mortal;\" and (2) that\n\"Socrates is _not_ a man;\" we could form no Conclusion, either that\nSocrates _was_ or _was not_ mortal. There would be no logical connection\nbetween the two premises, and therefore no Conclusion could be deduced\ntherefrom. Therefore, at least one premise must be affirmative.\n\nIV. _If one premise is negative, the conclusion must be negative._ This\nbecause \"if one term agrees and another disagrees with a third term,\nthey must disagree with each other.\" Thus if our Syllogism stated that:\n(1) \"Man is _not_ mortal;\" and (2) that: \"Socrates is a man;\" we must\nannounce the Negative Conclusion that: (3) \"Socrates is _not_ mortal.\"\n\nV. _That the Middle Term must be distributed; (that is, taken\nuniversally) in at least one premise._ This \"because, otherwise, the\nMajor Term may be compared with one part of the Middle Term, and the\nMinor Term with another part of the latter; and there will be actually\nno common Middle Term, and consequently no common ground for an\ninference.\" The violation of this rule causes what is commonly known as\n\"The Undistributed Middle,\" a celebrated Fallacy condemned by the\nlogicians. In the Syllogism mentioned as an example in this chapter, the\nproposition \"_Man_ is mortal,\" really means \"_All_ men,\" that is, Man in\nhis universal sense. Literally the proposition is \"All men are mortal,\"\nfrom which it is seen that Socrates being \"_a_ man\" (or _some_ of _all_\nmen) must partake of the quality of the universal Man. If the Syllogism,\ninstead, read: \"_Some_ men are mortal,\" it would not follow that\nSocrates _must_ be mortal--he might or might not be so. Another form of\nthis fallacy is shown in the statement that (1) White is a color; (2)\nBlack is a color; hence (3) Black must be White. The two premises\n_really_ mean \"White is _some_ color; Black is _some_ color;\" and not\nthat either is \"_all_ colors.\" Another example is: \"Men are bipeds;\nbirds are bipeds; hence, men are birds.\" In this example \"bipeds\" is not\ndistributed as \"_all_ bipeds\" but is simply not-distributed as \"_some_\nbipeds.\" These syllogisms, therefore, not being according to rule, must\nfail. They are not true syllogisms, and constitute fallacies.\n\nTo be \"_distributed_,\" the Middle Term must be the Subject of a\nUniversal Proposition, or the Predicate of a Negative Proposition; to be\n\"_undistributed_\" it must be the Subject of a Particular Proposition, or\nthe Predicate of an Affirmative Proposition. (See chapter on\nPropositions.)\n\nVI. _That an extreme, if undistributed in a Premise, may not be\ndistributed in the Conclusion._ This because it would be illogical and\nunreasonable to assert more in the conclusion than we find in the\npremises. It would be most illogical to argue that: (1) \"All horses are\nanimals; (2) no man is a horse; therefore (3) no man is an animal.\" The\nconclusion would be invalid, because the term _animal_ is distributed in\nthe conclusion, (being the predicate of a negative proposition) while it\nis not distributed in the premise (being the predicate of an affirmative\nproposition).\n\nAs we have said before, any Syllogism which violates any of the above\nsix syllogisms is invalid and a fallacy.\n\nThere are two additional rules which may be called derivative. Any\nsyllogism which violates either of these two derivative rules, also\nviolates one or more of the first six rules as given above in detail.\n\nThe _Two Derivative Rules of the Syllogism_ are as follows:\n\nVII. _That one Premise at least must be Universal._ This because \"from\ntwo particular premises no conclusion can be drawn.\"\n\nVIII. _That if one premise is Particular, the Conclusion must be\nparticular also._ This because only a universal conclusion can be drawn\nfrom two universal premises.\n\nThe principles involved in these two Derivative Rules may be tested by\nstating Syllogisms violating them. They contain the essence of the other\nrules, and every syllogism which breaks them will be found to also break\none or more of the other rules given.\n\n\n\n\nCHAPTER XVII.\n\nVARIETIES OF SYLLOGISMS\n\n\nThe authorities in Logic hold that with the four kinds of propositions\ngrouped in every possible order of arrangement, it is possible to form\nnineteen different kinds of valid arguments, which are called the\n_nineteen moods of the syllogism_. These are classified by division into\nwhat are called _the four figures_, each of which figures may be known\nby the position of the middle term in the premises. Logicians have\narranged elaborate and curious tables constructed to show what kinds of\npropositions when joined in a particular order of arrangement will make\nsound and valid syllogisms. We shall not set forth these tables here, as\nthey are too technical for a popular presentation of the subject before\nus, and because they are not necessary to the student who will\nthoroughly familiarize himself with the above stated Laws of the\nSyllogism and who will therefore be able to determine in every case\nwhether any given argument is a correct syllogism, or otherwise.\n\nIn many instances of ordinary thought and expression the _complete_\nsyllogistic form is omitted, or not stated at full length. It is common\nusage to omit one premise of a syllogism, in ordinary expression, the\nmissing premise being inferred by the speaker and hearer. A syllogism\nwith one premise unexpressed is sometimes called an _Enthymene_, the\nterm meaning \"in the mind.\" For instance, the following: \"We are a free\npeople, therefore we are happy,\" the major premise \"All free people are\nhappy\" being omitted or unexpressed. Also in \"Poets are imaginative,\ntherefore Byron was imaginative,\" the minor premise \"Byron was a poet\"\nis omitted or unexpressed. Jevons says regarding this phase of the\nsubject: \"Thus in the Sermon on the Mount, the verses known as the\nBeatitudes consist each of one premise and a conclusion, and the\nconclusion is put first. 'Blessed are the merciful: for they shall\nobtain mercy.' The subject and the predicate of the conclusion are here\ninverted, so that the proposition is really 'The merciful are blessed.'\nIt is evidently _understood_ that 'All who shall obtain mercy are\nblessed,' so that the syllogism, when stated at full length, becomes:\n'All who shall obtain mercy are blessed; All who are merciful shall\nobtain mercy; Therefore, all who are merciful are blessed.' This is a\nperfectly good syllogism.\"\n\nWhenever we find any of the words: \"_because_, _for_, _therefore_,\n_since_,\" or similar terms, we may know that there is an argument, and\nusually a syllogism.\n\nWe have seen that there are three special kinds of Propositions, namely,\n(1) Categorical Propositions, or propositions in which the affirmation\nor denial is made without reservation or qualification; (2) Hypothetical\nPropositions, in which the affirmation or denial is made to depend upon\ncertain conditions, circumstances, or suppositions; and (3) Disjunctive\nPropositions, in which is implied or asserted an _alternative_.\n\nThe forms of reasoning based upon these three several classes of\npropositions bear the same names as the latter. And, accordingly the\nrespective syllogisms expressing these forms of reasoning also bear the\nclass name or term. Thus, a Categorical Syllogism is one containing\nonly categorical propositions; a Hypothetical Syllogism is one\ncontaining one or more hypothetical propositions; a Disjunctive\nSyllogism is one containing a disjunctive proposition in the major\npremise.\n\n_Categorical Syllogisms_, which are far more common than the other two\nkinds, have been considered in the previous chapter, and the majority of\nthe examples of syllogisms given in this book are of this kind. In a\nCategorical Syllogism the statement or denial is made positively, and\nwithout reservation or qualification, and the reasoning thereupon\npartakes of the same positive character. In propositions or syllogisms\nof this kind it is asserted or assumed that the premise is true and\ncorrect, and, if the reasoning be logically correct it must follow that\nthe conclusion is correct, and the new proposition springing therefrom\nmust likewise be Categorical in its nature.\n\n_Hypothetical Syllogisms_, on the contrary, have as one or more of their\npremises a hypothetical proposition which affirms or asserts something\nprovided, or \"if,\" something else be true. Hyslop says of this: \"Often\nwe wish first to bring out, if only conditionally, the truth upon which\na proposition rests, so as to see if the connection between this\nconclusion and the major premise be admitted. The whole question will\nthen depend upon the matter of treating the minor premise. This has the\nadvantage of getting the major premise admitted without the formal\nprocedure of proof, and the minor premise is usually more easily proved\nthan the major. Consequently, one is made to see more clearly the force\nof the argument or reasoning by removing the question of the material\ntruth of the major premise and concentrating attention upon the relation\nbetween the conclusion and its conditions, so that we know clearly what\nwe have first to deny if we do not wish to accept it.\"\n\nBy joining a hypothetical proposition with an ordinary proposition we\ncreate a Hypothetical Proposition. For instance: \"_If_ York contains a\ncathedral it is a city; York _does_ contain a cathedral; therefore, York\nis a city.\" Or: \"If _dogs_ have four feet, they are quadrupeds; dogs\n_do_ have four feet; therefore dogs _are_ quadrupeds.\" The Hypothetical\nSyllogism may be either affirmative or negative; that is, its\nhypothetical proposition may either hypothetically _affirm_ or\nhypothetically _deny_. The part of the premise of a Hypothetical\nSyllogism which conditions or questions (and which usually contains the\nlittle word \"if\") is called the Antecedent. The major premise is the one\nusually thus conditioned. The other part of the conditioned proposition,\nand which part states what will happen or is true under the conditional\ncircumstances, is called the Consequent. Thus, in one of the above\nexamples: \"If dogs have four feet\" is the Antecedent; and the remainder\nof the proposition: \"they are quadrupeds\" is the Consequent. The\nAntecedent is indicated by the presence of some conditional term as:\n_if_, _supposing_, _granted that_, _provided that_, _although_, _had_,\n_were_, etc., the general sense and meaning of such terms being that of\nthe little word \"_if_.\" The Consequent has no special indicating term.\n\nJevons gives the following clear and simple _Rules regarding the\nHypothetical Syllogism_:\n\nI. \"If the Antecedent be affirmed, the consequent may be affirmed. If\nthe Consequent be denied, the Antecedent may be denied.\"\n\nII. \"Avoid the fallacy of affirming the consequent, or denying the\nantecedent. This is a fallacy because of the fact that the conditional\nstatement made in the major premise _may not be the only one_\ndetermining the consequent.\" The following is an example of \"Affirming\nthe Consequent:\" \"_If_ it is raining, the sky is overclouded; the sky\n_is_ overclouded; therefore, it _is raining_.\" In truth, the sky may be\noverclouded, and still it may _not_ be raining. The fallacy is still\nmore apparent when expressed in symbols, as follows: \"_If_ A is B, C is\nD; C _is_ D; therefore, A is B.\" The fallacy of denying the Antecedent\nis shown by the following example: \"_If_ Radium were cheap it would be\nuseful; Radium is _not_ cheap; therefore Radium _is not_ useful.\" Or,\nexpressed in symbols: \"_If_ A is B, C is D; A is _not_ B; therefore C\n_is not_ D.\" In truth Radium may be useful although not cheap. Jevons\ngives the following examples of these fallacies: \"If a man is a good\nteacher, he thoroughly understands his subject; but John Jones\nthoroughly understands his subject; therefore, he is a good teacher.\"\nAlso, \"If snow is mixed with salt it melts; the snow on the ground is\n_not_ mixed with salt; therefore it does _not_ melt.\"\n\nJevons says: \"To affirm the consequent and then to infer that we can\naffirm the antecedent, is as bad as breaking the third rule of the\nsyllogism, and allowing an undistributed middle term.... To deny the\nantecedent is really to break the fourth rule of the syllogism, and to\ntake a term as distributed in the conclusion which was not so in the\npremises.\"\n\nHypothetical Syllogisms may usually be easily reduced to or converted\ninto Categorical Syllogisms. As Jevons says: \"In reality, hypothetical\npropositions and syllogisms are not different from those which we have\nmore fully considered. _It is all a matter of the convenience of stating\nthe propositions._\" For instance, instead of saying: \"If Radium were\ncheap, it would be useful,\" we may say \"Cheap Radium would be useful;\"\nor instead of saying: \"If glass is thin, it breaks easily,\" we may say\n\"Thin glass breaks easily.\" Hyslop gives the following _Rule for\nConversion_ in such cases: \"Regard the antecedent of the hypothetical\nproposition as the subject of the categorical, and the consequent of\nthe hypothetical proposition as the predicate of the categorical. In\nsome cases this change is a very simple one; in others it can be\neffected only by a circumlocution.\"\n\nThe third class of syllogisms, known as _The Disjunctive Syllogism_, is\nthe exception to the law which holds that all good syllogisms must fit\nin and come under the Rules of the Syllogism, as stated in the preceding\nchapter. Not only does it refuse to obey these Rules, but it fails to\nresemble the ordinary syllogism in many ways. As Jevons says: \"It would\nbe a great mistake to suppose that all good logical arguments must obey\nthe rules of the syllogism, which we have been considering. Only those\narguments which connect two terms together by means of a middle term,\nand are therefore syllogisms, need obey these rules. A great many of the\narguments which we daily use are of this nature; but there are a great\nmany other kinds of arguments, some of which have never been understood\nby logicians until recent years. One important kind of argument is known\nas the Disjunctive Syllogism, though it does not obey the rules of the\nsyllogism, or in any way resemble syllogisms.\"\n\nThe Disjunctive Syllogism is one having a disjunctive proposition in its\nmajor premise. The disjunctive proposition also appears in the\nconclusion when the disjunction in the major premise happens to contain\nmore than two terms. A disjunctive proposition, we have seen, is one\nwhich possesses alternative predicates for the subject in which the\nconjunction \"_or_\" (sometimes accompanied by \"_either_\") appears. As for\ninstance: \"Lightning is sheet _or_ forked;\" or, \"Arches are _either_\nround or pointed;\" or, \"Angles are either obtuse, or right angled, or\nacute.\" The different things joined together by \"or\" are called\nAlternatives, the term indicating that we may choose between the things,\nand that if one will not answer our purpose we may take the other, or\none of the others if there be more than one _other_.\n\nThe _Rule regarding the Use of Disjunctive Syllogisms_ is that: \"If one\nor more alternatives be denied, the rest may still be affirmed.\" Thus if\nwe say that \"A is B or C,\" or that \"A is either B or C,\" we may _deny_\nthe B but still affirm the C. Some authorities also hold that \"If we\naffirm one alternative, we must deny the remainder,\" but this view is\nvigorously disputed by other authorities. It would seem to be a valid\nrule in cases where the term \"either\" appears as: \"A is _either_ B _or_\nC,\" because there seems to be an implication that one or the other alone\ncan be true. But in cases like: \"A is B _or_ C,\" there may be a\npossibility of _both being true_. Jevons takes this latter view, giving\nas an example the proposition: \"A Magistrate is a Justice-of-the-Peace,\na Mayor, or a Stipendiary Magistrate,\" but it does not follow that one\nwho is a Justice-of-the-Peace may not be at the same time a Mayor. He\nstates: \"After affirming one alternative we can only deny the others _if\nthere be such a difference between them that they could not be true at\nthe same time_.\" It would seem that both contentions are at the same\ntime true, the example given by Jevons illustrating his contention, and\nthe proposition \"The prisoner is either guilty or innocent\" illustrating\nthe contentions of the other side.\n\nA _Dilemma_ is a conditional syllogism whose Major Premise presents\nsome sort of alternative. Whately defines it as: \"A conditional\nsyllogism with two or more antecedents in the major, and a disjunctive\nminor.\" There being two mutually exclusive propositions in the Major\nPremise, the reasoner is compelled to admit one or the other, and is\nthen caught between \"the two horns of the dilemma.\"\n\n\n\n\nCHAPTER XVIII.\n\nREASONING BY ANALOGY\n\n\nWhat is called Reasoning by Analogy is one of the most elementary forms\nof reasoning, and the one which the majority of us most frequently\nemploy. It is a primitive form of hasty generalization evidencing in the\nnatural expectation that \"things will happen as they have happened\nbefore in like circumstances.\" The term as used in logic has been\ndefined as \"Resemblance of relations; Resemblances of any kind on which\nan argument falling short of induction may be founded.\" Brooks says:\n\"Analogy is that process of thought by which we infer that if two things\nresemble each other in one or more particulars, they will resemble each\nother in some other particular.\"\n\nJevons states the _Rule for Reasoning by Analogy_, as follows: \"If two\nor more things resemble each other in many points, they will probably\nresemble each other also in more points.\" Others have stated the same\nprinciple as follows: \"When one thing resembles another in known\nparticulars, it will resemble it also in the unknown;\" and \"If two\nthings agree in several particulars, they will also agree in other\nparticulars.\"\n\nThere is a difference between generalization by induction, and by\nanalogy. In inductive generalization the rule is: \"What is true of the\nmany is true of all;\" while the rule of analogy is: \"things that have\nsome things in common have other things in common.\" As Jevons aptly\nremarks: \"Reasoning by Analogy differs only in degree from that kind of\nreasoning called 'Generalization.' When _many things_ resemble each\nother in a _few properties_, we argue about them by Generalization. When\na _few things_ resemble each other in _many properties_, it is a case of\nanalogy.\" Illustrating Analogy, we may say that if in A we find the\nqualities, attributes or properties called _a_, _b_, _c_, _d_, _e_, _f_,\n_g_, respectively, and if we find that in B the qualities, etc., called\n_a_, _b_, _c_, _d_, _e_, respectively, are present, then we may reason\nby analogy that the qualities _f_ and _g_ must also belong to B.\n\nBrooks says of this form of reasoning: \"This principle is in constant\napplication in ordinary life and in science. A physician, in visiting a\npatient, says this disease corresponds in several particulars with\ntyphoid fever, hence it will correspond in _all_ particulars, and _is_\ntyphoid fever. So, when the geologist discovers a fossil animal with\nlarge, strong, blunt claws, he infers that it procured its food by\nscratching or burrowing in the earth. It was by analogy that Dr.\nBuckland constructed an animal from a few fossil bones, and when\nsubsequently the bones of the entire animal were discovered, his\nconstruction was found to be correct.\" Halleck says: \"In argument or\nreasoning we are much aided by the habit of searching for hidden\nresemblances.... The detection of such a relation cultivates thought. If\nwe are to succeed in argument, we must develop what some call a sixth\nsense of such relations.... The study of poetry may be made very\nserviceable in detecting analogies and cultivating the reasoning powers.\nWhen the poet brings clearly to mind the change due to death, using as\nan illustration the caterpillar body transformed into the butterfly\nspirit, moving with winged ease over flowering meadows, he is\ncultivating our apprehension of relations, none the less valuable\nbecause they are beautiful.\"\n\nBut the student must be on guard against the deceptive conclusions\nsometimes arising from Reasoning by Analogy. As Jevons says: \"In many\ncases Reasoning by Analogy is found to be a very uncertain guide. In\nsome cases unfortunate mistakes are made. Children are sometimes killed\nby gathering and eating poisonous berries, wrongly inferring that they\ncan be eaten, because other berries, of a somewhat similar appearance,\nhave been found agreeable and harmless. Poisonous toadstools are\noccasionally mistaken for mushrooms, especially by people not accustomed\nto gathering them. In Norway mushrooms are seldom seen, and are not\neaten; but when I once found a few there and had them cooked at an inn,\nI was amused by the people of the inn, who went and collected toadstools\nand wanted me to eat them also. This was clearly a case of mistaken\nreasoning by analogy. Even brute animals reason in the same way in some\ndegree. The beaten dog fears every stick, and there are few dogs which\nwill not run away when you pretend to pick up a stone, even if there be\nno stone to pick up.\" Halleck says: \"Many false analogies are\nmanufactured, and it is excellent thought training to expose them. The\nmajority of people think so little that they swallow these false\nanalogies just as newly fledged robins swallow small stones dropped into\ntheir open mouths.... This tendency to think as others do must be\nresisted somewhere along the line, or there can be no progress.\" Brooks\nsays: \"The argument from Analogy is plausible, but often deceptive. Thus\nto infer that since American swans are white, the Australian swan is\nwhite, gives a false conclusion, for it is really black. So to infer\nthat because John Smith has a red nose and is a drunkard, then Henry\nJones who also has a red nose is also a drunkard, would be a dangerous\ninference.... Conclusions of this kind drawn from analogy are frequently\nfallacious.\"\n\nRegarding the _Rule for Reasoning from Analogy_, Jevons says: \"There is\nno way in which we can really assure ourselves that we are arguing\nsafely by analogy. The only rule that can be given is this; that the\nmore closely two things resemble each other, the more likely it is that\nthey are the same in other respects, especially in points closely\nconnected with those observed.... In order to be clear about our\nconclusions, we ought in fact never to rest satisfied with mere analogy,\nbut ought to try to discover the general laws governing the case. In\nanalogy we seem to reason from one fact to another fact without\ntroubling ourselves either with deduction or induction. But it is only\nby a kind of guess that we do so; it is not really conclusive reasoning.\nWe ought properly to ascertain what general laws of nature are shown to\nexist by the facts observed, and then infer what will happen according\nto these laws.... We find that reasoning by analogy is not to be\ndepended upon, unless we make such an inquiry into the causes and laws\nof the things in question, that we really employ inductive and deductive\nreasoning.\"\n\nAlong the same lines, Brooks says: \"The inference from analogy, like\nthat from induction, should be used with caution. Its conclusion must\nnot be regarded as certain, but merely as reaching a high degree of\nprobability. The inference from a part to a part, no more than from a\npart to the whole, is attended with any rational necessity. To attain\ncertainty, we must show that the principles which lie at the root of the\nprocess are either necessary laws of thought or necessary laws of\nnature; both of which are impossible. Hence analogy can pretend to only\na high degree of probability. It may even reach a large degree of\ncertainty, but it never reaches necessity. We must, therefore, be\ncareful not to accept any inference from analogy as true until it is\nproved to be true by actual observation and experiment, or by such an\napplication of induction as to remove all reasonable doubt.\"\n\n\n\n\nCHAPTER XIX.\n\nFALLACIES\n\n\nA _Fallacy_ is: \"An unsound argument or mode of arguing, which, while\nappearing to be decisive of a question, is in reality not so; an\nargument or proposition apparently sound, but really fallacious; a\nfallacious statement or proposition, in which the error is not apparent,\nand which is therefore likely to mislead or deceive; sophistry.\"\n\nIn Deductive Reasoning, we meet with two classes of Fallacies; namely,\n(1) Fallacious Premise; and (2) Fallacious Conclusion. We shall now\nconsider each of these in turn.\n\n_Fallacious Premise_ is in effect _an unwarranted assumption of\npremises_. One of the most common forms of this kind of Fallacy is known\nas \"_Begging the Question_,\" the principle of which is the assumption of\na fundamental premise which is not conceded; the unwarrantable\nassumption of that which is to be proved; or the assumption of that by\nwhich it is to be proved, without proving it. Its most common form is\nthat of boldly stating some unproven fact, authoritatively and\npositively, and then proceeding to use the statement as the major\npremise of the argument, proceeding logically from that point. The\nhearer perceiving the argument proceeding logically often fails to\nremember that _the premise has been merely assumed_, without warrant and\nwithout proof and omitting the hypothetical \"_if_.\" One may proceed to\nargue logically from the premise that \"The moon is made of green\ncheese,\" but the whole argument is invalid and fallacious because of the\nfact that the person making it has \"begged the question\" upon an\nunwarranted premise. Hyslop gives a good example of this form of fallacy\nin the case of the proposition \"Church and State should be united.\"\nProof being demanded the advocate proceeds to \"beg the question\" as\nfollows: \"Good institutions should be united; Church and State are good\ninstitutions; therefore, Church and State should be united.\" The\nproposition that \"Good institutions should be united\" is fallacious,\nbeing merely assumed and not proven. The proposition sounds reasonable,\nand few will feel disposed to dispute it at first, but a little\nconsideration will show that while _some_ good institutions may well be\nunited, it is _not_ a general truth that _all_ should be so.\n\n\"Begging the Question\" also often arises from _giving a name to a\nthing_, and then assuming that we have _explained_ the thing. This is a\nvery frequent practice with many people--they try to _explain_ by merely\napplying names. An example of this kind is had in the case of the person\nwho tried to explain why one could see through a pane of glass by saying\n\"because it is transparent.\" Or when one explains that the reason a\ncertain substance breaks easily is \"because it is brittle.\" Moliere\nmakes the father of a dumb girl ask why his daughter is dumb. The\nphysician answers: \"Nothing is more easy than to explain it; it comes\nfrom her having lost the power of speech.\" \"Yes, yes,\" objects the\nfather, \"but the cause, if you please, why she has lost the power of\nspeech.\" The physician gravely replies: \"All our best authors will tell\nyou that it is the impeding of the action of the tongue.\"\n\nJevons says: \"The most frequent way, perhaps, in which we commit this\nkind of fallacy is to employ names which imply that we disapprove of\nsomething, and then argue that because it is such and such, it must be\ncondemned. When two sportsmen fall out in some manner relating to the\nsubject of game, one will, in all probability, argue that the act of the\nother was 'unsportsmanlike,' and therefore should not have been done.\nHere is to all appearance a correct syllogism:\n\n\"No unsportsmanlike act should be done; John Robinson's act was\nunsportsmanlike: Therefore, John Robinson's act should not have been\ndone.\n\n\"This is quite correct in form; but it is evidently the mere semblance\nof an argument. 'Unsportsmanlike' means _what a sportsman should not\ndo_. The point to be argued was whether the act fell within the\ncustomary definition of _what was unsportsmanlike_.\"\n\nArising from \"Begging the Question,\" and in fact a class of the latter,\nis what is called \"Reasoning in a Circle.\" In this form of fallacy one\nassumes as proof of a proposition the proposition itself; or, uses the\nconclusion to prove the premise. For instance: \"This man is a rascal\nbecause he is a rogue; and he is a rogue because he is a rascal.\" Or,\n\"It is warm because it is summer; and it is summer because it is warm.\"\nOr \"He never drinks to excess, because he is never intemperate in\ndrinking.\"\n\nBrooks says: \"Thus to argue that a party is good because it advocates\ngood measures, and that certain measures are good because they are\nadvocated by so excellent a party, is to reason in a circle. So when\npersons argue that their church is the true one, because it was\nestablished by God, and then argue that since it is the true church it\nmust have been founded by God, they fall into this fallacy. To argue\nthat 'the will is determined by the strongest motive' and to define the\nstrongest motive as 'that which influences the will,' is to revolve in a\ncircle of thought and prove nothing. Plato commits this error when he\nargues the immortality of the soul from its simplicity, and afterwards\nattempts to prove its simplicity from its immortality.\" It needs care to\navoid this error, for it is surprising how easily one falls into it.\nHyslop says: \"The fallacy of Reasoning in a Circle occurs mostly in\nlong arguments where it can be committed without ready detection....\nWhen it occurs in a long discourse it may be committed without easy\ndiscovery. It is likely to be occasioned by the use of synonyms which\nare taken to express more than the conception involved when they do\nnot.\" What is called a Vicious Circle is caused when the conclusion of\none syllogism is used for a proposition in another syllogism, which in\nits turn comes to be used as a basis for the first or _original\nsyllogism_.\n\n_Fallacious Conclusion_ is in effect _an unwarranted or irrelevant\nassumption of a logical conclusion_. There are many forms of this\nfallacy among which are the following:\n\n_Shifting ground_, which consists in the pretence of proving one thing\nwhile in reality merely a similar or related thing is being proved. In\nthis class is the argument that because a man is profane he must\nnecessarily be dishonest; or that because a man denies the inspiration\nof the Scriptures he must be an atheist.\n\n_Fallacious Questioning_, in which two or more related questions are\nasked, and the answer of one is then applied to the other. For\ninstance: \"You assert that the more civilized a community, the more\nsilk-hats are to be found in it?\" \"Yes.\" \"Then, you state that silk-hats\nare the promoters and cause of civilization in a community?\" A question\nof this kind is often so arranged that an answer either in the\naffirmative or the negative will lead to a false or fallacious\ninference. For instance, the question once asked a respectable citizen\non the witness stand: \"Have you stopped beating your mother?\" An answer\nof either \"Yes\" or \"No,\" was out of the question, for it would have\nplaced the witness in a false position, for he had never beaten his\nmother, nor been accused of the same.\n\n_Partial Proof_, in which the proof of a partial or related fact is used\nto infer a proof of the whole fact or a related one. For instance, it is\nfallacious to argue that a man has been guilty of drunkenness by merely\nproving that he was seen entering a saloon.\n\n_Appeal to Public Opinion_, in which the prejudices of the public are\nappealed to rather than its judgment or reason. In politics and\ntheological argument this fallacy is frequent. It is no argument, and is\nreprehensible.\n\n_Appeal to Authority, or Reverence_, in which the reverence and respect\nof the public for certain persons is used to influence their feelings in\nplace of their judgment or reason. For instance: \"Washington thought\nso-and-so, and therefore it must be right;\" or \"It is foolish to affirm\nthat Aristotle erred;\" or \"It has been believed by men for two thousand\nyears, that, etc;\" or \"What our fathers believed must be true.\" Appeals\nof this kind may have their proper place, but they are fallacies\nnevertheless, and not real argument.\n\n_Appeal to Profession_, in which an appeal is made to practices,\nprinciples or professions of the opponent, rather than to reason or\njudgment. Thus we may argue that a certain philosophy or religion cannot\nbe sound or good, because certain people who hold it are not consistent,\nor not worthy, moral or sober. This argument is often used effectively\nagainst an opponent, and is valid against him personally. But it is no\nvalid argument against his philosophy or belief, because he may act in\nviolation of them, or he may change his practices and still adhere to\nhis beliefs--the two are not joined.\n\n_Appeal to General Belief_, in which an appeal is made to general or\nuniversal belief, although the same may be unsupported by proof. This is\nquite common, but is no real argument. The common opinion may be\nerroneous, as history proves. A few centuries ago this argument could\nhave been used in favor of the earth being flat, etc. A half-century ago\nit was used against Darwin. Today it is being used against other new\nideas. It is a fallacy by its very nature.\n\n_Appeal to Ignorance_, in which an appeal is made to the ignorance of\nthe opponent that his conviction may follow from his inability to prove\nthe contrary. It is virtually no argument that: \"So-and-so must be true,\n_because you cannot prove that it is not_.\" As Brooks says: \"To argue\nthat there is no material world, because we cannot explain how the mind\nknows it to exist, is the celebrated fallacy of Hume in philosophy. The\nfact that we cannot find a needle in a haystack is no proof that it is\nnot there.\"\n\n_Introduction of New Matter_, also called _Non Sequitur_, in which\nmatter is introduced into the conclusion that is not in the premises.\nHyslop gives the following example of it: \"All men are _rational_;\nSocrates is a man; therefore, Socrates is _noble_.\" De Morgan gives the\nfollowing more complex example: \"Episcopacy is of Scripture origin; The\nChurch of England is the only Episcopal church in England; therefore,\nthe church established is the church that ought to be supported.\"\n\nOther fallacies, resembling in some respects those above mentioned, are\nas follows:\n\n_Fallacy of Ambiguous Terms_, in which different meanings of the same\nword are used to produce the fallacious argument. As Jevons says: \"A\nword with two distinct meanings _is really two words_.\"\n\n_Confusion between Collective and General Meanings of a Term_, of which\nJevons says: \"It would be obviously absurd to argue that because _all_\nthe books in the British Museum Library are sure to give information\nabout King Alfred, therefore any particular book will be sure to give\nit. By '_all_ the books in the British Museum Library,' we mean all\n_taken together_. There are many other cases where the confusion is not\nso evident, and where great numbers of people are unable to see the\nexact difference.\"\n\n_Arguing from the Collective to the General_, in which the fallacy\nconsists of arguing that because something is true of the whole of a\ngroup of things, therefore it is true of any of those things. Jevons\nsays: \"_All_ the soldiers in a regiment may be able to capture a town,\nbut it is absurd to suppose that therefore _every_ soldier in the\nregiment could capture the town single handed. White sheep eat a great\ndeal more than black sheep; but that is because there are so many more\nof them.\"\n\n_Uncertain Meaning of a Sentence_, from which confusion arises and\nfallacious argument may spring. Jevons says: \"There is a humorous way of\nproving that a cat must have three tails: Because a cat has one tail\nmore than _no_ cat; and _no cat_ has two tails; therefore, _any_ cat has\nthree tails.\" Here the fallacy rests upon a _punning_ interpretation of\n\"no.\"\n\n_Proving the Wrong Conclusion_, in which the attempt to confuse\nconclusions is made, with the result that some people will imagine that\nthe case is established. Jevons says: \"This was the device of the\nIrishman, who was charged with theft on the evidence of three witnesses,\nwho had seen him do it; he proposed to call _thirty_ witnesses who had\n_not_ seen him do it. Equally logical was the defense of the man who was\ncalled a materialist, and who replied, 'I am not a materialist; I am a\nbarber.'\"\n\n_Fallacy of Unsuccessful Argument_, in which is attempted the illogical\nconclusion that _because a certain argument has failed the opposite\nconclusion is proven_. This fallacy is quite common, especially in cases\nof juries. One side fails to prove certain contentions, and the jury\nleaps to the conclusion that the opposite contention must be correct.\nThis is clearly fallacious, for there is always the possibility of a\n_third_ explanation. In the case of a claim of _alibi_ juries are apt to\nfall into this fallacy. The failure of the attempt to establish an\n_alibi_ is often held to be in the nature of proof of the guilt of the\naccused. Old trial lawyers assert that a failure to establish a claimed\n_alibi_ tends to injure the chance of the accused more than direct\nevidence against him. Yet, as all logical reasoners will see, there is\nno logical validity in any such inference. As Jevons has well said: \"_No\nnumber of failures in attempting to prove a proposition really disprove\nit_.\" At the end of each failure the case simply stands in the same\nposition as before the attempt; _i.e._, \"not proven.\"\n\n_All Violations of the Rules of the Syllogism_ constitute fallacies, as\nmay be seen by forming a syllogism in violation of one or more of the\nrules.\n\nThe logicians, particularly those of ancient times, took great pains to\ndiscover and _name_ new variations of fallacies, many of which were\nhair-splitting in nature, and not worthy of being considered seriously.\nSome of those which we have enumerated may possibly be open to the same\ncriticism, but we have omitted many of the worst offenders against\npractical common sense. An understanding of the fundamental Laws of\nReasoning is sufficient to expose and unmask all fallacies, and such\nunderstanding is far more valuable than the memorizing of the _names_ of\nhair-splitting fallacies which would not deceive a child.\n\nIn addition to the above stated fallacies of Deductive Reasoning, there\nare other fallacies which are met with in _Inductive Reasoning_. Let us\nbriefly consider them.\n\n_Hasty and False Generalization_ is a common fallacy of this class.\nPersons sometimes see certain qualities in a few individuals of a class,\nand mistakenly infer that _all_ the individuals in that class must\npossess these same qualities. Travelers frequently commit this fallacy.\nEnglishmen visiting the United States for a few weeks have been known to\npublish books upon their return home making the most ridiculous\ngeneralizations regarding the American people, their assertions being\nbased upon the observation of a few scattered individuals, often not at\nall representative. Americans traveling abroad commit similar errors. A\nflying trip through a country does not afford the proper opportunity for\ncorrect generalization. As Brooks says: \"No hypothesis should be\naccepted as true until the facts are so numerous that there can be no\ndoubt of its being proved.\"\n\n_Fallacies of Observation_ result from incorrect methods of observation\namong which may be mentioned the following: (1) _Careless Observation_,\nor inexact perception and conception; (2) _Partial Observation_, in\nwhich one observes only a part of the thing or fact, omitting the\nremainder, and thus forming an incomplete and imperfect concept of the\nthing or fact; (3) _Neglect of Exceptions and Contradictory Facts_, in\nwhich the exceptions and contradictory facts are ignored, thereby giving\nundue importance to the observed facts; (4) _Assumption of Facts_ which\nare not real facts, or the assumption of the truth of things which are\nuntrue; (5) _Confusing of Inferences with Facts_, which is most\nunwarrantable.\n\n_Fallacies of Mistaken Cause_ result from the assumption of a thing as a\ncause, when it is not so, of which the following are familiar examples:\n_Substituting the Antecedent for the Cause_, which consists in assuming\na mere antecedent thing for a _cause_ of another thing. Thus one might\nassume that the crowing of the cock was the _cause_ of daybreak, because\nit _preceded_ it; or that a comet was the cause of the plague which\nfollowed its appearance; or in the actual case in which a child reasoned\nthat doctors _caused_ deaths, because observation had shown that they\nalways visited persons before they died; or that crops failed because a\nPresident of a certain political party had been inaugurated a few months\nbefore. Some fallacies of everyday reasoning are quite as illogical as\nthose just mentioned. _Substituting the Symptom for the Cause_, which\nconsists in assuming as a _cause_ some mere symptom, sign or incident of\nthe real cause. To assume that the pimples of measles were the _cause_\nof the disease, would be to commit a fallacy of this kind. We have\nmentioned elsewhere the fallacy which would assume silk-hats to be the\ncause of Civilization, instead of being a mere incident of the latter.\nPoliticians are fond of assuming certain incidents or signs of a period,\nas being the _causes_ of the prosperity, culture and advancement of the\nperiod, or the reverse. One might argue, with equal force, that\nautomobiles were the causes of national prosperity, pointing to the fact\nthat the more automobiles to be seen the better the times. Or, that\nstraw hats produced hot weather, for similar reasons.\n\n_The Fallacy of Analogy_ consists in assuming a resemblance or identity,\nwhere none exists. We have spoken of this in another chapter. Brooks\nsays, also: \"It is a fallacy to carry an analogy too far; as to infer\nfrom the parable of the praying of the importunate woman that God\nresembles the unjust judge.\"\n\nIn conclusion, we would call your attention to the following words from\nJevons, in which he expresses the gist of the matter: \"It is impossible\ntoo often to remind people that, on the one hand, _all correct reasoning\nconsists in substituting like things for like things_, and inferring\nthat what is true of one will be true of all which are similar to it in\nthe points of resemblance concerned in the matter. On the other hand,\n_all incorrect reasoning consists in putting one thing for another where\nthere is not the requisite likeness_. It is the purpose of the rules of\ndeductive and inductive logic to enable us to judge as far as possible\nwhen we are thus rightly or wrongly reasoning from some things to\nothers.\"\n\n\nFINIS.\n\n\n\n\nTRANSCRIBER'S NOTE:\n\n\nObvious typos and printer errors have been corrected without comment. In\naddition to obvious errors, the following changes have been made:\n\n  Page 18: \"Idea\" changed to \"Ideas\" in the phrase, \"... forming\n    Concepts or General Ideas.\"\n\n  Page 71: \"infuoria\" changed to \"infusoria\" in the phrase, \"... the\n    microscopic infusoria....\"\n\n  Page 135: \"disciple\" changed to \"discipline\" in the phrase, \"...\n    necessity of discipline for invention....\"\n\nOther than the above changes, no attempt has been made to correct common\nspelling, punctuation, grammar, etc. The author's usage is preserved as\nprinted in the original publication.","title":"The Art of Logical Thinking; Or, The Laws of Reasoning","tradition":"philosophy-ethics","translated_text":null,"word_count":34129}