Induction

“ There remains a third improper use of the term Induction, which it is of real importance to clear up, because the theory of Induction has been, in no ordinary degree, confused by it, and because the confusion is exemplified in the most recent and elaborate treatise on the inductive philosophy which exists in our language. The error in question is that of confounding a mere description, by general terms, of a set of observed phenomena, with an induction from them. ”

“ Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times. ”

“ Of Induction, therefore, we shall say no more at present, than that it at least is, without doubt, a process of real inference. The conclusion in an induction embraces more than is contained in the premisses. The principle or law collected from particular instances, the general proposition in which we embody the result of our experience, covers a much larger extent of ground than the individual experiments which are said to form its basis. ”

“ Finally the very form of induction itself must be new. "The induction which is to be available for the discovery and demonstration of sciences and arts must analyse nature by proper rejections and exclusions; and then, after a sufficient number of negatives, come to a conclusion on the affirmative instances, which has not yet been done, or even attempted, save only by Plato. ”

“ Not that induction is everything; it includes experiment, of course, and is punctuated by hypothesis. [54] (More, it is clearly but the servant of deduction, since the aim of all science is to predict by deduction from generalizations formed by induction; but just as clear is it that the efficacy of the whole business lies grounded in the faithfulness of the induction: induction is servant, but it has all men at its mercy.) ”

“ The Interrelation of Induction and Deduction.—Induction and deduction must go hand in hand in building up our world of knowledge. Induction gives us the particular facts out of which our system of knowledge is built, furnishes us with the data out of which general truths are formed; deduction allows us to start with the generalization furnished us by induction, and from this vantage ground to organize and systematize our knowledge and, through the discovery of its relations, to unify it and make it usable. ”

“ It is necessary to proceed by observation, by experiment, and then by induction, but with prodigious mistrust of induction. Induction consists in drawing conclusions from the particular to the general, from a certain number of facts to a law. ”

“ Induction infers a rule. Now, the belief of a rule is a habit. That a habit is a rule active in us, is evident. That every belief is of the nature of a habit, in so far as it is of a general character, has been shown in the earlier papers of this series. Induction, therefore, is the logical formula which expresses the physiological process of formation of a habit. Hypothesis substitutes, for a complicated tangle of predicates attached to one subject, a single conception. ”

“ In deduction, if the general rule is true, and the special case falls under the rule, the conclusion is certain; induction can ordinarily give no more than a probable conclusion, because we can never be sure that we have collated all instances. An induction is of the nature of an inference, but while an inference may be partial and hasty, an induction is careful, and aims to be complete. ”

“ It is not necessary to dwell at length on the futility of the formal notion of Induction. Formal Induction presupposes that enough particular instances have been collected to establish a general rule; but in actual practice inductions always repose, not on indiscriminate observation, but on a selection of relevant instances, and never claim to be based upon an exhaustive knowledge of particulars. ”

“ Whether we regard Induction and Deduction as correlative Processes belonging to one Method, each of which has been disproportionately in vogue at different epochs, or as distinctive Methods, having each their own Deductive and Inductive Processes, in either aspect, Induction is only a preparative labor, leading in the more important work of the application of the Law or Principle derived. ”

“ A second reason for this confused status in the field of inductive logic is the fact of its being more closely related to the events of every day living. Induction is the natural method of childhood; the popular method of the school room; and the most used method of common life. In consequence its ramifications are so varied and multitudinous, that it will take centuries of thinking to reduce the doctrine of induction to that uniformity and definiteness which so distinguishes deduction. ”

“ However true this intermingling of induction and deduction may be, the fact still remains true that in any given case the major movement is in one direction or the other, and that therefore in order to insure effective thinking measures must be taken accordingly. As a child formulates his conception of a verb, or words the characteristic essentials of the lily-family, or frames the rule for addition of fractions or the action of a base on a metal, he is concerned primarily with the form of the reasoning process known as induction. ”

“ The process of induction is a logical system of forming conclusions from the special to the general, by which we advance from many individual experiences to a general law; deduction, on the other hand, draws a conclusion from the general to the special, from a general law of nature to an individual case. ”

“ Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification. ”

“ Induction gathers general truths from particular facts;—and in her harvest, the corn and the reaper, the solid ears and the binding band, are alike requisite. All our knowledge of nature is obtained by Induction; the term being understood according to the explanation we have now given. And our knowledge is then most complete, then most truly deserves the name of Science, when both its elements are most perfect;—when the Ideas which have been concerned in its formation have, at every step, been clear and consistent ”

“ The process of reasoning by which we discover such laws is called induction. As we can seldom be sure that we have apprehended all the related facts, it is clear that our inductions must generally be incomplete. ”

“ The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us to Laws of Phenomena only. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. ”

“ True, he states the method or law of that change. But the method is discovered by induction. Induction is in turn annihilated by evolution. The fabric as it rises loses its foundation, and floats in the air, a baseless vision. ”

“ To begin with the conditions of direct Induction.—An Induction is an universal real proposition, based on observation, in reliance on the uniformity of Nature: when well ascertained, it is called a Law. ”

“ The indispensable foundation, therefore, of a scientific formula of induction, must be a survey of the inductions to which mankind have been conducted [pg 331] in unscientific practice; with the special purpose of ascertaining what kinds of uniformities have been found perfectly invariable, pervading all nature, and what are those which have been found to vary with difference of time, place, or other changeable circumstances. ”

“ Hence in form the most satisfactory induction is always incomplete, and differs in no wise from a bad one. 'All bodies fall to the ground' is an induction which has worked. 'All swans are white' broke down when black swans were discovered in Australia. The validity of an induction, then, is not a question of form.
The necessity for such selection no intellectualist theory of Induction has understood. All have aimed at exhaustiveness, and imagined that if it could be attained, inductive reasoning would be rendered sound, and not impossible. ”

“ For further considerations respecting the axioms of Contradiction and Excluded Middle, see the twenty-first chapter of An Examination of Sir William Hamilton’s Philosophy.100.Dr. Whewell thinks it improper to apply the term Induction to any operation not terminating in the establishment of a general truth. Induction, he says (Philosophy of Discovery, p. 245) , “is not the same thing as experience and observation. Induction is experience or observation consciously looked at in a general form. This consciousness and generality are necessary parts of that knowledge which is science.” ”

“ We saw in the preceding chapter that the principle of induction, while necessary to the validity of all arguments based on experience, is itself not capable of being proved by experience, and yet is unhesitatingly believed by every one, at least in all its concrete applications. In these characteristics the principle of induction does not stand alone. There are a number of other principles which cannot be proved or disproved by experience, but are used in arguments which start from what is experienced. ”

“ Further, the descriptions which are improperly confounded with induction, are nevertheless a necessary preparation for induction; no less necessary than correct observation of the facts themselves. Without the previous colligation of detached observations by means of one general conception, we could never have obtained any basis for an induction, except in the case of phenomena of very limited compass. ”

“ Scientist, inventor, mathematician, man of letters, alike are not quite true to fact when they claim that pure reason and an exclusive process of induction control their mental operations. I would raise the question whether there is any such thing as the exclusively inductive method. Is it not truer to speak of the deductive-inductive than of the inductive? The Mystic Sense, with its adventurous and sometimes blundering progress, holds so important a place that without it logic and induction would be as grist without a mill. ”

“ As a practice, induction is nothing but our old friend, the law of conditioned reflexes or of association. A child touches a knob that gives him an electric shock; after that, he avoids touching the knob. If he is old enough to speak he may state that the knob hurts when it is touched; he has made an induction based on a single instance. But the induction will exist as a bodily habit even if he is too young to speak, and it occurs equally among animals, provided they are not too low in the81 scale. The theories of induction in logic are what Freudians call a “rationalisation” ”

“ Induction raises perhaps the most difficult problem in the whole theory of knowledge. Every scientific law is established by its means, and yet it is difficult to see why we should believe it to be a valid logical process. Induction, in its bare essence, consists of the argument that, because A and B have been often found together and never found apart, therefore, when A is found again, B will probably also be found. This exists first as a “physiological inference”, and as such is practised by animals. ”

“ In every way, therefore, it is evident that to explain induction as the colligation of facts by means of appropriate conceptions, that is, conceptions which will really express them, is to confound mere description of the observed facts with inference from those facts, and ascribe to the latter what is a characteristic property of the former.
There is, however, between Colligation and Induction, a real correlation, which it is important to conceive correctly. Colligation is not always induction; but induction is always colligation. ”

“ Deduction is the derivation of the particular from the general, whereas induction is the process of deriving the general from the particular case. Now, quote any example of a brilliant achievement, which you feel illustrates the power of the inductive method. ”

“ But the Induction must first travel to all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself. ”

“ We have, therefore, the warrant of a rigid induction for considering it probable, in a degree undistinguishable from certainty, that the known conditions requisite for the sun's rising will exist to-morrow. ”

“ Most inductions require no conception but what was present in every one of the particular instances on which the induction is grounded. That all men are mortal is surely an inductive conclusion; yet no new conception is introduced by it. ”

“ He therefore linked induction and deduction closely together, and conceived them as necessarily complementary in scientific investigation. Either induction or deduction alone is absurd and impossible. By induction alone we should be obliged to examine all cases, an impossible undertaking. By deduction alone we should be in the same straits as the Scholastics, and never discover new laws. ”