Inductiveload

“ In its due place, it is a highly important part of every science; but it has no value when the fundamental principles, on which the whole of the demonstration rests, have not first been obtained by the induction of facts, so as to supply the materials of substantial truth. Without such materials, a series of demonstrations resembles physical science only as a shadow resembles a real object. To give a real significance to our propositions, Induction must provide what Deduction cannot supply. ”

“ The necessity of such a survey is confirmed by the consideration, that the stronger inductions are the touch-stone to which we always endeavor to bring the weaker. If we find any means of deducing one of the less strong inductions from stronger ones, it acquires, at once, all the strength of those from which it is deduced; and even adds to that strength; since the independent experience on which the weaker induction previously rested, becomes additional evidence of the truth of the better established law in which it is now found to be included. ”

“ The author has very carefully and accurately distinguished Induction from other processes not properly reasoning at all, as well as from deductive inferences. "The probability of an inductive inference is the result of an inference from established facts, and so is due to going beyond the premises under the stimulus of certain general principles which may be called the Principles of Induction" (p. 315) . In treating of the Inductive Method in the last chapter Dr. Hyslop says that the whole process may be included in two general classes, Acquisition and Verification. ”

“ We call an induction perfect when all the objects or events which can possibly come under the class treated have been examined. But in the majority of cases it is impossible to collect together, or in any way to investigate, the properties of all portions of a substance or of all the individuals of a race. The number of objects would often be practically infinite, and the greater part of them might be beyond our reach, in the interior of the earth, or in the most distant parts of the Universe. In all such cases induction is imperfect, and is affected by more or less uncertainty. ”

“ 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. ”

“ Now, Induction is mainly a process for finding the causes of effects: and in attempting to fathom the mode of tracing causes and effects in physical science, I soon saw that in the more perfect of the sciences, we ascend, by generalization from particulars, to the tendencies of causes considered singly, and then reason downward from those separate tendencies, to the effect of the same causes when combined. I then asked myself, what is the ultimate analysis of this deductive process; the common theory of the syllogism evidently throwing no light upon it. ”

“ 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. ”

“ Thus, that all life depends on the presence of oxygen is (1) an universal proposition; (2) a real one, since the 'presence of oxygen' is not connoted by 'life'; (3) it is based on observation; (4) it relies on the uniformity of Nature, since all cases of life have not been examined.
Such a proposition is here called 'an induction,' when it is inductively proved; that is, proved by facts, not merely deduced from more general premises (except the premise of Nature's uniformity) : and by the 'process of induction' is meant the method of inductive proof. ”

“ The inductive method, alone, I believe, as in the physical sciences, can enable us to arrive at sound conclusions—justify the formulation of theories to explain psychological phenomena. Because of the very difficulties of this field of research—one of which is that of submitting to experimental conditions complex psychological phenomena having so many factors—it is all the more incumbent that the inductive method should be employed. To my way viof thinking we should begin at the bottom and build up bit by bit, drawing, as we go, no wider conclusions than the facts developed warrant ”

“ If there is one thing above another which modern logic is emphasizing it is the unity of the mind and the contiguity of thinking. Induction and deduction are dove-tailed processes which characterize all thinking worthy of the name. Where induction ceases, deduction commences, and vice versa. It becomes the function of inductive thinking to establish a connection between what has been experienced and what has not been experienced. Therefore, the conclusion of an induction must always contain more than is implied in the premises. ”

“ It is not possible, without entering into this philosophy, to explain adequately how science which is Inductive differs from that which is not so; or why some portions of knowledge may properly be selected from the general mass and termed Science. It will be sufficient at present to say, that the sciences of which we have 43 here to treat, are those which are commonly known as the Physical Sciences; and that by Induction is to be understood that process of collecting general truths from the examination of particular facts, by which such sciences have been formed. ”

“ Under such disadvantages do we, in cases of this description, attempt the initial, or inductive step, in the application of the Deductive Method to complex phenomena. But such, fortunately, is not the common case. In general, the laws of the causes on which the effect depends may be obtained by an induction from comparatively simple instances, or, at the worst, by deduction from the laws of simpler causes, so obtained. ”

“ Whewell thinks it improper to apply the term Induction to any operation not terminating in the establishment of a general truth. Induction, he says (in p. 15 of his pamphlet) “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.” ”

“ 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. ”

“ 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. Whoever knows that any man has died, has all the conceptions involved in the inductive generalization. But Dr. Whewell considers the process of invention which consists in framing a new conception consistent with the facts, to be not merely a necessary part of all induction, but the whole of it. ”

“ 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 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. ”

“ There are two general ways of obtaining our basis for the process of Inductive Reasoning. One of these is called Perfect Induction and the other Imperfect Induction. Perfect Induction is possible only when we have had the opportunity of examining every particular object or thing of which the general idea is expressed. For instance, if we could examine every fish in the universe we would have the basis of Perfect Induction for asserting the general truth that "all fishes are cold-blooded." ”

“ By common experience, and more precisely by experiment, it is found possible to select from among the antecedents of an event a certain number upon which, so far as can be perceived, it is dependent, and to neglect the rest: to purge the cause of all irrelevant antecedents is the great art of inductive method. Remote or minute conditions may indeed modify the event in ways so refined as to escape our notice. Subject to the limitations of our human faculties, however, we are able in many cases to secure an unconditional antecedent upon which a certain event invariably follows. ”

“ 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. ”

“ 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. ”

“ Accordingly, in the cases, unfortunately very numerous and important, in which the causes do not suffer themselves to be separated and observed apart, there is much difficulty in laying down with due certainty the inductive foundation necessary to support the deductive method. This difficulty is most of all conspicuous in the case of physiological phenomena; it being seldom possible to separate the different agencies which collectively compose an organized body, without destroying the very phenomena which it is our object to investigate ”

“ 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. ”

“ We might call the method the Newtonian method, for all four stages are marked in the prolonged process by which he made good his theory of Gravitation.
To give the name of Inductive Method simply to all the four stages of an orderly procedure from doubt to a sufficient explanation is to encourage a widespread misapprehension. There could be no greater error than to suppose that only the senses are used in scientific investigation. There is no error that men of science are so apt to resent in the mouths of the non-scientific. ”

“ 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. ”

“ The complete process of thought involves both induction and deduction. Every general principle, unless it is self-evident, must either be arrived at through the process of induction, or be accepted without any attempt at verification. Having formed our generalizations, we use them as a basis for further thinking. If we find that the principle always holds, we are satisfied with its validity. In this testing of the generalization tentatively made, the process of thought is deductive. The fact is that in the process which we designate as induction, deduction enters to verify our inference. ”

“ The notion of Cause being the root of the whole theory of Induction, it is indispensable that this idea should, at the very outset of our inquiry, be, with the utmost practicable degree of precision, fixed and determined. If, indeed, it were necessary for the purpose of inductive logic that the strife should be quelled, which has so long raged among the different schools of metaphysicians, respecting the origin and analysis of our idea of causation; the promulgation, or at least the general reception, of a true theory of induction, might be considered desperate for a long time to come. ”