Induction (reasoning)

“ 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. ”

“ 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. ”

“ But it may not suit our purpose thus to restrict the conclusion. We may wish to make use of it in its broad general significance. Every day we are compelled to act upon imperfect inductions, as in the case of the street car. In such cases we must resort to certain rules or tests whereby we can determine the probability of the truth of the imperfect induction. We shall consider these rules or tests after we have discussed the application of inductive reasoning to inductive argument. ”

“ 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." ”

“ Induction is a kind of reasoning that may lead us into error; but that it follows a method which, sufficiently persisted in, will be Inductively Certain (the sort of certainty we have that a perfect coin, pitched up often enough, will sometime turn up heads) to diminish the error below any predesignate degree, is assured by man's power of perceiving Inductive Certainty. ”

“ 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. ”

“ Perfect Induction necessitates a knowledge of all the particulars forming a class; that is, all the individual objects, persons, things or facts comprising a class must be known and enumerated in this form of Induction. ”

“ Whatever be the most proper mode of expressing it, the proposition that the course of nature is uniform, is the fundamental principle, or general axiom of Induction. It would yet be a great error to offer this large generalization as any explanation of the inductive process. On the contrary, I hold it to be itself an instance of induction, and induction by no means of the most obvious kind. Far from being the first induction we make, it is one of the last, or at all events one of those which are latest in attaining strict philosophical accuracy. ”

“ Rule IV In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.
This rule we must follow that the argument of induction may not be evaded by hypotheses. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ But it is necessary to remark, that although, by this progressive transformation, all sciences tend to become more and more Deductive, they are not, therefore, the less Inductive; every step in the Deduction is still an Induction. ”

“ 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. ”

“ Why is a single instance, in some cases, sufficient for a complete induction, while in others, myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of induction. ”

“ 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. ”

“ Whether we are inquiring into a scientific principle or into an individual fact, and whether we proceed by experiment or by ratiocination, every step in the train of inferences is essentially inductive, and the legitimacy of the induction depends in both cases on the same conditions. ”

“ For after all, if we will consider, induction being the right path to knowledge, every man, whether he knows it or not, uses induction, more or less, by the mere fact of his having a human reason, and knowing anything at all ”

“ 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. ”

“ 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. ”

“ 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.” ”

“ These two laws justify inductive assumptions, and, in a sense, condition all thinking.
(9) Uniformity of nature gives man confidence, while universal causation arouses his curiosity. With these two weapons he is willing to “march into the unknown.”
(10) As the process of universalizing individual experiences, induction assumes the three forms of simple enumeration, analogy and analysis. The form adopted is not always elective but is controlled largely by the exigency of the case. ”

“ And this inference of one particular fact from another is a case of induction. It is of this sort of induction that brutes are capable; it is in this shape that uncultivated minds make almost all their inductions, and that we all do so in the cases in which familiar experience forces our conclusions upon us without any active process of inquiry on our part, and in which the belief or expectation follows the suggestion of the evidence with the promptitude and certainty of an instinct. ”

“ As regards Induction, surely you must admit that the initial part of the task falls not upon the Reason but upon the Imagination; which sees likenesses and leaps to general conclusions, mostly premature or false, but all containing a truth from which the falsehood must be eliminated. Thus, a child imagines, by premature Induction, that all men are (1) like his father ”

“ 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. ”

“ 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. ”

“ Now, this has not been done, or even attempted, except perhaps by Plato, who certainly uses this form of induction in some measure, to sift definitions and ideas. But much of what has never yet entered the thoughts of man, must necessarily be employed in order to exhibit a good and legitimate mode of induction, or demonstration; so as even to render it essential for us to bestow more pains upon it than have hitherto been bestowed on syllogisms. The assistance of induction is to serve us not only in the discovery of axioms, but also in defining our notions. ”

“ Why is man eager to undertake the “inductive hazard?” Because, through the laws of universal causation and uniformity of nature, his curiosity is aroused, and he is given confidence in nature’s activities.
10. THREE FORMS OF INDUCTIVE RESEARCH.
Induction is a matter of universalizing less universal experiences. In this the process may assume any one of three forms, namely: (1) Induction by simple enumeration; (inductio per enumerationem) ; (2) Induction by analogy; (3) Induction by analysis. ”

“ If we limit ourselves to such characters as have for us any importance, interest, or obviousness, then a synthetic conclusion may be drawn, but only on condition that the specimens by which we judge have been taken at random from the class in regard to which we are to form a judgment, and not selected as belonging to any sub-class. The induction only has its full force when the character concerned has been designated before examining the sample. These are the essentials of induction, and they are not recognized in attributing the validity of induction to the uniformity of Nature. ”

“ It is of the utmost importance for understanding the logic of induction, that we should form a distinct conception of what is meant by chance, and how the phenomena which common language ascribes to that abstraction are really produced. ”

“ At any one of these steps of Induction in the Table, the inductive proposition is a Theory with regard to the Facts which it includes, while it is to be looked upon as a Fact with respect to the higher generalizations in which it is included. In any other sense, as was formerly shown, the opposition of Fact and Theory is untenable, and leads to endless perplexity and debate. ”