What is inductive reasoning: John Stuart Mill


INDUCTION is the 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. The mere summing up of details in a single proposition is not induction, but colligation; induction always involves inference from the known to the unknown, from facts observed to facts unobserved.

The fundamental principle of induction is the proposition that the course of nature is uniform. The test of any induction is its consistency with inductions which have been found invariable in experience. If an induction conflicts with stronger inductions it must give way. It is the part of the logic of induction to find certain and universal inductions, and to use them as criteria.

At the root of the whole theory of induction is the notion of physical cause. To certain phenomena, certain phenomena always do, and, as we believe, always will, succeed. The invariable antecedent is termed the 'cause,' the invariable consequent, the 'effect.' Upon the universality of this truth depends the possibility of reducing the inductive process to rules.

Invariable sequence, however, seldom subsists between a consequent and one single antecedent; the consequent usually follows from the concurrence of several antecedents. In such a case it is usual to style the cause that antecedent which came last into existence, or whose share in the matter is the most conspicuous, or whose share in the matter is most easily prevented or encouraged. But the real cause is the whole of the antecedents, the whole of the contingencies of every description, which being realized, the consequent invariably follows. Yet even invariable sequence is not synonymous with causation. The sequence, besides being invariable, must be unconditional.

WE may define, therefore, the cause of a phenomenon to be the antecedent, or the concurrence of antecedents, upon which it is invariably and unconditionally consequent. To distinguish conditionally uniform sequences from those unconditionally uniform is part of the problem of induction. All phenomena have unconditional antecedents, and these antecedents have prior antecedents, and so on, till we come to one primeval cause or a conjunction of several--the so-called permanent causes.

In the analysis of sequences into conditional and unconditional, the first operation is to ascertain and distinguish antecedents and consequents. The next step is to trace the connexion between antecedents and consequents, and this we can do only by a consideration of some of the antecedents or consequents under other conditions; we must either find an instance in nature suited to our purposes, or by an artificial arrangement of circumstances make one. When we make an artificial arrangement, we are said to experiment; and experimentation has great advantages over observation in that it often enables us to obtain innumerable combinations of circumstances which are not to be found in nature.

There are four experimental principles, or canons, on which causation may be established or partly proven:

FIRST CANON. If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon. This is sometimes known as the method of agreement.

SECOND CANON. If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, and that one occurring only in the former, the circumstance in which alone the two instances differ is the effect or the cause, or a necessary part of the cause, of the phenomenon. This is sometimes known as the method of difference

THIRD CANON. If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ is the effect or cause, or a necessary part of the cause, of the phenomenon.

FOURTH CANON. Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.

To these four canons may be added a fifth, the method of concomitant variations. Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. The difficulty of discovering causation is greatly increased by the fact that in many cases there are plurality of causes and intermixture of effects.

Certain effects may be produced by diverse causes; thus heat may be produced by the sun and by friction. How can such causes be found? Here, the first canon fails, for causes, A B C and A D E, both producing effect a, might have A, and only A, in common, and yet not A, but B and D might be the cause of a. Only by an exhaustive analysis of antecedents and a multiplication of instances can plural causes be disproved by the method of agreement. It is necessary in most cases, and best in all cases, to use the method of difference, which is at once decisive, for if two instances, B C and A B C, are found, and the latter gives rise to a, and the former does not, it is at once evident that A is the cause of a.

Many effects are compounded, are the product of several causes. Such a compound may be quite a new product incomparable with its causes, or it may be simply composed of the effect of its several causes.

A compound of the first kind is seen in the chemical products of chemical substances. Thus hydrogen and oxygen may produce a new product, a new bundle of effects known as water. How are the causes in such cases to be unravelled? In most cases such compound effects can be unravelled by experiment, for such compounds can usually be made to reproduce their causes. Thus, water under certain circumstances may be made to reproduce its causes, oxygen and hydrogen. Complex mental effects, however, do not lend themselves to this simple mode of analysis, and we can only discover their causes by the slow process of studying the simple feelings themselves, and ascertaining synthetically, by an examination of their possible combinations, what they are capable of eventually producing.

A COMPOUND of the second kind, produced by the interplay of the regular effects of multiple causes, is always difficult to analyse, since the effects become mixed and mingled, and oppose or augment each other. Here we must fall back on the deductive method, which is the chief method by which we acquire knowledge of the conditions and laws of occurrence of the most complex phenomena.

It consists of three operations: firstly, direct induction; secondly, ratiocination; and, thirdly verification. In the first place, the consequents or laws of individual causes must be ascertained; in the second place the effect of various combinations of such causes must be estimated, and causes selected adequate to produce in combination the compound effect in question; and, in the third place, the causes so selected must be shown to produce the effect, unless frustrated by other known causes.

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