I. What is Induction?—1. Confining myself, then, to the material sciences, I shall proceed to offer my remarks on Induction with especial reference to Mr. Mill's work. And in order that we may, as I have said, proceed as intelligibly as possible, let us begin by considering what we mean by Induction, as a mode of obtaining truth; and let us note whether there is any difference between Mr. Mill and me on this subject.
"For the purposes of the present inquiry," Mr. Mill says (i. 347[266]), "Induction may be defined the operation of discovering and forming general propositions:" meaning, as appears by the context, the discovery of them from particular facts. He elsewhere (i. 370) terms it "generalization from experience:" and again he speaks of it with greater precision as the inference of a more general proposition from less general ones.
2. Now to these definitions and descriptions I assent as far as they go; though, as I shall have to remark, they appear to me to leave unnoticed a feature which is very important, and which occurs in all cases of Induction, so far as we are concerned with it. Science, then, consists of general propositions, inferred from particular facts, or from less general propositions, by Induction; and it is our object to discern the nature and laws of Induction in this sense. That the propositions are general, or are more general than the facts from which they are inferred, is an indispensable part of the notion of Induction, and is essential to any discussion of the process, as the mode of arriving at Science, that is, at a body of general truths.
3. I am obliged therefore to dissent from Mr. Mill when he includes, in his notion of Induction, the process by which we arrive at individual facts from other facts of the same order of particularity.
Such inference is, at any rate, not Induction alone; if it be Induction at all, it is Induction applied to an example.
For instance, it is a general law, obtained by Induction from particular facts, that a body falling vertically downwards from rest, describes spaces proportional to the squares of the times. But that a particular body will fall through 16 feet in one second and 64 feet in two seconds, is not an induction simply, it is a result obtained by applying the inductive law to a particular case.
But further, such a process is often not induction at all. That a ball striking another ball directly will communicate to it as much momentum as the striking ball itself loses, is a law established by induction: but if, from habit or practical skill, I make one billiard-ball strike another, so as to produce the velocity which I wish, without knowing or thinking of the general law, the term Induction cannot then be rightly applied. If I know the law and act upon it, I have in my mind both the general induction and its particular application. But if I act by the ordinary billiard-player's skill, without thinking of momentum or law, there is no Induction in the case.
4. This distinction becomes of importance, in reference to Mr. Mill's doctrine, because he has extended his use of the term Induction, not only to the cases in which the general induction is consciously applied to a particular instance; but to the cases in which the particular instance is dealt with by means of experience, in that rude sense in which experience can be asserted of brutes; and in which, of course, we can in no way imagine that the law is possessed or understood, as a general proposition. He has thus, as I conceive, overlooked the broad and essential difference between speculative knowledge and practical action; and has introduced cases which are quite foreign to the idea of science, alongside with cases from which we may hope to obtain some views of the nature of science and the processes by which it must be formed.
5. Thus (ii. 232) he says, "This inference of one particular fact from another is a case of induction. It is of this sort of induction that brutes are capable." And to the same purpose he had previously said (i. 251), "He [the burnt child who shuns the fire] is not generalizing: he is inferring a particular from particulars. In the same way also, brutes reason ... not only the burnt child, but the burnt dog, dreads the fire."
6. This confusion, (for such it seems to me,) of knowledge with practical tendencies, is expressed more in detail in other places. Thus he says (i. 118), "I cannot dig the ground unless I have an idea of the ground and of a spade, and of all the other things I am operating upon."