Chapter LXXXV: Section VII: Theory of Induction

Hence it follows that Induction is the only key to nature. This theory is Mill's masterpiece. Only so thorough-going a partisan of experience could have constructed the theory of Induction.

What, then, is Induction?

"Induction 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."[410]

This is the reasoning by which, having observed that Peter, John, and a greater or less number of men have died, we conclude that all men will die. In short, induction connects "mortality" with the quality of "man"; that is to say, connects two general facts ordinarily successive, and asserts that the first is the Cause of the second.

This amounts to saying that the course of nature is uniform. But induction does not set out from this axiom, it leads up to it; we do not find it at the beginning, but at the end of our researches.[411] Fundamentally, experience presupposes nothing beyond itself. No _à priori_ principle comes to authorize or guide her. We observe that this stone has fallen, that this hot coal has burnt us, that this man has died, and we have no other means of induction except the addition and comparison of these little isolated and transient facts. We learn by simple practical experience that the sun gives light, that bodies fall, that water quenches thirst, and we have no other means of extending or criticising these inductions than by other like inductions. Every observation and every induction draws its value from itself, and from similar ones. It is always experience which judges of experience, and induction of induction. The body of our truths has not, then, a soul distinct from it, and vivifying it; it subsists by the harmony of all its parts taken as a whole, and by the vitality of each part taken separately.

"Why is it that, with exactly the same amount of evidence, both negative and positive, we did not reject the assertion that there are black swans, while we should refuse credence to any testimony which asserted that there were men wearing their heads underneath their shoulders? The first assertion was more credible than the latter. But why more credible? So long as neither phenomenon had been actually witnessed, what reason was there for finding the one harder to be believed than the other? Apparently because there is less constancy in the colours of animals than in the general structure of their internal anatomy. But how do we know this? Doubtless from experience. It appears, then, that we need experience to inform us in what degree, and in what cases, or sorts of cases, experience is to be relied on. Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid. We have no ulterior test to which we subject experience in general; but we make experience its own test. Experience testifies, that among the uniformities which it exhibits, or seems to exhibit, some are more to be relied on than others; and uniformity, therefore, may be presumed, from any given number of instances, with a greater degree of assurance, in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform."[412]

Experience is the only test, and it is to be found everywhere.

Let us then consider how, without any help but that of experience, we can form general propositions, especially the most numerous and important of all, those which connect two successive events, by saying that the first is the cause of the second.

Cause is a great word; let us examine it. It carries in itself a whole philosophy. From the idea we have of Cause depend all our notions of nature. To give a new idea of Causation is to transform human thought; and we shall see how Mill, like Hume and Comte, but better than they, has put this idea into a new shape.

What is a cause? When Mill says that the contact of iron with moist air produces rust, or that heat dilates bodies, he does not speak of the mysterious bond by which metaphysicians connect cause and effect. He does not busy himself with the intimate force and generative virtue which certain philosophers insert between the thing producing and the product. Mill says:

"The only notion of a cause, which the theory of induction requires, is such a notion as can be gained from experience. The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it; independently of all consideration respecting the ulterior mode of production of phenomena, and of every other question regarding the nature of 'Things in themselves.'"[413]

No other foundation underlies these two expressions. We mean simply, that everywhere, always, the contact of iron with the moist air will be followed by the appearance of rust; the application of heat by the dilatation of bodies: "The real cause is the whole of these antecedents."[414] "There is no scientific foundation for distinguishing between the cause of a phenomenon and the conditions of its happening.... The distinction drawn between the patient and the agent is purely verbal. The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows."[415] Much argument has been expended on the word necessary: "If there be any meaning which confessedly belongs to the term necessity, it is _unconditionalness._ That which is necessary, that which must be, means that which will be, whatever supposition we may make in regard to all other things."[416] This is all we mean, when we assert that the notion of cause includes the notion of necessity. We mean that the antecedent is sufficient and complete, that there is no need to suppose any additional antecedent, that it contains all requisite conditions, and that no other condition need exist. To follow unconditionally, then, is the whole notion of cause and effect. We have none else. Philosophers are mistaken when they discover in our will a different type of causation, and declare it an example of efficient cause in act and in exercise. We sec nothing of the kind, but there, as elsewhere, we find only continuous successions. We do not see a fact engendering another fact, but a fact accompanying another. "Our will," says Mill, "produces our bodily actions as cold produces ice, or as a spark produces an explosion of gunpowder." There is here, as elsewhere, an antecedent, the resolution or state of mind, and a consequent, the effort or physical sensation. Experience connects them, and enables us to foresee that the effort will follow the resolution, as it enables us to foresee that the explosion of gunpowder will follow the contact of the spark. Let us then have done with all these psychological illusions, and seek only, under the names of cause and effect, for phenomena which form pairs without exception or condition.

Now, to establish these connections of phenomena, Mill discovers four methods, and only four--namely, the Methods of Agreement,[417] of Difference,[418] of Residues,[419] and of Concomitant Variations.[420] These are the only ways by which we can penetrate into nature. There are no other, and these are everywhere. And they all employ the same artifice, that is to say, elimination; for, in fact, induction is nothing else. You have two groups, one of antecedents, the other of consequents, each of them containing more or fewer elements, ten, for example. To what antecedent is each consequent joined? Is the first consequent joined to the first antecedent, or to the third, or sixth? The whole difficulty and the only possible solution lie there. To resolve the difficulty, and to effect the solution, we must eliminate, that is, exclude those antecedents which are not connected with the consequent we are considering.[421] But as we cannot exclude them effectually, and as in nature the pair of phenomena we are seeking is always surrounded with circumstances, we collect collect various cases, which by their diversity enable the mind to lop off these circumstances, and to discover the pair of phenomena distinctly. In short, we can only perform induction by discovering pairs of phenomena; we form these only by isolation; we isolate only by means of comparisons.