It is commonly urged that the axiom of causation cannot be derived from experience, because experience only proves that many things have causes, whereas the axiom declares that all things have causes. The syllogism, "many things which come into existence have causes, A has come into existence: therefore A had a cause," is obviously fallacious, if A is not previously shown to be one of the "many things." And this objection is perfectly sound so far as it goes. The axiom of causation cannot possibly be deduced from any general proposition which simply embodies experience. But it does not follow that the belief, or expectation, expressed by the axiom, is not a product of experience, generated antecedently to, and altogether independently of, the logically unjustifiable language in which we express it.
In fact, the axiom of causation resembles all other beliefs of expectation in being the verbal symbol of a purely automatic act of the mind, which is altogether extra-logical, and would be illogical, if it were not constantly verified by experience. Experience, as we have seen, stores up memories; memories generate expectations or beliefs—why they do so may be explained hereafter by proper investigation of cerebral physiology. But, to seek for the reason of the facts in the verbal symbols by which they are expressed, and to be astonished that it is not to be found there, is surely singular; and what Hume did was to turn attention from the verbal proposition to the psychical fact of which it is the symbol.
"When any natural object or event is presented, it is impossible for us, by any sagacity or penetration, to discover, or even conjecture, without experience, what event will result from it, or to carry our foresight beyond that object, which is immediately present to the memory and senses. Even after one instance or experiment, where we have observed a particular event to follow upon another, we are not entitled to form a general rule, or foretell what will happen in like cases; it being justly esteemed an unpardonable temerity to judge of the whole course of nature from one single experiment, however accurate or certain. But when one particular species of events has always, in all instances, been conjoined with another, we make no longer any scruple of foretelling one upon the appearance of the other, and of employing that reasoning which can alone assure us of any matter of fact or existence. We then call the one object Cause, the other Effect. We suppose that there is some connexion between them: some power in the one, by which it infallibly produces the other, and operates with the greatest certainty and strongest necessity.... But there is nothing in a number of instances, different from every single instance, which is supposed to be exactly similar; except only, that after a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist.... The first time a man saw the communication of motion by impulse, as by the shock of two billiard balls, he could not pronounce that the one event was connected, but only that it was conjoined, with the other. After he has observed several instances of this nature, he then pronounces them to be connected. What alteration has happened to give rise to this new idea of connexion? Nothing but that he now feels those events to be connected in his imagination, and can readily foresee the existence of the one from the appearance of the other. When we say, therefore, that one object is connected with another we mean only that they have acquired a connexion in our thought, and give rise to this inference, by which they become proofs of each other's existence; a conclusion which is somewhat extraordinary, but which seems founded on sufficient evidence."—(IV. pp. 87-89.)
In the fifteenth section of the third part of the Treatise, under the head of the Rules by which to Judge of Causes and Effects, Hume gives a sketch of the method of allocating effects to their causes, upon which, so far as I am aware, no improvement was made down to the time of the publication of Mill's Logic. Of Mill's four methods, that of agreement is indicated in the following passage:—
" ... where several different objects produce the same effect, it must be by means of some quality which we discover to be common amongst them. For as like effects imply like causes, we must always ascribe the causation to the circumstance wherein we discover the resemblance."—(I. p. 229.)
Next, the foundation of the method of difference is stated:—
"The difference in the effects of two resembling objects must proceed from that particular in which they differ. For, as like causes always produce like effects, when in any instance we find our expectation to be disappointed, we must conclude that this irregularity proceeds from some difference in the causes."—(I. p. 230.)
In the succeeding paragraph the method of concomitant variations is foreshadowed.
"When any object increases or diminishes with the increase or diminution of the cause, 'tis to be regarded as a compounded effect, derived from the union of the several different effects which arise from the several different parts of the cause. The absence or presence of one part of the cause is here supposed to be always attended with the absence or presence of a proportionable part of the effect. This constant conjunction sufficiently proves that the one part is the cause of the other. We must, however, beware not to draw such a conclusion from a few experiments."—(I. p. 230.)
Lastly, the following rule, though awkwardly stated, contains a suggestion of the method of residues:—