ternal sight exactly reproduces the external. Therefore, in axioms of figures, the mental sight cannot be opposed to the actual; imagination cannot contradict sensation. In other words, the contraries of such axioms will be inconceivable. Thus axioms, although their contraries are inconceivable, are experiments of a certain class, and it is because they are so that their contraries are inconceivable. At every point there results this conclusion, which is the abstract of the system: every instructive or fruitful proposition is derived from experience, and is simply a connecting together of facts.

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." 1

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. Fundamentally, experience presupposes noth

1 Mill's "Logic." i. 315.

"We must first observe, that there is a principle implied in the very statement of what Induction is; an assumption with regard to the course of nature and the order of the universe; namely, that there are such things in nature as parallel cases; that what happens once,

will, under a sufficient degree of similarity of circumstances, happen again, and not only again, but as often as the same circumstances recur. This, I say, is an assumption, involved in every case of induction. And, if we consult the actual course of nature, we find that the assumption is warranted. The uni

ing 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." 3

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 sucis, to find what description."-Mill's "Logic," i. 337:

verse, so far as known to us, is so constituted, that whatever is true in any one case, is true in all cases of a certain description; the only difficulty

Mill's "Logic," i. 351.

cessive 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.'" 4 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." 5 "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 "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." 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 Mill's "Logic," i. 359.

Ibid. i, 360.

• Ibid. i. 365.

supposition we may make in regard to all other things." 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 see 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.

66

Now, to establish these connections of phenomena, Mill discovers four methods, and only four-namely, the Methods of Agreement, of Difference, of Residues,10 and of Concomitant

Mill's "Logic," i. 372.

"If we take fifty crucibles of molten matter and let them cool, and fifty solutions and let them evaporate, all will crystallize. Sulphur, sugar, alum, salt -substances, temperatures, circumstances-all are as different as they can be. We find one, and only one, common fact-the change from the liquid to the solid state-and conclude, therefore, that this change is the invariable antecedent of crystallization. Here we have an example of the Method of Agreement. Its canon is:

I. 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.'"-Ibid. i.

spects the two cases are as similar as possible, since we have the same bird in both, and they take place in immediate succession. They differ only in the circumstance of immersion in carbonic acid gas being substituted for immersion in the atmosphere, and we conclude that this circumstance is invariably followed by suffocation. The Method of Difference is here employed. Its canon is:

"II. 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, 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."-Ibid. i. 423.

10 ["A combination of these methods is sometimes employed, and is termed the Indirect Method of Difference, or the Joint Method of Agreement and

11

Variations. 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.12 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 various cases, which by their

Difference. It is, in fact, a double employment of the Method of Agreement, first applying that method to instances in which the phenomenon in question occurs, and then to instances in which it does not occur. The following is its

canon:

III. 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 the cause, or a necessary, part of the cause, of the phenomenon.'"]— Mill's "Logic," i. 429.

con

"If we take two groups-one of antecedents and one of consequents-and can succeed in connecting by previous investigations all the antecedents but one to their respective consequents, and all the consequents but one to their respective antecedents, we clude that the remaining antecedent is connected to the remaining consequent. For example, scientific men had calculated what ought to be the velocity of sound according to the laws of the propagation of sonorous waves, but found that a sound actually travelled quicker than their calculations had indicated. This surplus, or residue of speed, was a consequent for which an antecedent had to be found. Laplace discovered the antecedent in the heat developed by the condensation of each sonorous wave, and this new element, when introduced into the calculation, rendered it perfectly accurate. This is an example of the Method of Residues, the canon of which is as follows:

"IV. Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain an

tecedents, and the residue of the phenomenon is the effect of the remaining antecedents.'"-Mill's "Logic," i. 431.

11" Let us take two facts-as the presence of the earth and the oscillation of the pendulum; or, again, the presence of the moon and the flow of the tide. To connect these phenomena directly, we should have to suppress the first of them, and see if this suppression would occasion the stoppage of the second. Now, in both instances, such suppression is impossible. So we employ an indirect means of connecting the phenomena. We observe that all the variations of the one correspond to certain variations of the other; that all the oscillations of the pendulum correspond to certain different positions of the earth; that all states of the tide correspond to positions of the moon. From this we conclude that the second fact is the antecedent of the first. These are examples of the Method of Concomitant Variations. Its canon is:

"V. 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.'"Mill's Logic," i. 435.

12 The Method of Agreement," says Mill ("Logic," i. 424), "stands on the ground that whatever can be eliminated, is not connected with the phenomenon by any law. The Method of Difference has for its foundation, that whatever cannot be eliminated, is connected with the phenomenon by a law." The Method of Residues is a case of the Method of Differences. The Method of Concomitant Variations is another case of the same method; with this distinction, that it is applied, not to the phenomena, but to their variations.