It may be said, and I think with truth, that these observations scarcely apply to a material world conceived in a purely mechanical fashion. In such a world negligibility is theoretically measurable. The mass of Sirius, without doubt, modifies the weight of the pen with which I am writing. But the effect is demonstrably infinitesimal, and negligibility is not assumed, but proved. Laplace’s calculator, surveying the universe, would have no difficulty either in fixing his attention on particular repetitions which exemplify the “laws of nature,” or in regarding them as integral parts of a single mechanical whole, whose successive phases (if the law of energy dissipation be universal) can never be repeated.
But this does not lighten the difficulty. The world may, or may not, be a single mechanical system; but, if it is, the fact can only be empirically known to us through induction: and induction assumes negligibility, and cannot, so far as I can see, move a step without it. Choose the most perfect experiment on record, idealise its conditions to your heart’s content; for greater security, suppose it repeated even to weariness, how will you be advanced? There are, I suppose, millions of circumstances, for the most part utterly unknown, which have co-existed with all the experiments already tried, but will have vanished before the next experiment is undertaken. Does this disturb you? Do you ask yourself whether, among the unnumbered circumstances in which the world of to-day differs from the world of yesterday, there may not be one which is necessary to the expected effect? Not at all. You brush them aside. You say they may be neglected. And doubtless you do well. But why? Not on any grounds which observation or reasoning can supply, not on any grounds formulated in the logic of induction, or the calculus of chances. You trust yourself to a feeling of antecedent probability;—the intuitive probability on whose importance I dwelt in the last lecture, which is not the flower of experience but its root;—and your trust will sometimes be betrayed.
The principle of negligibility, or (in terms of belief) the belief that observed regularities may often be treated as if they were complete and self-contained cases of cause and effect, separable from contemporary events, is thus a necessary presupposition of concrete science; and, like other presuppositions, it is incapable of scientific proof. We often hear it said, indeed, that principles of this kind should be regarded as hypotheses verified by an ever-increasing volume of experimental proof. They are found to work; what more can be desired?
But it is not accurate to say that these and other fundamental principles are, or ever have been, regarded either by common sense or science as inferences from experience or as hypotheses requiring verification. Nor is it accurate to suggest that verification differs essentially from any other kind of experimental evidence except in the date of its occurrence. If evidence follows conjecture, but not otherwise, it is called verification; and though, from the point of view of method, this chronological order is of immense importance, from the point of view of logic it is nothing. A doubtful conjecture (let us suppose) is “verified” by experiment. If the experiment had come earlier there would have been no conjecture, but there would have been equal evidence, indeed the same evidence. It is true that without the conjecture there might have been no experiment, and that without the experiment there might have been no proof. But, though the conjecture occasioned the proof, it certainly adds nothing to its force, and we therefore come back to the question already discussed—namely, whether principles without which no inference from experiences is possible, can be themselves inferred from experiences?—a question to which, as I conceive, only one answer is possible. Experiences may produce habit, and habit may produce expectation, and this process may masquerade as induction. But expectations thus engendered belong to the causal series, not the cognitive. Physiology and psychology may explain them. But they can neither be proved nor treated as axiomatic.
Axiomatic they certainly are not; nor do they possess the universality and precision of outline which we are accustomed to associate with axioms. It is curious, in this connection, to note that the philosophers who are most firmly resolved to root the principle of regularity (they ignore negligibility) in experience always insist on giving it that absolute character which our inferences from experience rarely possess. The notion that fundamental beliefs should be liable to exception, should be capable of degrees, and should apply unequally in different fields of observation, is as abhorrent to them as to any metaphysician out of the opposite camp. One would suppose, to hear them talk, that, unless causation be universal, experience is worthless.
IV
The region where these uncompromising doctrines show to least advantage is human character. I do not propose to discuss causation and free will; but I may with advantage say something on a less hackneyed theme, namely, negligibility and foreknowledge. The thesis I desire to maintain is that, in dealing with a human character, full foreknowledge is theoretically impossible, even though free will be wholly absent, and the succession of psychic states be completely determined. Practically impossible we know it to be. But most determinists would hold that this impossibility is due partly to our ignorance and partly to our incapacity. We know too little either of the general laws of mind, or of individual character, or of surrounding circumstances, to make accurate forecasts; and, even if we possessed the requisite information, we could not use it, owing to the irremediable weakness of our powers of calculation. It is this contention that I wish to traverse. I hold that, had we the supernatural powers of Laplace’s calculator, armed with a knowledge of the human heart which supernatural powers of observation could alone supply, we should still fail, because we are face to face with that which is inherently incalculable.
The contrary opinion is due, I think, to an imperfect comprehension of the doctrines I have touched on in this lecture. All human foreknowledge depends on detecting old sequences in a new context. The context, of course, is always new. There is never full or complete repetition. But, unless there be partial repetitions embedded in the universal flux, prescience is impossible. This is the doctrine of “negligibility.”
Now consider two illustrative examples.
First, imagine yourself standing on the edge of a valley down which a landslip has just let loose the waters of some great reservoir in the hills. The catastrophe is sudden in its onset, brief in its duration, wildly irregular in its character. Even the most tumultuous cataract retains a certain steadiness of outline: and few sights are more impressive than the stationary waves in a great rapid. But there is here no trace of order imposed on disorder, fixity on motion. The rushing wall of water, spouting into foam over every obstacle it encounters, the tossing flood that follows furiously behind, seem in their brief violence to present the very ideal of incalculable confusion. But we know it is not so. In the presence of such a spectacle our calculator would not feel a moment’s embarrassment. He could forecast without difficulty the whole scene down to its minutest eddy; the motions of each drop obey laws with which he was perfectly familiar; and the total effect, catastrophic though it be, is but the sum of all these component examples of natural uniformity.