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?