The men of the 'seventies were, after all, in many cases more anxious to damage theology than to build up Philosophy. They read Hume without any delicate sense for his urbane ironies, and believed in good faith that he and John Stuart Mill between them had shown that by a mysterious process called 'induction' it is possible to prove rigorously universal conclusions in science without universal premisses. A scientific law, according to them, is only a convenient short-hand notation in which to register the 'routine of our perceptions'. Thus we have known of a great many men who have died, and have never known of any man who lived to much over a hundred without dying. The universal proposition 'all men are mortal' is a short expression for this information, and it is nothing more. It ought to have been obvious that, if this is a true account of science, all scientific 'generalizations' are infinitely improbable. The number of men of whom we _know_ that they have died is insignificant by comparison with the multitude of those who have lived, are living, or will live, and we have no guarantee that this insignificant number is a fair average sample. So again, unless there are true universal propositions which are not 'short-hand' for any plurality of observed facts whatever, we cannot with any confidence, however faint, infer that a 'regular sequence' or 'routine' which has been observed from the dawn of recorded time up to, say, midnight, August 4, 1919, will continue to be observed on August 5, 1919. How, except by relying on the truth of some principle which does not depend itself on the validity of 'generalization', can we tell that it is even slightly probable that the nature of things will not change suddenly at the moment of midnight between August 4 and August 5, 1919? What is called 'inductive' science certainly has 'pulled off' remarkable successes in the past, but we can have no confidence that these successes will be repeated unless there are much better reasons for believing in its methods and initial assumptions than any which the scientific man who is an amateur 'empiricist' in his philosophy can offer us. We may note, in particular, that this empiricism, which has been expounded most carefully by Pearson and Mach, coincides with Hegelian Absolutism in leading to the denial of the truth of mathematics. It would be a superfluous task to argue at length that, e.g., De Moivre's theorem or Taylor's theorem is not a short-hand formula for recording the 'routine of our perceptions'.