We find the same situation in all other cases, and we conclude that the statements which have been mistaken for material a priori propositions are purely tautological, they convey no knowledge and their a priori validity is due, as it always must be, to their form. There is no genuine knowledge a priori.
Hume has seen this very clearly, as everybody knows; and all attempts to avoid his result in a round about way are in vain. (There is no logic of induction, there are rules of induction of course, but they are practical prescriptions which guide our expectations and actions, they have absolutely no logical character.)
I see no reason why the philosopher should regret this. Induction is necessary and important in the domain of actions, which belongs to life, not to theory and science (although it belongs to the pursuit of science, which is part of life) and for life and action the important thing is belief an expectation, not reasoning and absolute truth. Modern science, at any rate, is perfectly reconciled with the idea that all its general statements, all ist formulations of natural laws, must be considered as hypothecal and may have to be revised one day. The progress of scientific knowledge is none the worse for this attitude, it helps the scientific not to be dogmatic and keep his mind open to new ideas, and the impossibility of a logical proof of the general validity of his laws need not, and does not, shake in the least his practical belief that his description and explanation of the world is continually growing more accurate and more complete, that his knowledge is forever becoming more and more unified by continually diminishing the number of symbols requiered for the description, thereby showing the world to be a real universe. (Those who really know the spirit of science have always protested against the popular accusation of science as being fickle and unstable, giving up her old theories and replacing them by new ones. The truth is that no theory which has at all been verified by experience was ever entirely overthrown; on the contrary, its essential framework by which the structure of nature is expressed has always been absorbed by the new theories, and the only changes consist in the addition of new details affording better approximation, and the abandonment of misleading intuitive illustrations which do not form part of the theory but just serve to facilitate the understanding and the use of the theory. It is natural that these in-
