Abstract

There is a considerable divergence of opinion about the meaning of mathematics, and it is only with hesitation that I, as a theoretical physicist concerned mainly with geophysics, venture to discuss a matter that professional logicians differ about. Nevertheless I am concerned with the problems of the acquirement of knowledge by scientific methods, and the solutions of these problems involve pure mathematics, the validity of which one is usually willing to take for granted. But the logical schools are not so willing, and aim at demonstration. Logic must be true in all possible worlds, and all empirical propositions must be rigorously excluded. A scientist, on the other hand, is interested mainly in empirical propositions, and mathematics is primarily a tool for investigating their relations. The proof of mathematics would therefore have interest for science, provided that the proof is sufficiently general to cover scientific requirements. If it is not, and the subject matter of the proof is restricted so that it fails to cover the scientific use of mathematics, then in its scientific application it is merely an analogy, and we are no better off than we should be if we simply took the validity of mathematics as it stands as a postulate.