The effort to meet the Society's request for a talk on this topic has been a humbling experience. The literature is vast; it contains the names of the ancient philosophers, of Newton, Leibniz, Bergson, Planck, Einstein, and of many contemporary men of learning. Yet some deep doubts and differences remain which, in the case of statistical physics, may be at least hinted at by quotations which are at variance with each other (Appendices A, B). A survey of this field is therefore out of the question (but see [5]). Here it will be easier for all concerned if, instead, I present a point of view.