The fifth volume of the Collected Papers of C. S. Peirce, entitled Pragmatism and Pragmaticism, contains papers dealing with two distinguishable, but interconnected doctrines: Pragmatism and Critical Common-sensism. The latter, antedating in its earliest expositions the first formulation of the pragmatic doctrine in 1877, 8, is however later conceived by Peirce as a consequence of pragmatism. The two doctrines will be advisedly treated here in isolation, and first pragmatism.

One of the most thankless tasks in the field of the philosophy of science is the arranging of the sciences. If philosophy is to fulfill the partial rôle of being the “science of the sciences” it is sure to return to this undertaking time and time again. Sometimes it will refer to the enterprise as “the classification of the sciences,” sometimes as the formulation of “the system of the sciences,” and occasionally in the grand manner as a description of the “order of Nature.” I prefer to speak of “arranging” the sciences.

The subject to which I invite your attention this evening is a very recent development in mathematics which happens to be of great importance to philosophy.

The question may perhaps be raised why a terrifying topic like mathematics as introduced into an Institute of Philosophy. There are two answers to this question. In the first place my talk this evening will not be a “mathematical lecture” in any ordinary sense of the term, and no mathematical knowledge whatsoever will be presupposed. In the second place, even if it were to be a mathematical lecture, such an audience as is here assembled tonight would find nothing terrifying in the prospect.

The movement for the Unity of Science has been making headway for a number of years, and each year more workers in the various scientific domains have expressed their interest in it by participating in the discussion of its aims and its specific problems. A characteristic feature of this movement which explains this growing interest is that it does not propose a “super-science” which is to legislate to the special sciences. Its proposal of a Unity of Science is of a different kind, not based upon some grand metaphysical view of any sort. Those who are active within this movement are emphatic in their insistence that instead of aiming at a synthesis of the different sciences on the basis of a prior and independent philosophy, the special sciences will themselves supply their own synthesizing glue. For appreciating the significance of this movement it is therefore necessary to keep in mind that its tendency is toward a unified science, departmentalized into special sciences, and not toward an artificial and speculative juxtaposition of an autonomous philosophy and an autonomous group of sciences.

It is the purpose of this paper to present a theory of probability derived from two-valued logic—the logic of which an aspect is given in Part I, Section A, of Principia Mathematica. The symbolic system of Mr. Keynes, given in his Treatise on Probability, will be shown to be a part of our system. We have, however, little if anything in common with his philosophical analysis; a definition of Keynes’ fundamental probability relation, free from psychological or material reference, will be given, enabling us to offset some of the objections to his theory.