It is not the aim of the present essay to defend the principle of empiricism against apriorism or anti-empiricist metaphysics. Taking empirism for granted, we wish to discuss, the question what is meaningful. The word ‘meaning’ will here be taken in its empiricist sense; an expression of language has meaning in this sense if we know how to use it in speaking about empirical facts, either actual or possible ones. Now our problem is what expressions are meaningful in this sense. We may restrict this question to sentences because expressions other than sentences are meaningful if and only if they can occur in a meaningful sentence.

When science of the 20th century is spoken of in opposition to that of the 19th century, a particularly characteristic attribute is often cited: namely, that since the time of Galileo and Newton the task of science has been to explain everything mechanistically. By analogy the world was to be conceived as a great machine. But the theories of the 20th century, above all the relativity and quantum theories, caused a revolution in science. It is seen today that nature can be described and understood not ‘mechanistically’ but only through abstract mathematical formulas. The world is no longer a machine but a mathematical formula.

Columbus and Galileo are usually considered the prime revolutionaries whose discoveries in the physical world brought on the spiritual revolution in modern life, but during the first full century of the modern world another discoverer was so regarded by Sir Thomas Browne. In the “experiments, grounds, and causes,” of the compass needle, he said, Dr. William Gilbert “discovered more in it than Columbus or Americus ever did by it.” Like Columbus, Gilbert made his discovery unwittingly. The navigator had been in search of Asia when he found a new continent; the doctor in seeking a reason for magnetic action led men's attention to reasoning on a new theory of Matter. Through his magnetical researches, the old logical conception of a continuous, soul-animated matter held by the conservative doctors and alchemists was discredited. The discoveries of all three, Columbus, Galileo, and Gilbert, were in many ways interrelated, and of course no single mind released the curiosities of the modern world unaided. What the scientists had to find out in their own laboratories and their own reasoning was persuasive evidence that matter is divorced from spirit, and for a time in the seventeenth century some of the fundamental hypotheses which indicated the divorce derived from magnetism.

In these days of Gestalttheorie it seems not untimely to inquire whether psychology itself does not stand in need of being recognized as a configuration of complementary parts. The suggestion, it is true, tends at the first to be repudiated by the implacability of the schools with their claims and counterclaims resounding on every side. On further analysis, however, such controversy seems to acquire the very different significance of having permitted certain partial aspects of the whole field to become well-articulated, even if in somewhat exaggerated form. In other words, if there is any underlying unity in psychology, then the very overstatements of the school zealots while unwittingly defeating their own purpose may have been doing the science a real service by throwing its basic pattern into bold relief. In broadest terms this seems to describe what has been happening in psychology in the recent past and to define the present stage of its development.

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.

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.