The progress of psychology as scientific theory has been handicapped by the circumstance that it has been inclined to deal with two kinds of problems: on the one hand, with emotions, instincts, complexes, ideas, etc.; on the other, with the working of the sense-organs and of the central and sympathetic nervous system. To approach the first task it has had to create a system of mentalistic or introspective concepts, like the ones mentioned; to deal with the second enterprise it has adopted the physical language used by the natural sciences.

In view of the importance of the philosophical method argued in Mr. C. I. Lewis's “Experience and Meaning,” I wish to call attention to ambiguities which may have an important bearing on one of his conclusions. The method for which he argues is a certain empirical test of meaningfulness. It is his ‘positivistic’ inference from this method which I wish to challenge. To do so I shall present four points: (1) A summary of his empirical test of meaningfulness; (2) A ‘non-positivistic’ (or ‘dualistic’) hypothesis which Mr. Lewis rejects; (3) An analysis of this hypothesis in view of his test; (4) The theory of universals implied in my analysis.

Deduction has frequently been condemned as a useless intellectual instrument because of its tautological character. To thoroughgoing opponents of rationalism, the pretensions of deduction are on the same level with those of induction. Both presume to yield more knowledge from the fact that we have some knowledge; and this is an impossible paradox, which not even so powerful an opponent of the “Philosophy of Experience” as Bradley could resolve to his own satisfaction. I wish in this brief note to indicate how this semblance of paradox may very easily be removed without having to deny, as has often been thought necessary, the tautologicality of deduction.

Though some doubts about the principle that every proposition is either true or false were entertained even by Aristotle, both the number and the vigor of criticisms of this principle have been increasing in recent years. This paper attempts a restatement and a re-examination of the issues involved in this dispute, and in particular an evaluation of the effects on the argument of such recent discoveries as that of the “many-valued logics.”

For the most part, this paper is an attempt to understand such a statement as this: “The proposition represents the fact by virtue of a structural identity between it and the fact.” The statement is a familiar and important one in modern philosophy. It is, for example, one of the tenets of Logical Positivism.

Despite the skepticism of many mathematicians and logicians as to the possibility of any test which will show conclusively the consistency or independence of the members of a postulate set, several methods have nevertheless been devised and employed, e.g., the empirical methods of Russell and Huntington, the internal method of Hilbert, and the reflective method of Royce. However, with the possible exception of Hilbert's method (which is still available only in the form of fragments and suggestions), these techniques require us to forsake the purely formal or abstract mode of analysis, and instead to rely in some sense on “concrete representations” or “interpretations” or “modes of action” which are said to “satisfy” the postulates in question. In short, they are all interpretational methods—and here is the crux of the problem. “Is it possible,” queries Weiss, “that the only way we can determine whether a set is consistent is by seeing all the postulates actually exemplified in some object? If so, we must arbitrarily assume that the object is self-consistent, so that the proof of consistency must ultimately rest on a dogma. As independence rests on consistency there are therefore no satisfactory proofs as yet of either independence or consistency.” The question “is thus answered,” according to Young, “only by reference to a concrete representation of the abstract ideas involved, and it is such concrete representations that we wished especially to avoid. At the present time, however, no absolute test for consistency is known.” Moreover, “suppose,” says the late Dr. Eaton, “that the system has no interpretation: how can the consistency (and) independence … of the postulates be shown? There should be some analytic way—purely in the realm of the abstract, without interpretation—of establishing these properties of a set of postulates. This is an important problem that awaits solution.”

It was Kronecker who sought to avoid the use in mathematics of all numbers (negatives, fractions, irrationals) other than the positive integers, and he outlined the means for carrying through this program. In the introductory sections of his memoir he briefly indicates the personal philosophy which made such a project appear desirable.

The historic task of Leibniz was to furnish a philosophy of personality, and at the same time, and in harmony with it, a general interpretation of the physical world. He conceives therefore of a plurality of Real Beings which in their most developed form he proposes to call individuals, defining individuality in terms of unique experience. Further, he finds the monads, or so-called metaphysical points, to be centres of life, held together by their own inner or intensive force and therefore impenetrable. Consequently, when we enquire whether the Real Beings are parts of the universe, we find that since the universe is the aggregate of monadic forces, all Real Being is finite, and so in order to deal with the problem of Theism we have to reconcile the concept of divine personality with what we may define as personality in the case of human beings.

A striking characteristic of contemporary science is its emphasis upon probability. This is especially notable in quantum mechanics.

There is a respect in which probability is the same for all scientific theories. Verifiability requires that any theory predict certain numbers which can be compared with the numbers gained by actual operations of measuring. In actual practice these numbers, which we shall term theoretical measurables and operative measurables respectively, never correspond. It becomes necessary, therefore, for the scientist to specify when the deviation between them is such that verification occurs. These specifications are defined by the theory of errors in which the concept of probability has an essential place and a specific meaning. But the theory of errors is the same for all applications; hence, probability as defined by the theory of errors is the same for all scientific theories.