It is the purpose of this paper to review the present status of discussion concerning the concept of probability. The exposition will consist of six sections: (1) A brief statement of the most important traditional views of the concept of probability: subjective and objective; (a) A brief criticism of two traditionally important conceptions: a priori probability and the Principle of Indifference; (3) A criticism of an outstanding example of the subjective theory of probability, the theory of F. P. Ramsey; (4) A criticism of the most widely known of the objective logical theories of probability, the theory of J. M. Keynes; (5) Some remarks concerning the results of the recent work of Reichenbach and von Mises with particular reference to clarification of the concept of probability; (6) A summary of the case for the frequency interpretation of probability, revealing its basic importance in the light of present evidence.

In a review of my book “Wahrscheinlichkeitslehre”, Dr. Ernest Nagel has recently criticized some of my ideas on probability and induction. His review includes a good exposition of my ideas, and I have to thank him for his serious attempts to do justice to my results. He attacks, however, some very essential points of my theory. I may be allowed, therefore, to answer him as frankly and thoroughly as he attacks me.

The following comments represent what seem to me promising lines of approach to some of the broader issues in the philosophy of logic. They are offered, it is perhaps unnecessary to say, with the intent of stimulating rather than foreclosing discussion. And if the conclusions advanced are formulated loosely and with only a crude indication of the arguments which support them, I hope that thereby they will provoke all the more the free flow of discourse which it is the object of this Conference to promote.

Professor Schiller's question, “Must philosophers disagree?” can be answered in the negative if a technique can be worked out whereby it becomes possible to answer the question, “What are they talking about?” It is the aim of the ensuing remarks to provide at least the outline of such a technique and to illustrate its possible effectiveness in the specific context of controversies about the nature of time. That philosophers may continue to disagree in spite of the suggestions offered is, of course, to be expected in view of the long history of failures which compromise positions have encountered. The fate of the conciliator usually has been to receive the contempt of the embattled polemicists, and the fate of his peacemaking, to be construed as just another theory. Of course, this is in most cases the ulterior motive for his pretended altruism in assuming the rôle of arbitrator. Yet there are theories and theories. A position like that of Hume on the question of causality may reasonably be opposed to that of Leibniz but not in the same sense as to that of Kant. For the latter does attempt to provide a bridge between rationalism and empiricism and to do justice to the valid claims of each. The theory of time here proposed immodestly attempts a rapprochement among the multitudinous doctrines of time by setting forth one more doctrine.

Recent advances in quantum physics have led to a renewal of interest in the problem of human freedom and in the wider problem of indeterminism. It is important to recognize, however, that if every denial of determinism is to be called indeterminism, the latter term covers a wide range of logically distinguishable positions. We should perhaps speak in the plural number of indeterminisms rather than of indeterminism. For determinism may be defined, simply, as the doctrine that every event has a cause; or we may add that the effect is always uniquely determined; or that when the effect is complex it can always be exhaustively analyzed into components each of which is the effect of a component of the cause; or that every cause directly or indirectly includes the entire universe. And in the case of each of these, or of still other interpretations of determinism, the denial would be a form of indeterminism.

In the works which constitute his distinguished contribution to philosophy, Emile Meyerson has advanced and defended the opinion that scientific explanation consists in transforming empirically discovered natural laws into statements of identity in time. This contention, which it is the purpose of the present paper to examine, is of great interest both on its own account and by reason of its intimate connection with Meyerson's central thesis that all thought consists essentially in similar processes of identification. Indeed so intimate is this connection that our present inquiry although it deals explicitly only with the nature of scientific explanation nevertheless constitutes by implication an examination of the more general thesis also, for if scientific explanation is not a process of identification then obviously not all thought is identificatory.

Ludwig Wittgenstein and certain of his friends and followers have offered an interesting answer to the question of the relation “one fact (such as a sentence) [must] have to another in order to be capable of being a symbol for that other”. The answer in brief, as Russell puts it, is that, “in order that a certain sentence should assert a certain fact there must … be something in common between the structure of the sentence and the structure of the fact”. Wittgenstein himself in the Tractatus usually denominates this common element as logical structure. The sentence is said to picture its fact; it reflects, mirrors, shows or exhibits by means of its own structure the structure of the fact it is about. Critics and interpreters generally agree with Russell's broad characterization of the theory but disagree greatly as to the exact nature of this postulated common structure. Consequently, the evaluation of the theory which this paper proposes to make must include an examination of its several alternative interpretations.

It has been said that a language will delineate and limit the logical concepts of the individual who speaks it. Conversely, a language is an organ for the expression of thought, of concepts and principles of classification. True enough, the thought of the individual must run along its grooves; but these grooves, themselves, are a heritage from individuals who laid them down in an unconscious effort to express their attitude toward the world. Grammar contains in crystallized form the accumulated and accumulating experience, the Weltanschauung of a people.