Philosophy of science is the organized expression of a growing intent among philosophers and scientists to clarify, perhaps unify, the programs, methods and results of the disciplines of philosophy and of science. The examination of fundamental concepts and presuppositions in the light of the positive results of science, systematic doubt of the positive results, and a thorough-going analysis and critique of logic and of language, are typical projects for this joint effort. It is not necessary to be committed to a belief that science and philosophy are or should be one, or else that “never the twain shall meet.” If anything, there is to be expected a wholesome regard for the value of established science in furnishing a foil for philosophy and a check on its old extravagances. This does not mean that even the best-established science may not be subject to most devastating criticism by analysis of its foundations. In fact, despairing of the philosophy of the schools, science has done it largely for itself. The theories of gravitation, atomicity, electro-magnetism, evolution, relativity and quanta have all arisen through drastic revisions of complacent fundamental “truths.”

Philosophers have ever declared that their problems lie at a different level from the problems of the empirical sciences. Perhaps one may agree with this assertion; the question is, however, where should one seek this level. The metaphysicians wish to seek their object behind the objects of empirical science; they wish to enquire after the essence, the ultimate cause of things. But the logical analysis of the pretended propositions of metaphysics has shown that they are not propositions at all, but empty word arrays, which on account of notional and emotional connections arouse the false appearance of being propositions. This conception that the “propositions” of metaphysics, including those of ethics, have no theoretical content, is to be sure still disputed. We shall not, however, enter here on its demonstration, but, under its guidance, will limit ourselves to non-metaphysical and non-ethical (non-evaluating) philosophical problems.

The purpose of this paper is to make clear (1) that the widely recognized formulations of the principle of induction do not express the most fundamental rule of induction; (2) that the current view concerning the probability of induction must be revised in terms of a frequency theory of probability; (3) that on this basis the problem of induction in its traditional form is a pseudo-problem; and (4) that the principle of induction must be interpreted as a pragmatic or operational maxim.

When I undertook to write an article for mathematical laymen on the mathematical infinite. I did not realize the depths of my own layness, I do now. Having refreshed my memory of the classics of infinity by re-reading among other things the famous papers of Cantor and Zermelo, and having struggled like a boa constrictor to swallow the latest papal bull on the human significance of the infinite, I am completely reduced to what Professor E. W. Hobson aptly and somewhat indignantly calls Mathematical Nihilism.

The foundation of the mathematical theory of probabilities is still a controversial subject. There are schools of insufficient reasoning and of cogent reasoning, of a priori determination and of frequency determination, of subjective and of objective probability. Two main difficulties exist. The first is the definition of equally like events. The second difficulty is the relation between the laws of causal natural science (mechanics, electrodynamics, etc.) and the laws of statistical regularity. Is it really necessary to add to the laws of mechanics one or more independent “laws of large numbers” to explain the regularities in dice throwing? In all these cases different answers exist, and the existence of a mathematical theory of probabilities remains a kind of miracle, as esoteric to the further domain of natural science as the resurrection of the dead.

Reference to quantum theory has become quite the fashion, and to base an expectation on an already receding episode with relativity theory, a great philosophical assault of interpretation of quanta is brewing in many quarters. The author of this series of studies would be content if by a plain statement of “what is the case” at this stage he could stem the more quixotic efforts, or rather reveal their unreal character to the spectators who may be enmeshed in the spell cast over such adventures. It is constantly necessary to restate the physicists' claims plainly in their positive content—as Einstein himself did once for relativity theory—so that one may know what is no-man's land and what is everyman's land in the new territory. This in itself is largely but a hope since there is no unanimity as to all the facts, and, worse, unanimity is no guarantee of stability. Nevertheless, the painstaking revision that is constantly going on on the experimental front enables us to arrange at least the data on a well-ordered scale of reliability. It then becomes much easier to detect false props to otherwise attractive theories, to discriminate live matter from the débris of progress, and to speculate on future growth. For such reasons the present examination of the various quantum theories will proceed from a presentation of facts and theories to their appraisal and then to a proposal concerning the organization of the facts, concepts and theories. The subject is very complex: There are several quantum theories, some of which are already referred to as “classical” although these themselves were anti-classical (anti-Newtonian); all have claimed success in their time; all have serious hiatuses, including the present. The author has chosen to hark back to some of the older issues before appraising the latest claims.

Biologists have as yet taken but little cognizance of the revolution in human thought which has been inaugurated by physicists in the last five years, and philosophers have stressed its negative rather than its positive side.

The historical origin and the experimental basis of the concept of physical determinism indicate that this basis was removed with the acceptance of the kinetic theory of matter, while its difficulties are increased by the admission that human nature, in its entirety, is a product of natural causation. An indeterministic view of causation has the advantages (a) of unifying the concept of natural law in different spheres of human experience and (b) of a greater generality, which precludes the acceptance of the special case of completely deterministic causation, so long as this is an unproved assumption. It is not inconsistent with the orderliness of the world, or with the fruitful pursuit of natural knowledge. It enriches rather than weakens the concept of of causation. It possesses definite advantages with respect to the one-sidedness of human memory, and to the phenomena of aiming and striving observable in man and other animals. Among biological theories it appears to be most completely in harmony with the theory of natural selection, which in its statistical nature resembles the second law of thermo-dynamics.

In an indeterministic world natural causation has a creative element, and science is interested in locating the original causes of effects of special interest, and not merely in pushing a chain of causation backwards ad infinitum. These contrasting tendencies are illustrated by a critique of the mutation theory, and by an attempt more closely to define the sense in which indeterministic causation should be thought of as creative.

“A New Budget of Paradoxes” will be a section of our Journal devoted to the pathological. It is not mere amusement. The old “Budget of Paradoxes,” edited by Augustus De Morgan is our model both for choice of material and for humaneness toward the Don Quixotes of Thought.