The principle of insufficient reason is one of those philosophic concepts that are highly symptomatic concerning the ultimate presuppositions of the person who accepts them as fundamental. This principle asserts that where we do not have sufficient reason to regard one possible case as more probable than another, we may treat them as equally probable. It has been violently rejected by various logicians, asserted to produce absurdities, and yet has remained persuasively attractive, being accepted, for example, by such an outstanding logician as Dotterer. It may hence be worth while to inquire what the acceptance of this principle implies and what is the source of its persuasiveness.

This essay is a refutation of Hume on causal inference. The decisive point of the refutation is that Hume's argument is invalid unless it is assumed, contrary to his own relational theory of time, that mere difference in dates can affect the course of nature. In the preliminary discussion of sections II and III the words “cause,” “effect,” and “causal relation” are employed in a nontechnical sense, which is exemplified in such statements as “Fire causes heat”, “Lightning and thunder are causally related”, “When one turns the steering wheel to the right, the effect is that the car moves to the right”, and so on. But in order to forestall rebuttals in defense of Hume one needs a greater precision in terminology as well as in conception of causality. Section IV aiming at precision gives a statement of the principles of causality which is in accordance with the position of modern science. An examination of this statement shows that the validity of causal inference must be accepted along with a relational theory of time. A comment on causal inference in relation to induction brings the discussion to a close.

In this paper certain basic assumptions about causation will be made explicit and then an attempt will be made to show, on the basis of those assumptions, that causation must be supplemented by an extra-causal operation of a selective nature. It is hoped that our assumptions will have in their own right a certain general acceptability, but since assumptions or “postulate sets”, whether antecedently acceptable or not are usually chosen for the purpose of proving something already deemed desirable, a word should be said as to why it was thought desirable to argue for selectivity.

“Reason,” said Lao Tze some twenty five hundred years ago, “is of all things the emptiest. Yet its use is inexhaustible.” With equal justice, he might have said the same of language. But Lao Tze, whose profound metaphysical probing appeared to carry him beyond the reach of linguistic aid, was led to insist that “Those who know do not speak; those who speak do not know.” Yet the “Old Philosopher,” as he is known to the Chinese, might be said to admit, by the very implications of his insistence, that language can exercise the greatest influence on thought, if only, in his viewpoint, to nullify it. Today we acknowledge this influence by reversing the great metaphysician's statement, those without speech (i.e. language) in some form or other cannot know.

Most of man's organs can be utilized in more than one way. His hands can be used to grip and to push, his throat can serve to swallow and to expel, he uses his tongue to taste and to talk, his nose to breathe and to smell.

If each mode of activity required the use of a different organ, a man would have to be much more cumbersome than he now is, or he would have to give up doing some of the things of which he is now capable. He would need at least a score of hands if he needed one with which to grasp, another with which to lift, a third with which to push, a fourth with which to twist etc. Because he has only two, capable of doing twenty different things, he is much more compact and flexible than he otherwise would be.

Science has become independent of its possible applications and misapplications to human welfare. In so far as the practical application of his theories has created, and is creating instruments of war more devastating than man has ever known, the scientist might perhaps feel responsible for the fate of our world. However, this pernicious application of science is purely incidental—just as incidental as the beneficial uses to which science can be put. Science and the pursuit of theoretical truth should be unaffected by world events even of the most catastrophic nature. Yet this conviction, however natural we may deem it, is not unchallenged. On the contrary, this war is being waged between two groups of powers, one of which frankly declares science to be solely in the service of the race and the state, while the other group still holds to a science for truth's sake.

Psychological investigations are supposed to deal with the behavior of animals, including of course, the human being. They are supposed to deal with the broad, general problem of how and why we behave the way we do.

Most psychologists however, are still dealing with their particular science from the strictly biological point of view, and overlooking by and large, the ever gradual development of psychology into a social rather than biological science. Nevertheless, important methodological contributions are being made. These contributions show a progressive awareness of the societal influences to which Psychology is particularly susceptible. The problems dealt with and the way in which they are handled, reflect conditions in the everyday world. Even the experimenter in an ivory laboratory but reflects the current and wholly erroneous viewpoint fostered by interested groups, that science must be impartial and oblivious to human suffering and human welfare.

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.

Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated.

Up to the present time the science of physics has given us no purely physical theory by which the characteristic formal properties of sensation can be derived. No explanation of the sense world purely in terms of the postulated physical world has been forthcoming, so that the psychologist has had either to ignore sensations or consider them as at least partially unaccountable additions to the entities of physics.

That there is, nevertheless, a purely physical explanation of the sense world we hope the following pages will make clear. We will present a theory in which the characteristic properties of sensation are derived from postulated physical entities.

In a paper read before the last Congress for the Unity of Science, Dr. Milton Singer distinguishes three main phases in the recent history of logic. The achievement he considers most characteristic of the first period is the development of the class calculus or so-called Boolean algebra. It begins with the work of Boole and DeMorgan and culminates in Schroeder's Algebra of Logic. In a minimum formulation, the results of this first stage can be summed up as, first, simplification and generalization of the traditional syllogistic machinery by means of a rather efficient new symbolism, and, second, adoption of the axiomatic method. To restate the last point: Boolean algebra was, since Leibniz, the first explicit attempt to construct what we call a formal system or calculus. Not realized at that time, however, or at least not adequately expressed, was the importance of the more recent distinction between scientific calculi on the one hand and purely linguistic or logical calculi on the other. As a consequence of this lack of explicit insight, the class calculus appeared to be on a par with scientific calculi, say, for instance, axiomatized geometry, Euclidean or otherwise. Its analytical character, even if it was seen, could not be formulated.