The disagreement with regard to the validity of the principle of causality, existing to-day among scientists, has its roots in the diversity of definitions of the principle itself rather than in a problematic scientific situation. As far as the formulation of quantum theory is complete its bearing upon philosophical questions can be fixed with precision provided the questions are phrased intelligibly. But a question is intelligible from a scientific point of view only if it satisfies two conditions: (1) the meaning of its terms must be fixed; (2) it must be in accord with the conventions of the science to which the question is put.

The controversy which has raged between those who accept Aristotelian Logic and those who reject it, seems to continue. It is, I believe, advisable to consider the arguments on both sides. Modern Logicians for the most part insist that Aristotelian Logic breaks down, i.e. it is not true for all meanings of the terms. On the other hand there are those who insist on the validity of Aristotelian Logic claiming that those values for which it fails are not permissible values. But there is one who stands almost entirely alone in his position—namely Professor H. B. Smith—who maintains that Aristotelian Logic breaks down because and only because its interpretation into Boolean terms has been accomplished by means of a definition that is not forced upon us and which, since it gives up desirable principles, is to be rejected.

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

The striking synthetic effort made by Bohr to unite radiation facts with atomic structure facts led to the formulation of his “quantum theory of atomic structure,” which with a large group of subsequent developments, is now usually referred to as the “classical quantum theory.” As a conceptual aid it takes over the idea of an “astronomical atom” consisting of a positive nucleus around which electrons revolve in definite orbits, more or less in the fashion of the solar system. More or less. The similarities and differences as a bit of description are interesting and impressive, but when the theory is reduced to its postulates—and it is this which interests us here—it sounds very much like a re-statement (for a purpose) of the Planckian decisions.

Mathematical methods in biology occupy a somewhat peculiar position, and the attitude of many biologists toward them is similar to that of many practical engineers toward what is called pure scientific research. The modern progressive engineer recognizes the value of pure science, which seeks for truth regardless of any possibility of practical applications; yet he still frequently shows a definite dislike towards such investigations. The whole history of civilization demonstrates that discoveries which, at the time they were made, did not show any signs of the possibility of being turned into practical use, now lie at the basis of many useful engineering devices. As Professor R. A. Millikan has said, we owe our present-day civilization to Galileo. Every educated person, be he pure scientist or engineer, recognizes this fact. And yet the frame of mind of the “practical” man is not too receptive to investigations which do not show at least some remote prospects of practical applications. Unless he can see at least hypothetically some practical results of such research, he will not give it his whole-hearted enthusiasm. The ultimate criterion in the evaluation of any research still remains its practical use. Those pure scientists who have had close contact with what is called “industrial research” know only too well the truth of the above statement.

Time, space and matter are the most pervasive and inescapable aspects of the physical universe. And yet, notwithstanding the fact that they represent the most fundamental and ubiquitous characteristics of reality, they have always presented elements of mystery to the human mind. Thus on the level of common thought we ponder how the withering hand of time reaches from out the past into the future to bring decay and destruction to all things; and on the more sophisticated level, after the fashion of Immanuel Kant, we are puzzled by certain antinomies of thought concerning the necessity for an origin, and an end, of the universe in time and space, in the face of the equally necessary reasons for regarding the universe as being unlimited in its space and time dimensions. In either case, however, we are paying tribute to the tantalizing nature of these problems concerning the cosmic framework of space-time-matter in which we live, and move, and have our being. Indeed, it is not too much to say that genuine philosophy took its origin in Zeno's paradoxes of motion, and will have its final consummation when it solves Kant's antinomies.

The extent to which the scientific method has yielded to analysis in recent years serves only to emphasize by contrast the presence within that method of an irrational element. For it is becoming increasingly evident that whatever one may say of the logical and psychological character of the pre-inductive operations, of the formal processes involved in deducing the consequences of a given theory, of the technique of experimental corroboration, and of certain other aspects of the scientific method, there is one phase of the movement which remains a surd. This is the act of the creative imagination through which hypotheses and theories are called into being. Its mysterious character is exhibited in the terminology which is employed in describing it, in the variety and inconstancy of the conditions which give rise to it, in the apparent impossibility of controlling it, and in the impossibility of recognizing completely the adequacy of its results when it does occur. It is variously described as an act of intuition, mystic revelation, divine insight, a flash of understanding; it arises out of the greatest variety of conditions: acute and prolonged attention to the data in the confinement of the laboratory, or the complete relaxation of a walk in the country, or the intense mental effort upon a problem in a wholly unrelated field; it forbids direction, in fact it seems to arise most readily when the element of effort and control is conspicuously absent; it cannot even be certainly identified, for many supposed acts of discovery prove later to have produced only groundless fancies and absurd creations of the unguided imagination.