My contention in what is to follow is that in a very important sense we have no atomic secret whatsoever. It is not ours to hide or to share. More than ever it is ours to seek. So far it remains quite undiscovered.

Like good philosophers we must pay attention to the terms used in our assertions. We must point out where we meet the requirements of usage and where we decide to use terms in a definite way, although usage is vague. Thus, the term “atomic” is a misnomer, but it is a misnomer here to stay. It means “nuclear.” Like all good people we must continue saying “atomic” in this connection when we mean “nuclear,” but we must not forget this fact and substitute what we know about the atom for what we do not know about the nucleus. We must also realize that the term “secret” has at least a double use: one, which means that the knowledge is possessed by an exclusive few; another, which means that the knowledge is possessed by no one, as in the expression “a secret of Nature.”

Among the subject matters which logicians like at times to investigate are the forms of postulation that other branches of inquiry employ. Rarely, however, do they examine the postulates under which they themselves proceed. It long contented them to offer something they called a “definition” for logic, and let it go at that. They might announce that logic dealt with the “laws of thought,” or with “judgment,” or that it was “the general science of order“; More recently they are apt to connect it in one or another obscure way with linguistic ordering.

The history of Western culture exhibits a profound cleavage of opinion on the nature of what its members take to be reality. On the one hand, there are those for whom certain aspects, at least, of the “real” exist in the human mind only. Others assign as the sole basis of reality the world of non-mental objects. This difference of temperament is so pervasive that it forms a perennial theme, not only for philosophers, but also for scientists, poets, and other students of the vast panorama of the world and its people.

This paper represents an attempt to indicate the idea of a logic slightly more general than sentential calculus, which is applicable to many philosophical issues. In particular, I shall use this generalized calculus to discuss a variation of the logic of imperatives. In part I, certain general considerations about indicative calculi provide the basis, as well as indicate the need, for the more formal construction of part II. Part III illustrates the analytical power of the tool constructed, and tries to show its relevance for philosophy.

Extensive and profound as philosophic speculation on the nature of knowledge may have been during the last twenty-five centuries, it must be conceded that it has, on the whole, failed in its undertaking. In fact, we do not seem to be much closer to the solution of the epistemological problem than were Kant and Hegel or, for that matter, Plato and Aristotle. Obviously enough, the problem should now be approached in some new way, perhaps one growing out of recent scientific findings.

The epoch-making revolution that has been taking place in mathematics and physics during the past hundred years is gradually changing our whole conception of reality and of the function of science in regard to it. We have discovered that the “common sense” view of the world which has become ingrained in the feeling-thought habits of Western man, especially since the seventeenth century, contains elements of serious limitation and even an illusion both from the standpoint of immediately intuited experience and from that of demonstrated scientific fact. Moreover, by a long drawn out tortuous process, lasting over many centuries and involving the constant creation and correction of an enormously complicated scientific structure, we have finally arrived at an understanding of what may be the root of our difficulty. It seems that certain peculiarities of the over-all grammatical structure of those languages that have conditioned the feeling-thought world of the West have tended to lead us astray. Their correction, however, has so far been possible only through the invention of new esoteric languages, such as the symbolism of mathematics and the new logic. By means of these “languages of science” modern mathematicians and physicists have at last succeeded in freeing themselves from the shackles of their everyday speech and “common sense” concepts, at least so far as their scientific work is concerned.