# PREFACE

The present monograph contains a brief and, as far as possible, popular discussion of a logical conception developed by the author over a period of many years; its fundamentals are given in a number of works, mainly in four books: Philosophical Problems of Many-Valued Logic (Translation from the Russian; Humanities Press, New York; and Reidel, Dordrecht, Holland, 1963), Foundations of the Logical Theory of Scientific Knowledge (Complex Logic) Revised (Translation from the Russian [Boston Studies in the Philosophy of Science, Vol. 9], Reidel, Dordrecht, Holland, 1973), Komplexe Logik (Translation from the Russian; Berlin, Braunschweig, Basel, 1970), Logical Physics (Moscow, 1972). The author wishes to note that the formation of this conception is to a considerable degree based on the ideas of such outstanding logicians as J. Lukasiewicz, K. Ajdukiewicz, C. I. Lewis, H. Reichenbach, R. Carnap, G. von Wright. The author also considers it his pleasant duty to thank H. Wessel, A. A. Ivin, G. A. Smirnov, A. M. Fedina, E. A. Sidorenko, G. A. Schegol'kova, G. A. Kuznetsov and V. Shtel'tsner, who were the author's collaborators for some time and promoted the formulation and development of a number of ideas. The author is especially grateful to H. Wessel whose contribution was of substantial importance. The task of the logical orientation, presented here, is seen by us first of all as that of formulating a sufficiently accurate and rich language for the methodology of experimental sciences, in terms of which a rigorous deduction might be realized. It should be a special language. And as every special language, it must not be translated into ordinary language for the simple reason that it represents just an addition to ordinary language and a development of the latter in a certain direction. The special language would have been superfluous if it were possible to translate it into the ordinary one. And when, in further discussion, we shall formulate certain statements written in the language of logic, also in terms of ordinary language, our purpose will be exclusively that of explanation. The language which is at present used for discussing the problems of the methodology of experimental sciences represents a set of ill-defined, ambiguous, unstable and logically unrelated linguistic expressions. In addition, they do not provide an adequate and forthright description of the methodological situation in modern science. As far as we understand it, logic does not imply the improvement of this existing language. It implies only the elaboration of logic in this direction in general, an elaboration based on deeper foundations; the final result of such an elaboration is supposed to be a set of linguistic means that can be evaluated only in a retrospective way as an improvement of the language of scientific methodology. Our assertions, accepted in logic and obtained in it as corollaries, do not represent the results of generalization of experimental material, nor can they be interpreted as assumptions with respect to the objects of reality. They are nothing but parts of the definitions of linguistic expressions or are obtained from such definitions as logical consequences. Let us give an example. The question whether a physical body can simultaneously occupy different places is usually answered in the negative. And the question, why it is impossible, is usually answered: this is how the world is made. But the structure of the world has nothing to do with it. And how can one guarantee that our assertion will be valid at all past and future times and in all spatial locations? Our confidence in the fact that a physical body cannot simultaneously occupy different places is a logical consequence of the implicit definition of the expression 'different places'. Indeed, when are the locations (spatial domains) regarded as different? From the intuitive point of view two locations x and y are different if and only if they do not have common points. But real 'points' are physical bodies. So if one makes the definition of the expression 'different locations' explicit, the following is obtained. Two locations x and y are considered (called) different if and only if for any physical body a the following assertion is valid: if a occupies one of x and y, it does not occupy at the same time the other one of them. From this definition an assertion logically follows: a physical body cannot simultaneously occupy different places. We do not have to stress the importance of the analysis of the above linguistic expressions. Complaints about the ambiguity and uncertainty of terminology became commonplace. Monstrous forms and dimensions are acquired by speculations related to the obscurity of terminology. Even comparatively simple problems turn out to be practically unsolvable due to the ignorance or neglect of the logical methods of constructing terminology. Consider the following interesting example. It appears obvious that a process having no beginning does not start. And if a process does not start, it does not exist. But the Universe is a process having no beginning in time. And at the same time the Universe exists. How can these statements be reconciled? We leave it to the reader to resolve this paradox, and if she succeeds, let her take notice of the role belonging to terminological aspects in this situation. The work necessary for solving this problem would be just a special case of the work that is supposed to be raised to the professional level by logic. We do not consider it to be our task to review the state and history of this kind of logical research. It is our intention to offer to the attention of the reader a special point of view concerning a certain set of problems; our presentation will be based only on well-known and popular facts of the linguistic practice of humans. To understand this book, no special training in logic is required. What is required is just a sincere desire to investigate the essence of the matter, some patience and tolerance. Although the monograph represents further development of the ideas discussed in the author's works cited above, and an addition to them, it can be understood independently of them as a completely autonomous construction.