In this stimulating study of the logical character of selected fundamental topics of physics, Zinov'ev has written the first, and major, stage of a general semantics of science. In that sense he has shown, by rigorous examples, that in certain basic and surprising respects we may envision a reducibility of science to logic; and further that we may detect and eliminate frequent confusion of abstract and empirical objects. In place of a near chaos of unplanned theoretical languages, we may look toward a unified and epistemologically clarified general scientific language. In the course of this work, Zinov'ev treats issues of continuing urgency: the non-trivial import of Zeno's paradoxes; the residually significant meaning of'cause' in scientific explanation; the need for lucidity in the conceptions of 'wave' and 'particle', and his own account of these; the logic of fields and of field propagation; Kant's antimonies today; and, in a startling apergu, an insightful note on 'measuring' consciousness. Logical physics, an odd-appearing field of investigation, is a part of logic; and as logic, logical physics deals with the linguistic expressions of time, space, particle, wave, field, causality, etc. How far this may be taken without explicit use of, or reference to, empirical statements is still to be clarified, but Zinov'ev takes a sympathetic reader well beyond a realist's expectation, beyond the classical conventionalist. Zinov'ev presents his investigations in four chapters and an appendix of technical elucidation. Chapter One, on the general theory of inference and terms, serves to express and clarify the author's conception of the principles and rules of logic which are requisite for proper analysis and deductive structuring of all expressions and all terms taken quite generally. With a rapid sweep from his early discussion of terms and statements, of the standard and non-standard notions of inference, and of elementary operators, Zinov'ev brings us to his analysis of definitions: implicit, incomplete, pseudo-, operational, and standard, and then to his discussion of multiple meanings. With Chapter Two, his special theory of inference and terms, Zinov'ev attacks the logic of terms (he sees all terms as designating objects), and we find that anything may be an object: empirical and abstract. Now we have a dense but lucid exposition of sets, and of Zinov'ev's 'clusters', and then of the modal operators. The cluster is especially interesting with the property such that we may speak about spatial relations - dimensions, motions, displacements etc., - with reference to clusters (but not ordinarily with reference to classes or sets); and thereby we may expect Zinov'ev to set forth a distinctive notion of'order' and 'succession' and such. Chapter Three deals with the central notions of arithmetic. With Chapter Four, the title essay on logical physics itself, Zinov'ev applies his logical apparatus to empirical individuals in their spatial and temporal relations. Among the interesting and perhaps striking sections are those on the 'minimal length', on irreversibility of time, on the fundamental 'beam', on the universe as a whole, on causal relations, on the logic of microphysics, on forecasts, and finally on the status of statements about the universe as a whole and in its fundamental nature. Such considerations of'hypothetical ontology' as Zinov'ev provides (pp. 239-248) will perhaps be of greatest interest to philosophers as we reflect on this treatise in its many arguments and elucidations. And he has made it clear that the analytic explication of the logical structure of general hypotheses about the Universe (however much such logical analysis may be demanded if we are to be reasonable) must "not be confused with their acceptance". And yet logic helps to sort out the cases: statements for which it is impossible to check the extent of their truth; statements for which logic is competent to accept or reject them; statements for which logic is competent to say they are uncertain. How surprising and important the results will be to scientists and philosophers may be estimated from at any rate one result: "assertions about minimal dimensions and durations and maximal velocities represent logical assertions, while those about the finiteness and the infinity of the Universe are extralogical ones, although it seems [intuitively] that the opposite should be true" (p. 241).
This work appeared in 1972 in the first edition (in Russian; Moscow: Nauka), and then somewhat revised and expanded in 1975, edited by H. Wessel (in German; Berlin: Akademie-Verlag). We are grateful to Dr. Wessel for his encouragement and advice in the preparation of this English-language edition. We are also very glad to recognize the careful and intelligent translation into English that has been provided by Dr. Olga Germogenova of Moscow, who consulted with the author throughout her work; we must also thank A. A. Zinov'ev for his patient cooperation through many years and in the course of his personal difficulties in Moscow and Munich, and not least for the extensive revisions and expansions which he prepared for this English translation which is the work's third edition. We also wish to note Zinov'ev's related paper on 'The Non-traditional Theory of Quantifiers', in Language, Logic, and Methods (Boston Studies in the Philosophy of Science, Vol.31, 1983, pp. 355-408). We thank Carolyn Fawcett for her editorial assistance throughout our final work on the manuscript, and Katie, Platt for her careful proof correcting.