Review-essay of N. A. Vasil'ev, Imaginary logic (Russian), edited by V. A. Smirnov

Abstract

This review analyzes the logical work of the Russian philosopher N. A. Vasil'ev on the occasion of the publication of an anthology (edited by Prof. V. A. Smirnov) of the logical writings of Vasil'ev and his commentators.

The reviewer underscores the eclectic and multitudinous aspects of the logical thought of the logician-philosopher from Kazan'. His thought is deemed to be the most significant trait d'union between aristotelian syllogistics and the development of the new non-classical logics.

In this essay, the reviewer therefore reconstructs, on the one hand, the relationship between Vasil'ev and the German psychologist tradition of the second half of the nineteenth century (especially Sigwart) and, on the other hand, the links with the research carried out by Lukasiewicz. She then examines the contents of the "imaginary logic" of Vasil'ev (1910-1913) and in particular the rejection of the principles of non-contradiction and of excluded middle, as well as the relationship of Vasil'ev's "imaginary logic" with the "imaginary geometry" of Lobachevskij.

The reviewer does not accept the role of precursor to certain nonclassical logics (in particular paraconsistent and many-valued logics) which some scholars (A. Arruda, G. Kline, Smirnov himself, and others) have chosen to attribute to Vasil'ev's work. On the contrary, she maintains that the importance of the logical work of Vasil'ev should be evaluated from the historical point of view, according to which Vasil'ev's work is understood to be within the "transitional" philosophical thought of the end of the nineteenth century and to mark the origin of the non-classical logics of this century.