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.