The Fate of One Forgotten Idea: N.a.vasiliev and His Imaginary Logic

The fate of logical ideas is whimsical. Very often time only gives us the opportunity to appraise the strength of forecasting of the scholar, the scale of his ideas, their orientation to the future, and the role and place of the scholar in the intellectual history of mankind. ''Time has a difficult delivery, but never a miscarriage''-as one aphorism put it. Today, the significance of the logical works-only a few articles-of Kazan University philosophy professor, N.A.Vasiliev (1880-1940), is becoming ever more apparent. He was the first to introduce the considerations of inconsistency into formal logic, manifesting at that time an understanding of dialectical spirit (in Kant's or Hegel's sense). In his early years, Vasiliev was attracted to poetry. As if predicting the fate of his own ideas, he wrote: ''We are the quickly dying flame / And again a burning fire''. Actually, his ideas, expressed at the very beginning of the XX-th century, entitle us to call Vasiliev a thinker who anticipated the development of many parts of contemporary non-classical logic, especially its most pioneering and novel parts. Already in 1910 Vasiliev abandoned the law of contradiction and constructed a logic without this law. That is why he is justifiably considered as a forerunner of paraconsistent logic, which incarnates the idea of non-Aristotelian logic. Through his critique (and rejection) of the law of excluded middle, Vasiliev anticipated the birth of another alternative to classical logic, viz., intuitionistic logic. Moreover, due to introduction of new classed of judgements (and, respectively, new meanings of truth) he may be viewed as the predecessor of many-valued logic, which expanded the capability of classical logic. All of this enables us to compare cum grano salis the role of Vasiliev in logic with that of N.I.Lobachevskii in geometry: Lobachevskii's ideas gave rise to non-Euclidian, non-classical geometry; Vasiliev's ideas gave rise to non-Aristotelian, non-classical logic. Lobachevskii called his geometry "imaginary"; Vasiliev, too, called his logic "imaginary". Lobachevskii opened new horizons in the development of mathematics; Vasiliev, as well, opened qualitatively new perspectives in the development of formal logic, especially regarding the treatment of contradictory statements. Even though there were no new ideas in Vasiliev's logic, he is worthy of close study as one of the most original and prominent Russian logicians. A close look at Vasiliev's life and work shows us that he is not only the founder of original non-classical logical theories, but a thinker with …