The paper deals with the factors which enabled N. A. Vasiliev to put forward in 1910-12 the idea of logics free of the laws of contradiction and excluded middle, the idea of metalogic and to construct his imaginary logic as novel non-classical system. It is shown that background of Vasiliev's ideas lies deeply in Russia's culture and particular approach to logical discourse. Several Russian scholars expressed ideas similar to Vasiliev's though not in such explicit form. This period might be called the prehistory of paraconsistency. Real history of paraconsistency starts with N.C.A. da Costa's works.
The life and work of the Russian scholar Ivan E. Orlov (September 1, 1886-October 13, 1936) is described here in detail for the first time. Orlov is well known as one of the pioneers of relevant logic, but he was also interested in a wide variety of other topics including philosophy, chemistry, and music theory. This article shows that the sociopolitical climate of the 1920s and 1930s exerted a significant influence on the style and content of Orlov's work. It theorizes that this climate determined to a considerable degree the evolution of Orlov's interests and also his fate. The Wolfhound Era hurls itself against my shoulders, But I am not by nature a wolf. Osip Mandel'shtam (1931)
This article presents the story of S. A. Yanovskaya's epiphanyÐparticularly, her shift from hard-line communist orthodoxy and hostility towards`bourgeois minded' Soviet-Russian mathematicians to vigorous support of mathematical logic. In light of this evidence, S. A. Yanovskaya (1896±1966) may be considered as a spiritual leader and administrative founder of modern mathematical research and education in the USSR/Russia.
In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880A. Vasiliev ( -1940 noted this opposition and stressed that the way for the novel -non-Aristotelian -logic was already paved. He made an attempt to construct non-Aristotelian logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What reasons forced him to reassess the status of particular propositions and to replace the square of opposition by the triangle of opposition? What arguments did Vasiliev use for the introduction of new classes of propositions and statement of existence of various levels in logic? What was the meaning and role of the "method of Lobachevsky" which was implemented in construction of imaginary logic? Why did psychologism in the case of Vasiliev happen to be an important factor in the composition of the new 'imaginary' logic, as he called it?
Mathematics Subject Classification (2000). 03-03, 03A05, 03B50, 03G20, 03G25, 01A55-01A60, 01A70. Keywords. Non-Aristotelian logic, square of opposition, triangle of opposition, classifications of propositions, the law of non-self-contradiction, metalogic. A. Vasiliev (1880A. Vasiliev ( -1940 is considered as a forerunner of contemporary non-classical logic, and especially of paraconsistent and multi-valued logic. In his imaginary logic (first work published in 1910) he "removed from the canons of thought" the laws of contradiction and excluded middle, introduced new classes of propositions, a novel mechanism of reasoning related to these propositions, and the idea of metalogic. His mode of argumentation was informal and the starting point in constructing his new logic is his analysis of the propositions embodied in the traditional Aristotelian syllogistic square diagram.
Professor of Kazan University Nicolai
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