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'One needs to ensure endless possible logical systems. That one, who will become ensured in this, will share Giordano Bruno's feeling when he imagined an endless Universe.'

Nikolay Vasiliev, 1912

Nikolay Vasiliev
Alexey Losev

Nikolay Alexandrovich VASILIEV (29.06.1880, Kazan — 31.12.1940, Kazan) — Russian logician, philosopher, psychologist, poet, the forerunner of paraconsistent and multi-valued logics.

His father was a fairly well-known mathematician Professor Alexander V. Vasiliev, his grandfather was outstanding sinologist Professor Vassily P. Vasiliev, and his great grandfather was the prominent astronomer Ivan M. Simonov, who was a close colleague of Nikolay Lobachevsky.

Aiming to be a psychologist, Vasiliev studied at the medical faculty (1904) and the historico-philological faculty of Kazan University (1906), where he was honored with candidate degree. Afterwards he was offered the position of privat-dozent (Associate Prof.) at Kazan University.

As a university student Vasiliev was enthusiastic about symbolist style poetry and published some books of verses of his own (for example,'The longing for eternity') and translations of the poetry of Emile Verhaeren and Algernon Swinburne.

Although Vasiliev outlined the logic of relatives paper by Charles Peirce as early as in 1897, it was only in 1908 that he entirely devoted himself to logic.

On May 18, 1910 Vasiliev presented a lecture (published in October that same year) 'On Partial Judgements, on the Triangle of Opposites, on the Law of Excluded Fourth' in which he put forward for the first time ever the idea of (non-Aristotelian) logic, free of the laws of excluded middle and contradiction. Reasoning by analogy with the 'imaginary' geometry of Lobachevsky, Vasiliev called his novel logic 'imaginary', for he assumed it was valid for the worlds where the above-mentioned laws did not hold, worlds with beings having other types of sensations. He distinguished levels of logical reasoning, and introduced the notion of metalogic.

Vasiliev spent 1912-13 in Western Europe (mostly Germany) and published his salient works Logic and Metalogic and Imaginary (non-Aristotelian) logic. Vasiliev constructed non-Aristotelian logic using the concepts, and even the manner of reasoning, common to Aristotelian logic. He was aware of the achievement in mathematical logic (and even carefully studied Ernst Schroeder's works) but did not make an attempt to formalise 'imaginary' logic.

His only work in a foreign language (English) — concise abstract of his 'imaginary logic' — was published in Naples in 1924.

In 1914 when World War I broke out, Vasiliev was drafted into the army, where he became seriously mentally ill. Nevertheless he returned to teaching at Kazan University, but in 1922 was ousted by the new Bolshevik administration. This act aggravated his ailment: Vasiliev spent most of the following 20 years in mental hospital, and thus rescued from the Stalin regime. He died on December 31, 1940. The place where he was buried is unknown.

The pioneer ideas of Vasiliev were rediscovered in the early 1960s and they formed a basis mainly for paraconsistent logic. Some well-known scholars in 1960s consider his work to be the precursor of multi-valued logic. The informal style and conceptual riches of Vasiliev's works make them especially valuable.


By Vasiliev:

Vasiliev N.A. Imaginary Logic. Moscow, 1989 (in Russian).

On Vasiliev:

Arruda A.I. 'Survey of Paraconsistent Logic'. In: Mathematical logic in Latin America Eds. Arruda A.I., Chuaqui R., Da Costa N.C.A., Amsterdam: New York: Oxford. North-Holland, 1980, pp.1-41.

Bazhanov V.A. N.A. Vasiliev (1880 — 1940). Moscow, 1988 (in Russian).

Bazhanov V.A. 'The Fate of One Forgotten Idea: N.A.Vasiliev and His Imaginary Logic'. In: Studies in Soviet Thought, 1990, vol.39, N3-4, pp.333-334

Bazhanov V.A. 'Charles Peirce's Influence on Logical Ideas of N.A. Vasiliev'. In: Modern Logic, 1992, vol. 3. N 1, pp. 48-56

Bazhanov V.A. 'The Origins and Emergence of Non-Classical Logic in Russia (Nineteenth Century until the Turn of the Twentieth Century)'. In: Zwischen traditioneller und moderner Logik. Nichtklassiche Ansatze. Mentis-Verlag, Paderborn, 2001, S.205 — 217.


Valentin A. Bazhanov, Ph.D., Prof.

Ulyanovsk State University (Russia)



International Society for Philosophers