Nicolai A. Vasiliev - Work in Logic

Work in Logic

Although Vasiliev outlined an abstract about the article on the "logic of relatives" by Charles Sanders 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 Third" 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 Schröder's works) but did not make an attempt to formalise "imaginary" logic.

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