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International Studies in Phenomenology and Philosophy

Book | Chapter

182762

Interpretations

Venanzio Raspa

pp. 105-126

Abstract

This chapter offers a review of the interpretations of imaginary logic that have appeared over the last hundred years. The early readers of Vasil'ev's work can be grouped as displaying one or another of two tendencies, either sharp criticism (e.g. K. A. Smirnov) or notable appreciation (e.g. N. N. Luzin). After two decades of silence, Russian and Polish scholars began to write about Vasil'ev. But in order to appreciate his logical ideas, the development of non-classical logics, like many-valued and paraconsistent logics, as well as a revalorization and formalization of syllogistic, have been necessary. Some scholars interpret imaginary logic in a many-valued key, either as a forerunner of many-valued logic or in terms of a reconstruction of imaginary logic as a many-valued one (L. Chwistek. H. Greniewski, A. I. Mal'tsev, T. Kwiatkowski, G. L. Kline, N. Rescher, M. Jammer). In the 1970s, the paraconsistent interpretation was proposed by A. I. Arruda and was further developed by several scholars (L. Z. Puga, Newton C. A. da Costa, A. S. Karpenko, V. L. Vasyukov, O. Bueno, I. M. L. D'Ottaviano). Others interpreted Vasil'ev as a founder of intensional logics (G. Priest and R. Routley), as a theoretician of logical pluralism and of impossible worlds. Another line of interpretation reconstructs Vasil'ev's logic in terms of a syllogistic adapted to modern standards (V. A. Smirnov, T. P. Kostiuk, V. I. Markin, D. Zaitsev, A. Kouznetsov, W. Suchoń). Finally, systematic historical investigations about Vasil'ev have also emerged (V. A. Bazhanov, F. Cavaliere, R. Vergauwen, E. A. Zaytsev, W. Stelzner). The chapter closes with the proposal to use some formalized reconstructions of imaginary logic as an adequate logical basis for Meinong's object theory.

Publication details

Published in:

Raspa Venanzio (2017). Thinking about contradictions: the imaginary logic of Nikolai Aleksandrovich Vasil'ev, Springer, Dordrecht.

Pages: 105-126

DOI: 10.1007/978-3-319-66086-8_6

Full citation:

Raspa Venanzio (2017). Interpretations, in Thinking about contradictions, Dordrecht, Springer, pp. 105-126.