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Many-Valued Logics and Suszko's Thesis Revisited

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Abstract

Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it.

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Authors and Affiliations

  1. Institute for Advanced Studies, University of Sao Paulo Research Group on Logic and Foundations, Av. Professor Luciano Gualberto, trav. J, 374, CEP 05655-010, Sao Paulo, Brazil. E-mail

    Marcelo Tsuji

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  1. Marcelo Tsuji
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Tsuji, M. Many-Valued Logics and Suszko's Thesis Revisited. Studia Logica 60, 299–309 (1998). https://doi.org/10.1023/A:1005020217249

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