Conditions of applicability of classical logic to philosophical reasoning

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Abstract. The conditions for the applicability of the classical logic of statements to philosophical reasonings are investigated. This research is carried out within the framework of various semantics for many-valued logics. As the latter, the semantics of many-valued logics, the meta-theory of Zinoviev’s truth values, the elementary theory of truth and falsehood operators were considered.

In the meta-theory of logical semantics, in which semantics are constructed for many-valued logics, classical logic is hold. In this meta-theory, the theory of J-operators (introduced by Rosser and Turquette) is used. The theory of J-operators is part of the meta-theory of logical semantics. A semantic statement of the form “P haves the value vk” meaningfully corresponds to the formula Jk(P). It is shown that for classical object-language formulas P, for which the condition (P takes a designated value or P takes an anti-designated value), classical logic takes place.

The synthesizing approach in A. Zinoviev’s studies and constructions led to the fact that he combined logic, ontology and methodology into a unified science, in which the first are its aspects. Only in the process of exposition, he distinguishes in it three parts: 1) basic logic, 2) logical ontology, and 3) logical methodology. This is a radical difference from the approaches of D. Hilbert and A. Tarski separating the object-language from the metalanguage, semantics from the syntax.

The elementary theory of truth and falsehood operators was also considered, which was founded in the Boole-Frege semantics, generalized to the non-classical case. It is shown that for the formula of the object language P for which the condition (informally expressed) is satisfied, the formula P is either true or false, then for it there is a classical two-valued logic.

It is noted that the conditions considered are close to the definitions of the utterance in natural language.

About the authors

S A Pavlov

Institute of Philosophy of RAS

Author for correspondence.


12/1 Goncharnaya Str., Moscow, 109240, Russia


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Copyright (c) 2018 Pavlov S.A.

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