Conditions of applicability of classical logic to philosophical reasoning

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 v^k” meaningfully corresponds to the formula J_k(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.