Conditions of applicability of classical logic to philosophical reasoning
 Authors: Pavlov S.A.
 Issue: Vol 22, No 2 (2018)
 Pages: 139148
 Section: Ontology and epistemology
 URL: http://journals.rudn.ru/philosophy/article/view/18709
 DOI: http://dx.doi.org/10.22363/231323022018222139148
Abstract
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 manyvalued logics. As the latter, the semantics of manyvalued logics, the metatheory of Zinoviev’s truth values, the elementary theory of truth and falsehood operators were considered.
In the metatheory of logical semantics, in which semantics are constructed for manyvalued logics, classical logic is hold. In this metatheory, the theory of Joperators (introduced by Rosser and Turquette) is used. The theory of Joperators is part of the metatheory 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 objectlanguage formulas P, for which the condition (P takes a designated value or P takes an antidesignated 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 objectlanguage from the metalanguage, semantics from the syntax.
The elementary theory of truth and falsehood operators was also considered, which was founded in the BooleFrege semantics, generalized to the nonclassical 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 twovalued logic.
It is noted that the conditions considered are close to the definitions of the utterance in natural language.
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 manyvalued logics. As the latter, the semantics of manyvalued logics, the metatheory of Zinoviev’s truth values, the elementary theory of truth and falsehood operators were considered. In the metatheory of logical semantics, in which semantics are constructed for manyvalued logics, classical logic is hold. In this metatheory, the theory of Joperators (introduced by Rosser and Turquette) is used. The theory of Joperators is part of the metatheory 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 objectlanguage formulas P, for which the condition (P takes a designated value or P takes an antidesignated 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 objectlanguage from the metalanguage, semantics from the syntax. The elementary theory of truth and falsehood operators was also considered, which was founded in the BooleFrege semantics, generalized to the nonclassical 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 twovalued logic. It is noted that the conditions considered are close to the definitions of the utterance in natural language.
S A Pavlov
Institute of Philosophy of RAS
Author for correspondence.
Email: sergey.aph.pavlov@gmail.com
12/1 Goncharnaya Str., Moscow, 109240, Russia

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