RUDN Journal of PhilosophyRUDN Journal of Philosophy2313-23022408-8900Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)1870910.22363/2313-2302-2018-22-2-139-148Research ArticleConditions of applicability of classical logic to philosophical reasoningPavlovS A<p>-</p>sergey.aph.pavlov@gmail.comInstitute of Philosophy of RAS1512201822213914822062018Copyright © 2018, Pavlov S.A.2018<p><strong>Abstract.</strong> 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 Zinovievs truth values, the elementary theory of truth and falsehood operators were considered.</p>
<p>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 <em>J</em>-operators (introduced by Rosser and Turquette) is used. The theory of <em>J</em>-operators is part of the meta-theory of logical semantics. A semantic statement of the form P haves the value v<sup>k</sup> meaningfully corresponds to the formula <em>J</em><sub>k</sub>(P). It is shown that for classical object-language formulas <em>P</em>, for which the condition (<em>P</em> takes a designated value or <em>P</em> takes an anti-designated value), classical logic takes place.</p>
<p>The synthesizing approach in A. Zinovievs 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.</p>
<p>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 <em>P</em> for which the condition (informally expressed) is satisfied, the formula <em>P</em> is either true or false, then for it there is a classical two-valued logic.</p>
<p>It is noted that the conditions considered are close to the definitions of the utterance in natural language.</p>classical logiclogical semanticstruefalseconditions of applicabilityлогика высказыванийлогическая семантикаистиналожьусловия применимости[Anisov AM. Sovremennaya logika. Moscow, 2002.][Anshakov OM., Rychkov SV. O mnogoznachnykh logicheskikh ischisleniyakh. Semiotika i informatika. Vyp. 19. Moscow, 1982.][Aristotel'. Kategorii. Aristotel'. Soch.: v 4 t. T. 2. Moscow., 1978. 13b15.][Bessonov AV. K osnovaniyam logicheskoi teorii istiny. Filosofiya nauki. 1999; 5 (1):52—63.][Gil'bert D., Akkerman V. Osnovy teoreticheskoi logiki. Moscow, 1947.][Zinov'ev AA. Logika nauki. Moscow, 1971.][Zinov'ev AA. Faktor ponimaniya. Moscow, 2006.][Pavlov SA. Ischislenie predikatov istinnosti i lozhnosti. Logicheskii analiz estestvennykh yazykov: 2-i Sovetsko-Finskii kollokvium po logike. Moscow, 1979.][Pavlov SA. Ontologicheskii tezis obobshchennoi Bul' Ç Frege semantiki. Vestnik Rossiiskogo universiteta druzhby narodov, Seriya: Filosofiya. 2016;(1):58—69.][Popov VM. Ob odnoi chetyrekhznachnoi paranormal'noi logike. Logika i V.E.K. Moscow, 2003.][Tarskii A. Semanticheskaya kontseptsiya istiny i osnovaniya semantiki. Analiticheskaya filosofiya: stanovlenie i razvitie. M., 1998.][Frege G. O smysle i znachenii. Logika i logicheskaya semantika. Moscow, 2000.][Łukasievicz J. Investigations Into the Sentential Calculus. Amsterdam; L.; Warszawa, 1970. P. 131—152.][Pavlenko AN. The epistemological glaucoma and psematical paradox (autological feature of truth and heterological feature of false). Vestnik Rossiiskogo universiteta druzhby narodov. Seriya: Filosofiya. 2018; (2).][Pavlov SA. Designated Operator Theory and Domain of Symbol Expressions. Book of abstracts 15th Congress of Logic, Methodology and Philosophy of Science CLMPS. Helsinki, 2015. P. 263—264.][Pawlow SA. Einige nichttraditionelle Ideen in der Logi. Philosophie und Naturwissenschaften in Vergangenheit und Gegenwart. Heft 5: Philosophische Probleme der Logik. Berlin, 1978.][Rosser JB., Turquette AR. Many-valued logics. 1987. Vol. 120. Nouvelle serie. P. 311—334.]