THE SUBSTITUTIONAL QUANTIFICATION IN BASIC LOGIC AND ONTOLOGICAL COMMITMENTS IN FORMAL MATHEMATICAL THEORIES
V. Tselishchev1,2, A. Bessonov1,2
1Novosibirsk State University, 2, Pirogov St., Novosibirsk, 630090
2Institute of Philosophy and Law, Siberian Branch RAS, 8, Nikolaev St., Novosibirsk, 630090
Keywords: семантика, онтологические допущения, подстановочная квантификация, атомарные предложения, истина, semantics, ontological assumptions, substitutional quantification, atomic sentences, truth
Abstract
The article deals with problems of semantics for the substitutional quantification in contrast with objectual quantification, and related ontological commitments of theories. Three difficulties with the substitution quantification is considered, namely, the argument about the lack of names, the argument about the redundancy of numeric characters, the argument of the unnamed objects. It is shown that the Geach- Lavine semantics is quite satisfactory for establishing the equivalence of two interpretations.
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