HYPER-INTENSIONALITY IN RELATIONSHIP BETWEEN RUSSELL'S RAMIFIED THEORY OF TYPE AND SUBSTITUTIONAL THEORY
Vitaliy Valentinovich Tselishchev, Aleksandr Valerievich Khlebalin
Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Sciences, 8 Nikolaeva str., Novosibirsk, 630090, Russia
Keywords: интенсиональность математического дискурса, теория типов, подстановочная теория, универсальность логики, гиперинтенсинальный парадокс, intensionality of mathematical discourse, theory oftype, substitutional theory, universality of logic, hyper-intensional paradox
Abstract
The article analyzes the problem of intensionality of mathematics in B. Russell's logicism program. We argue that the intensional approach applied in Principia Mathematica is associated with the emergence of the hyper-intensional paradox in Russell's substitutional theory. Russel considered his substitutional theory as a tool for resolving paradoxes in terms of preserving a universalist interpretation of logic, which is incompatible with his theory of type. The reproduction of the hyper-intensional paradox in the substitutional theory resulted in giving it up in Principia Mathematica in favor of the ramified theory of type.
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