INTENSIONALITY IN MATHEMATICS AND IMPOSSIBLE POSSIBLE WORLDS
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 математики, модальная логика, семантика возможных миров, невозможные возможные миры, intensionality of mathematics, modal logic, possible worlds semantics, impossible possible worlds
Abstract
The paper analyzes a method of explication of detection and explication of intensionality of mathematical discourse by means of possible worlds semantics. Although there is an idea about extensionality of mathematics, mathematical results, particularly Gödel's Second Incompleteness Theorem, essentially depend on how the meaning of mathematical terms is interpreted. The authors show that this difficulty can be overcome by means of possible worlds semantics. At the same time, the thesis is substantiated that Kripke’s possible worlds semantics does not solve the mentioned problem because it assumes extensionisonalization of the intensional content. Whereas Hintikka’s possible worlds semantics and his concept of impossible possible worlds are a fruitful approach for discovering and explaining the intensionality of mathematical discourse.
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