Philosophical Insights and Technical Work: The Fates of Paradoxes
The article analyzes Vsevolod Ladov's arguments in favor of the interpretation of Wittgenstein's approach to “solving” the paradoxes of self-reference as preferable to the hierarchical approach. It is proved that the unification of Russell's theory of types and Tarski's concept of metalanguage as representatives of the hierarchical approach for solving paradoxes is superficial and leads to the loss of their substantive specificity. It is shown that Wittgenstein's position leads to a significant limitation of the theoretical and proving possibilities of mathematics. It is argued that the proposed interpretation of Wittgenstein's criticism of Russell's theory of types ignores the meaningful context of the complex evolution of Russell's position regarding the paradoxes of set theory and the impact that this evolution had on Wittgenstein's own position. The authors point out the problematic nature of the interpretation of the position of the “early” Wittgenstein as an adequate critique for the solution of the paradoxes of set theory proposed by Russell.
Keywords
set-theoretic paradoxes,
logicism,
Substitution Theory,
Type Theory,
Wittgenstein,
RussellAuthors
| Tselishchev Vitaliy V. | Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences | leitval@gmail.com |
| Khlebalin Aleksandr V. | Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of Sciences | sasha_khl@mail.ru |
Всего: 2
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