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Философские прозрения и техническая работа: судьбы парадоксов

Философские прозрения и техническая работа: судьбы парадоксов

Abstract

Анализируются аргументы В. Ладова в пользу интерпретации подхода Витгенштей-на к «решению» парадоксов самореференции в качестве предпочтительного перед иерархическим подходом. Доказывается, что объединение теории типов Б. Рассела и концепции метаязыка А. Тарского как представителей иерархического подхода к ре-шению парадоксов поверхностно и ведет к утрате их содержательной специфики. Показано, что позиция Витгенштейна приводит к существенному ограничению тео-ретико-доказательных возможностей математики. Утверждается, что предло-женная интерпретация критики Витгенштейном теории типов Рассела игнорирует содержательный контекст сложной эволюции позиции Рассела в отношении пара-доксов теории множеств и то влияние, которое эта эволюция оказала на позицию самого Витгенштейна. Указывается на проблематичность интерпретации позиции «раннего» Витгенштейна как адекватной критики решения парадоксов теории мно-жеств, предложенного Расселом. 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.

Country
Russian Federation
Related Organizations
Keywords

Рассела теория типов, Витгенштейн, Людвиг 1889-1951, теоретико-множественные парадоксы

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green