Wittgenstein’s Tractatus Logico-Philosophicus and a Hierarchical Approach to Solving Logical Paradoxes
Keywords: paradoxes, logic, philosophy of mathematics, semantics, theory of types, language, metalanguage, self-reference, hierarchical approach
AbstractThe hierarchical approach to the solution of logical paradoxes is considered in the article. The foundations and main theses of the hierarchical approach are analysed through consideration of Russell’s theory of types and Tarski’s semantic conception. Basic arguments critical of such an approach that have been formulated in logical and epistemological research are presented. A specific characteristic of Wittgenstein’s position in the context of the hierarchical approach expressed by him in Tractatus Logico-Philosophicus is identified. The Wittgensteinian version of the hierarchical approach is the most stable in the relation to the critical arguments considered. If we still want to evaluate the hierarchical approach as an acceptable solution to the problem of logical paradoxes, we should employ its Wittgensteinian interpretation, because it is able to overcome the serious critical arguments against the approach presented in contemporary research on logic, epistemology, and the philosophy of mathematics.
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