The Idea of Limiting the Type Theory in the Philosophy of Mathematics in the Context of the Criticism of Epistemological Relativism

The article examines the criticism of relativism in modern epistemology in comparison with studies on logic and the philosophy of mathematics. Frederic Fitch's idea to limit the use of Bertrand Russell's theory of types is discussed. The author of the article claims that Fitch's idea relates to the problems of the philosophy of mathematics, but it cannot be applied in the field of epistemology. The results of Carl Kordig's studies are critically evaluated. In order to demonstrate the inconsistency of relativism in modern epistemology Kordig tries to rely on Fitch's works on the philosophy of mathematics. The inconsistency of some modern relativistic concepts using the reductio ad absurdum argument based on the self-reference phenomenon is shown. Fitch's idea of limiting Russell's theory of types was to apply this theory to self-referential reasonings that lead to paradoxes but not to apply it to other reasonings containing self-referentiality. This idea may well be used in the field of the philosophy of mathematics. However, difficulties arise when we try to transfer this idea from the field of the philosophy of mathematics to epistemology. If we continue to apply Russell's theory of types in relation to paradoxical self-referential reasoning, then this theory will justify the relativistic type of thinking. The author of the article claims that if we want to criticize relativism using the reductio ad absurdum argument based on the phenomenon of self-referentiality, as Kordig does, then we must completely abandon Russell's theory of types.

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