January 1, 2025

On the Types and Conditions of Paradoxes

Key Points

Borisov's critique highlights two key difficulties in defining set-theoretic paradoxes, especially concerning Richard's paradox.
The distinction between types I and II of set-theoretic paradoxes may not be fully applicable, particularly for linguistic aspects.
Terminology like negative and positive formulas holds formal relevance but can be seen as speculative in practical terms.
The article explores how self-referential premises contribute to the derivability of contradictions in set-theoretic paradoxes.

Abstract

The article examines the conditions for set-theoretic paradoxes proposed by Borisov, as well as his critique of Ladov’s approach to a unified solution to the paradoxes. It is shown that Borisov’s position faces two difficulties. Firstly, the proposed distinction between types I and II of set-theoretic paradoxes is not entirely relevant. At the very least, Richard’s paradox, one of the conditions of which Borisov defines as a linguistic aspect, can be interpreted without the use of linguistic concepts. Secondly, the proposed terminology (negative and positive formulas) is relevant only formally, while in reality it is speculative in nature. Additionally, the issue of considering the derivability of a contradiction from a self-referential premise as a necessary condition for set-theoretic paradoxes is addressed.

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Cite This Study

Alexandr G. Andrushkevich (Wed,) studied this question.

synapsesocial.com/papers/68af4eb9ad7bf08b1ead78ce https://doi.org/https://doi.org/10.5840/eps202562338