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On Russell’s Paradox with Nails and Strings

Author:

András, Ferenc

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

February 9, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10089

Downloads:

30

Keywords:

paradox, Russell’s paradox

Abstract:

Russell’s paradox challenges the foundations of naive set theory, questioning the assumption that every predicate determines a corresponding set. This paper explores the paradox through an alternative illustrative framework using nails and strings, offering an intuitive yet rigorous representation of the membership relation. By analyzing how self-referential structures emerge within this model, the paper highlights three possible resolutions: hierarchical, restrictive, and temporal. The discussion ultimately suggests that a weakened, nominalist interpretation of set formation can preserve the principle Russell refuted, albeit with significant conceptual modifications.

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