Reflections on Russell's antinomy

TL;DR

This paper analyzes Russell's antinomy across different deductive systems, exploring alternative inferential paths that avoid contradiction and discussing the implications for logical coherence and paradox resolution.

Contribution

It introduces alternative formal approaches to Russell's antinomy that preserve system coherence, challenging the notion that paradoxes are inherently irresolvable.

Findings

Alternative inferential paths avoid contradiction

Preservation of logical coherence in the presence of antinomies

Reevaluation of paradox resolution strategies

Abstract

We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted one, that allow for the formal assertion of the antinomy without deriving the contradiction, thus preserving the coherence of the system. In light of this, the purpose of this article is to propose a review of the consequences of asserting Russell's antinomy and, by extension, the widespread belief that any attempt to resolve a paradox is doomed to failure.