Relevant First-Order Logic $LP^\#$ and Curry's Paradox resolution

TL;DR

This paper proposes a non-classical resolution to Curry's Paradox and Shaw-Kwei paradox that avoids rejecting contraction, contributing to the ongoing exploration of semantic paradoxes in logic.

Contribution

It introduces a novel approach using relevant first-order logic $LP^#$ to resolve Curry's Paradox without rejecting contraction.

Findings

Successfully resolves Curry's Paradox without contraction rejection

Provides a non-classical logical framework for semantic paradoxes

Enhances understanding of non-classical logic applications

Abstract

In 1942 Haskell B.Curry presented what is now called Curry paradox which can be found in a logic independently of its stand on negation.In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry's Paradox and Shaw-Kwei paradox without rejection any contraction postulate is proposed.