Relevant First-Order Logic LP# and Curry’s Paradox Resolution
Pure and Applied Mathematics Journal
Volume 4, Issue 1-1, January 2015, Pages: 6-12
Received: Nov. 19, 2014; Accepted: Nov. 22, 2014; Published: Jan. 19, 2015
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Author
Jaykov Foukzon, Israel Institute of Technology, Department of Mathematics, Haifa, Israel
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Abstract
In 1942 Haskell B. Curry presented what is now called Curry's 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' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗_n^C
Keywords
Curry's Paradox, Shaw-Kwei's, Paradox, Relevance Logics, Ƚukasiewicz Logic, Abelian Logic
To cite this article
Jaykov Foukzon, Relevant First-Order Logic LP# and Curry’s Paradox Resolution, Pure and Applied Mathematics Journal. Special Issue: Modern Combinatorial Set Theory and Large Cardinal Properties. Vol. 4, No. 1-1, 2015, pp. 6-12. doi: 10.11648/j.pamj.s.2015040101.12
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