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A Critique of Self-Reference: What Gödel's Theorem Really Proves

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

July 25, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/8819

Downloads:

594

Keywords:

self-reference, self-subject, theorem of the inconsistent self-subjects, liar paradox, Grelling-Nelson paradox, Russell's predicate paradox, Russell's set paradox, Richard paradox, Gödel's first incompleteness theorem

Abstract:

This article introduces a new perspective for the analysis of self-referential sentences, and proves the conditions under which they are inconsistent. The Liar Paradox, Grelling-Nelson Paradox, Russell's Predicate Paradox, Russell's Set Paradox and Richard Paradox are proved to meet such conditions. The same is proved of the ordinary language interpretation of Gödel's undecidable formula if the corresponding formal calculus is complete. In consequence, Gödel's Theorem VI only holds if that calculus is not complete, which makes the theorem unnecessary. All proofs and arguments in this article are developed within the framework of a simplified system of ordinary logic also defined in this paper.