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How definitive is the standard interpretation of Goedel's Incompleteness Theorem?

2003/07/05 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · Psychology · #03B10 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Logic, Reasoning, and Knowledge #Philosophy and Theoretical Science #math.GM #msc:03B10

paper · pdf · doi:10.48550/arxiv.math/0307074

12 pages; an HTML version is available at http://alixcomsi.com/How_definitive_is_the_standard.htm

arxiv created 2003/07/05 · openalex publication_date 2003/07/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Standard interpretations of Goedel's "undecidable" proposition, [(Ax)R(x)], argue that, although [~(Ax)R(x)] is PA-provable if [(Ax)R(x)] is PA-provable, we may not conclude from this that [~(Ax)R(x)] is PA-provable. We show that such interpretations are inconsistent with a standard Deduction Theorem of first order theories.

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