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Are there parts of our arithmetical competence that no sound formal system can duplicate?

2002/10/30 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · #03B10 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Logic, programming, and type systems #math.GM #msc:03B10

paper · pdf · doi:10.48550/arxiv.math/0210456

v2; introduced standardised ACI compliant notation for citations; 9 pages; this paper reproduces Meta-theorem 1 and related Meta-lemmas from my earlier paper http://arXiv.org/abs/math.GM/0210078 ; an HTML version is available at http://alixcomsi.com/index01.htm

openalex publication_date 2002/10/30 · arxiv created 2003/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1995, David Chalmers opined as implausible that there may be parts of our arithmetical competence that no sound formal system could ever duplicate. We prove that the recursive number-theoretic relation x=Sb(y 19|Z(y)) - which is algorithmically verifiable since Goedel's recursive function Sb(y 19|Z(y)) is Turing-computable - cannot be "duplicated" in any consistent formal system of Arithmetic.

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