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

Bhupinder Singh Anand
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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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Bhupinder Singh Anand. 2003-05-19. Are there parts of our arithmetical competence that no sound formal system can duplicate?. https://arxiv.org/abs/math/0210456

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