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

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

2002-10-30

arxiv.org/abs/math/0210456v2

Mathematics

General Mathematics

v2; introduced standardised ACI compliant notation for citations; 9 pages; this paper reproduces Meta-theorem 1 and related Me

Scientific paper

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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