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