arXiv math/02104562002-10math.GM

在我们的算术能力中，是否有某些部分是任何健全的正式系统都无法复制的？

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

Bhupinder Singh Anand

备注：: 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

摘要：

1995年，大卫·查默斯（David Chalmers）认为，我们的算术能力中可能有一部分是任何健全的正式系统都无法复制的，这是令人难以置信的。我们证明了递归数论关系x=Sb（y 19| Z（y））-其在算法上是可验证的，因为Goedel的递归函数Sb（y 19| Z（y））是图灵可计算的，不能在任何一致的形式算术系统中被“复制”。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。