Chapter

The Limits of Human Mathematics (2001)

Nathan Salmon

in Metaphysics, Mathematics, and Meaning

Published in print November 2005 | ISBN: 9780199284719
Published online February 2006 | e-ISBN: 9780191603235 | DOI: http://dx.doi.org/10.1093/0199284717.003.0014
 The Limits of Human Mathematics (2001)

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Gödel’s claim is defended that his famous incompleteness theorems yield the result, as a mathematically established fact, that the mathematical problem-solving capacity of the human mind either exceeds that of any finite machine or is incapable of solving all of mathematics’ mysteries. The issue turns on the nature of mathematical proof by the human mind. Of particular relevance is the question of whether the deductive basis of human mathematics is decidable.

Keywords: decidability; Gödel; incompleteness; machine; mathematics; mind

Chapter.  13287 words. 

Subjects: Philosophy

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