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The British Journal for the Philosophy of Science 2004 55(4):731-737; doi:10.1093/bjps/55.4.731
© 2004 by British Society for the Philosophy of Science
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Mathematics and the Mind*

Michael Redhead

Centre for Philosophy of Natural and Social Science, The London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK, mlr1000{at}HERMES.cam.ac.uk

Granted that truth is valuable we must recognize that certifiable truth is hard to come by, for example in the natural and social sciences. This paper examines the case of mathematics. As a result of the work of Gödel and Tarski we know that truth does not equate with proof. This has been used by Lucas and Penrose to argue that human minds can do things which digital computers can't, viz to know the truth of unprovable arithmetical statements. The argument is given a simple formulation in the context of sorites (Robinson) arithmetic, avoiding the complexities of formulating the Gödel sentence. The pros and cons of the argument are considered in relation to the conception of mathematical truth.

* Paper contributed to the Conference entitled The Place of Value in a World of Facts, held at the LSE in October 2003.


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This article has been cited by other articles:


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