Mathematics and the mind

British Journal for the Philosophy of Science 55 (4):731-737 (2004)
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Abstract

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.

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Author's Profile

Michael Redhead
Last affiliation: London School of Economics

Citations of this work

Truth and provability: A comment on Redhead.Panu Raatikainen - 2005 - British Journal for the Philosophy of Science 56 (3):611-613.

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References found in this work

Minds, Machines and Gödel.John R. Lucas - 1961 - Philosophy 36 (137):112-127.
Minds, Machines and Gödel.J. R. Lucas - 1961 - Etica E Politica 5 (1):1.
Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
The Freedom of the Will.J. R. LUCAS - 1971 - British Journal for the Philosophy of Science 22 (4):382-387.

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