David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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British Journal for the Philosophy of Science 55 (4):731-737 (2004)
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.
|Keywords||Arithmetic Logic Mathematics Mind Truth|
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