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Lucas against Mechanism

Published online by Cambridge University Press:  25 February 2009

David Lewis
Affiliation:
University of California at Los Angeles.
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J. R. Lucas argues in “Minds, Machines, and Gödel”, that his potential output of truths of arithmetic cannot be duplicated by any Turing machine, and a fortiori cannot be duplicated by any machine. Given any Turing machine that generates a sequence of truths of arithmetic, Lucas can produce as true some sentence of arithmetic that the machine will never generate. Therefore Lucas is no machine.

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Discussion
Copyright
Copyright © The Royal Institute of Philosophy 1969

References

1 Philosophy, 36 (1961): 112127.Google Scholar

2 Lucas arithmetic belongs to a class of extensions of Peano arithmetic studied by Turing, A. M. in “Systems of Logic Based on Ordinals”, Proceedings of the London Mathematical Society, sec. 2, 45 (1939): 161228CrossRefGoogle Scholar, and by Feferman, S. in “Transfinite Recursive Progressions of Axiomatic Theories”, Journal of Symbolic Logic, 27 (1962): 259316.CrossRefGoogle Scholar

3 I am indebted to George Boolos and Wilfrid Hodges for valuable criticisms of an earlier version of this paper.

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