Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-03T02:01:41.456Z Has data issue: false hasContentIssue false
  • English
  • Français

Lucas against Mechanism

Published online by Cambridge University Press:  25 February 2009

David Lewis
David Lewis
Affiliation:
University of California at Los Angeles.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Discussion
Information
Philosophy , Volume 44 , Issue 169 , July 1969 , pp. 231 - 233
Copyright
Copyright © The Royal Institute of Philosophy 1969

References

1 Philosophy, 36 (1961): 112–127.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): 161–228CrossRefGoogle Scholar, and by Feferman, S. in “Transfinite Recursive Progressions of Axiomatic Theories”, Journal of Symbolic Logic, 27 (1962): 259–316.CrossRefGoogle Scholar

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