Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T06:51:35.505Z Has data issue: false hasContentIssue false

Lucas Against Mechanism II: A Rejoinder

Published online by Cambridge University Press:  01 January 2020

J.R. Lucas*
Affiliation:
Merton College, Oxford

Extract

David Lewis criticizes an argument I put forward against mechansim on the grounds that I fail to distinguish between OL, Lucas's ordinary potential arithmetic output, and OML, Lucas's arithmetical output when accused of being some particular machine M; and correspondingly, between OM the ordinary potential arithmetic output of the machine M, and ONM, the arithmetic output of the machine M when accused of being a particular machine N. For any given machine, M, N, O, P, Q, R,... etc., I can in principle (my critics are often very charitable in speaking as though I could in practice, but let me revert to an ideal mind) calculate a Godel sentence for that machine - indeed infinitely many, depending on the Godel numbering scheme adopted. The Godel sentence of a particular machine can, I claim, be seen to be true, if that machine is adequate for Elementary Peano Arithmetic. Hence, if I were accused of being M, I can on that supposition see that the Godel sentence of M is true, since I am capable of Elementary Peano Arithmetic and the machine M is said to be an adequate characterization of me.

Type
Research Article
Copyright
Copyright © The Authors 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Lewis, DavidLucas Against Mechanism II,’ this Journal, 9 (1979) 373-6Google Scholar