[FOM] The Lucas-Penrose Thesis
shapiro.4 at osu.edu
Fri Sep 29 16:58:02 EDT 2006
>I am a little disturbed that a seminal paper on the Lucas argument, "God,
>the Devil, and Goedel," by my teacher, Paul Benacerraf, has not been cited
>in the discussion of FOM. Aside from making all the points mentioned by
>participants on FOM, it shows that there is another hidden assumption in the
>argument, namely that if I am a machine, then I can know which one.
Agreed. Actually, all we can conclude is that, for every e, if a properly
idealized version of myself is Turing machine e, then I cannot *prove*
(with mathematical certitude, as Godel put it) that I am e. It is possible
that I can have very good inductive evidence that I am e.
Godel made essentially this point in the Gibbs lecture. It nicely
complements Benacerraf's conclusion (all of which assumes we go along with
the idealizations that make the theorem applicable).
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