[FOM] The Lucas-Penrose Thesis

[Stewart Shapiro]

>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).