[FOM] The Lucas-Penrose Thesis

[Eray Ozkural]

On 9/28/06, A.P. Hazen <a.hazen at philosophy.unimelb.edu.au> wrote:
>         (4) But we human mathematicians can know that human mathematics
>            is (ultimately) consistent (because  we would revise our
>            axioms if we found a contradiction, so the contradiction
>            would -- ultimately -- be eliminated)

Obviously, Step 4 is suspect here, I do not see any
evidence that human mathematicians know their
mathematics to be consistent, it is only that they have
not found an obvious inconsistency. If you sneak this
assumption in, I suspect that you should also be able to
prove things such as humans having infinite computation
capacity and being able to solve the halting problems.

Godel himself puts forward a similar argument in his
Gibbs lecture, thus neither Penrose nor Lucas have
any originality in this spiritual argument as far as I
can tell.

Regards,

-- 
Eray Ozkural, PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://myspace.com/malfunct
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy