[FOM] The Lucas-Penrose Thesis
praatika@mappi.helsinki.fi
praatika at mappi.helsinki.fi
Fri Sep 29 04:44:12 EDT 2006
Robbie Lindauer <robblin at thetip.org>:
> Actually, Lucas replied to this at length in the Freedom of the Will.
Certainly, but whether the reply is any good is a different matter.
> In particular the (short version) reply is this:
>
> If the machine proposed by a mechanist as a model of the mind is NOT
> consistent, it will produce ANY statement as true, and hence not be a
> model of a human mind.
And what on earth guarantees that a human mind is consistent? As I said,
even many eminent logicians have believed in inconsistent theories.
> In particular, a machine which is inconsistent will produce "1 + 1 = 3"
> as a theorem. A human (sane one) will be able to see that that is
> obviously false.
So can a machine, say, one which lists the theorems of Robinson
arithmetic.
> The argument is structured thus:
>
> 1) IF the machine proposed as a model of the mind is consistent then
> there exists a godel sentence G for the formalism represented by the
> machine which a Human can recognize true and which that machine can not
> produce as true. (Godel's Theorem)
No, he/she cant. Only if he/she could "see" that the formal system is
consistent. But that is not in general possible.
This is not replying the objection, but ignoring it, and repeating the
false claim.
> 2) IF the machine proposed as a model of the human mind is INCONSISTENT
> then it will produce nonsense that a human will recognize as such. In
> particular, if it is an arithmetic machine, the machine has as a
> theorem '1 = 0'.
See above.
Anyway, this reply demands that a mechanist must provide a particular
machine as a model of the human mind. But this amounts to changing the
subject. Orginally, the claim at stake was whether there could be a Turing
machine which would be able to prove everything that a human mind can.
Best, Panu
Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm
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