[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 

> 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

E-mail: panu.raatikainen at helsinki.fi

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