[FOM] The Lucas-Penrose Thesis vs The Turing Thesis

[Arnon Avron]

I apologize for not resisting this time the temptation to reply
to Robbie Lindauer, but he has pushed himself to such
an awkward corner, that I simply cannot miss this opprtunity...

On Mon, Oct 09, 2006 at 11:26:12AM -0700, Robbie Lindauer wrote:
> On Oct 8, 2006, at 12:05 AM, aa at post.tau.ac.il wrote:
> 
> > I dont agree with the rest of your message, but 
> > I see no point to argue with you. Obviously, the fact that no 
> > expert (whether that expert believes that we are machines or not)
> > accepts your arguments, does not cause you to try to 
> > understand what is wrong with them --- and it never will.
> 
> 
> As for the "no expert" clause, what one person considers an expert, 
> another considers a lunatic.  

There are some objective criterions, you know. Goedel theorems
are *theorems* of mathematical logic, and so the experts on them
are the mathematical logicans, especially those who made contributions
to the subject (like generalizing and/or improving the results
and their proofs). I guess that according to you, Goedel himself
would not be considered as an expert on his theorem, but as
a lunatic ...

> Hence my universal disdain for 
> axiomatic  mathematics as fairy tales.
> 
> Welcome to Philosophy.

Only to a certain part of the present world of philosophy:
the people  who think that one need not know much about some area, or 
have a deep understanding  of it, in order to have strong 
opinions about it. Luckily, not all philosophers are like this.

> As entertaining as this is, I suspect that your issue may be with 
> exactly this sentence below:
> 
> >> If there were a computer program that has all the theorems of PA as
> >> theorems and is consistent, then, potentially, a human can determine 
> >> an
> >> undecidable sentence for that computer program.
> 
> Since, for someone who rejects the Lucas theory, the human can not 
> potentially decide the sentence for the given machine in question.   
> The problem is that the onus for explaining WHY the human can not 
> decide this question -not even potentially- lies clearly with the 
> mechanist.  Without ASSUMING that a particular brand of materialism is 
> true, call it Turing Machine Materialism, (as if there were no other 
> choices!) there's no particular reason to assume the 
> conclusion either.

You totally confuse things here, and forgot who is claiming
what. So let me remind you: the debate is *not* whether the
"Turing Machine Materialism" is true or not. The debate is
whether it is refuted by Lucas Theory or not. I, as a mechanist, have
never pretended to have a logico-mathemastical proof of mechanism
(I have my reasons for believing, not being sure, that 
"Turing Machine Materialism" is most probably true- but these
reasons have no mathematical necessaity, and they are not relevant
to FOM). It is *you* (and Lucas and Penrose) who claim to
have a logico-mathemastical *proof* that "Turing Machine Materialism"
is wrong - and so the onus for *proving* (not just explaining)
any assumption that you use in your argument lies on you. To refute 
your claim for having  a *proof* of your beliefs one does not have to
disproof any of your assumptions, or even to give any reason
why s/he thinks a certain assumption is false. It suffices to isolate
just one assumption you use which you cannot prove, and your
claim for proving your thesis is destroyed.

Let me elaborate. According to what you have written yourself,
the most that Lucas theory shows is an implication of the
form A->B, where A is the claim that human can potentially decide 
the sentence for the given machine, and B is the claim that
human is not a machine. Now your argument has the following form:

We have proved A->B (let us assume that you did)
There is no particular reason to doubt A
Hence B.

Unfortunately, mathematicians and logicans do not accept this 
method of "proof".  In particular, "having no reason to doubt A" 
does not count for them as a proof  of A. This lunaticism
is very unfortunate:  Otherwise I could have earned
1,000,000$ for proving that P is not equal NP - by just pointing out  
that there is no particular reason to doubt this claim...

Wellcome to the world of logic and mathematics.

Arnon Avron