[FOM] The Lucas-Penrose Thesis

[Robbie Lindauer]

On Oct 2, 2006, at 1:14 AM, Arnon Avron wrote:

> It is amazing how what was supposed to be a *logical* argument
> was forced to become a "this is uninteresting" argument... Well,
> the abovementioned theory is at least as interesting as the
> Lucas-Penrose "proof" is, because the logical possibility
> of this theory totally refutes that "proof"!

As with ALL theories, they rest on unproved metaphysical assumptions.  
For instance, is the law of excluded middle true?  Is there a PROOF of 
this?

In particular, though, the offense of the mechanist is aggregious.  
They are proposing the possibility of an unpresentable theory.  The 
logical possibility of a non-theory?  A ghost-theory.  The theory that 
there may be something but we can't propose any particular candidate 
for it?  Once you look at it, it's gone!  Boo!

Look carefully at what you're believing:

According to the mechanist there IS  a formalism which is a person, BUT 
we can never present that formalism because if we did, we'd be able to 
produce the godel sentence for it, refuting the claim that it was what 
it was purported to be.

This is a clear case of of the "magic happens here" kind of science 
which (I thought) was rejected in the 1600's or so.


>     I would add here that the theory that humans are not machine
> can much less qualify as a scientific hypothesis than the
> abovementioned theory.

That has not been proposed by me, although the theory that Humans are 
souls has been proposed as a scientific theory many times and I think 
it remains unrefuted.  Certainly it is not refuted by the possibility 
of the ghost-mechanism theory above.

My attitude is that the concepts "human" and "machine" are impossibly 
vague, to the point of making such a claim effectively meaningless.  Is 
a start-system a machine?  Is a mind "downloaded into a computer" a 
person?  Such questions and possibilities simply don't have any 
decisive answers as far as I know.  Are you prepared to answer them 
definitively, with proof?

> What is more, it provides a
> partial explnation why we know about our own brain less than
> about most other scientific subjects, and perhaps predicts
> that we shall never be able to fully understand the way it works.
> At least for  me this is very interesting.

We know quite a lot about our brains.  What we know little about is how 
our brains are minds.  How or why we "feel things" or "think things" or 
"know things" or "want things", etc.   There is extensive literature on 
both subjects, but little connecting the two.  For physiology of the 
brain, there are lots of good medical journals, and for introspection 
on how people "feel and are" there is some 4000 years of poetry 
available in writing as a good starting point.

>> The claim is that it is impossible (logically) for a given machine to
>> determine the truth of (any of) its Godel sentences and that it is not
>> (logically) impossible for humans to do decide the godel sentence
>> for that given machine.
>
> If humans are machines, and it is impossible (logically) for a given
> machine to  determine the truth of (any of) its Godel sentences,
> then (by pure logic) it *is* (logically) impossible for humans
> to decide their own godel sentences. Your argument *assumes* that
> humans are not machines - it does not prove it (this circularity
> is typical to the "Proofs for the believers" type of "proofs").

If there is a formalism which minimally produces all the truths of 
arithmetic, we have a mechanical method for producing an undecidable 
sentence sentence for it, right?  It is available to me and to the 
person for whom the system is a proposed representation.  And while it 
may be physically impossible for him to decide or determine what 
his/her undecidable sentence is and decide whether or not it's true, it 
surely isn't logically impossible!  What I can do, they can do, right?  
That's what we mean by "logically possible" not "physically possible".

So the argument is as effective as Godel's argument is.  It may be that 
there is a system of mathematics which is so complex that it is 
impossible (physically) for anyone to tell whether or not there is a 
Godel-undecideable sentence for it.  But this doesn't keep us from 
believing that there is a Godel-undecideable sentence for it, right?

Let me put the question this way:  If -someone- can decide the 
undecidable sentence for a given formalism, then anyone can, logically 
speaking, right?

But all this is rehashing without detail the here unanswered replies to 
objections of Lucas available in his excellent book "The Freedom of the 
Will" and in other publications, mostly available online from his 
website.

An aside to praatika:
	Saying an argument is ineffective don't make it so.  One would have 
to, I think, provide a definitive answer to the detailed arguments by 
Lucas available in many places.  I haven't seen any proposal that 
you've done that somewhere or that it's been done here under our noses. 
  What I  have seen are repetitions of objections that Lucas answered 
twenty-some years ago.

Best Wishes,

Robbie Lindauer