[FOM] The Lucas-Penrose Thesis

Arnon Avron aa at tau.ac.il
Mon Oct 2 04:14:31 EDT 2006

lucas-Penrose "proof" that humans are not machines belong
to the class of ""Proofs" for the believers". They resemble
in this respect the well-known classical "proofs" for the existence
of God. The main feature of "Proofs for the believers"
is that have never convinced anybody to accept their
conclusion. The only persons who might "accept" them are
those who believe their conclusion at the first place
because of other reasons (Slater's first postings on the subject
provide a good example).

The arguments of Lucas and Penrose have been totally refuted
several times in the past (and indeed in more than one way, but
this is because there are *several* clear mistakes in them,
*not* because it is not clear what is the mistake!). 
Still, the believers continue, and will continue in the future.
They will never agree that their proofs are simply not
proofs (despite the fact that even they should have noticed their
failure to convince others, even those who they otherwise repect
as brilliant logicans. Somehow, when it comes to Lucas-Penrose
argument, those brilliant logicans become extremely stupid, 
and just cannot understand the unshakable logical argument...)
I think that there is really no point in repeating on FOM
the mistakes of Lucas-Penrose proof. Everyone who 
does not quite see what is wrong with them,
and *really*  wishes to understand, needs only read the papers
already cited in this threads. However, in order not to be blamed 
that I was not arguing to the point, I'll refer now to two illuminating
claims made by Lindauer. I am not going to convince him, of course,
And he will certainly come up with some reply. I shall not response
to it, and I would advise others not to continue with this 
fruitless discussion between believers and non-believers (unless 
they have a really new argument that cannot be found in existing 
> The theory "There may be a machine that is a model of your mind but we
> can never say which one it is" is uninteresting, at best obtuse and 
> certainly wouldn't qualify as a scientific hypothesis.  

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"!
    I would add here that the theory that humans are not machine
can much less qualify as a scientific hypothesis than the
abovementioned theory. However, personally I would not classify
it as "uninteresting" because of this. It is philosophically
(and perhaps morally - I am not sure) interesting - and so is
the abovementioned theory (which, "uninteresting" as it is,
I personally tend to believe). 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.

> 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").

Arnon Avron

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