Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >What about Penrose's second argument?
> >
> >Penrose doesn't know whether he is F, but let F' be F supplemented by
> >the assumption that Penrose is F.
>
> I assume you mean some fixed point: F' is F supplemented by some
> statement S satisfying
>
> S <-> Penrose is F supplemented with S
>

No, I don't think I necessarily mean that. If Penrose can be simulated
by a Turing machine, then we can consider the set of sentences that he
would prefix a star to, on the assumption that he is F. And this set
would have to be r.e.

> What reason is there to believe that F' is sound, even if F
> is?
>

Well, if Penrose's reasoning faculty is sound then adjoining the true
hypothesis that F is sound would only yield true statements.

> >On the assumption that he is F, Penrose can see the truth of
> >the Goedel sentence for F'. Therefore, if Penrose is actually F,
> >F' proves its own Goedel sentence and therefore
> >is not sound.
>
> I think that conclusion is correct. F' would be unsound
> (probably inconsistent). That doesn't at all imply that
> Penrose isn't F. It means that F proves not(S). But that's
> true---Penrose *isn't* F supplemented with S, he's just F.
>
> I'm not sure whether F would be able to prove "Penrose is
> not F". But even so, it wouldn't be a disaster---it would
> show that his beliefs were unsound, but Penrose didn't
> claim that they were sound, he only claimed the pi-1
> consequences were sound. And "Penrose is F" is not
> an arithmetical sentence.
>

It probably is essential to Penrose's argument that his reasoning
faculty is completely sound.

> --
> Daryl McCullough
> Ithaca, NY

.

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