Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >Daryl McCullough wrote:
> >> Rupert says...
> >>
> >> >> If you consider the "Godel sentence for Penrose"
> >> >>
> >> >> G <-> Penrose does not unassailably believe G
> >> >>
> >> >> then Penrose cannot consistently maintain his soundness
> >> >> with respect to sentences such as G.
> >>
> >> >This sentence leads to paradox.
> >>
> >> No, it doesn't.
>
> >The reason Penrose "can't make sense" of the sentence is that he argues
> >about it to himself and gets into contradictions, same as with the liar
> >paradox.
>
> Yes, it certainly has similarities with the liar paradox, but in
> contrast with the liar paradox, it isn't a paradox. It doesn't
> lead to a contradiction. For Penrose to *believe* it leads to
> a contradiction, but for the sentence to be *true* doesn't lead
> to a contradiction.
>
> So, yes, it is like the liar paradox, except that it isn't a paradox.
>

The contradiction only appears at the level of Penrose's belief system,
so it's not as startling. However, when Penrose reasons about this
sentence, he almost certainly will get himself into contradictions. I
think that's a good enough reason to call the sentence paradoxical.
> --
> Daryl McCullough
> Ithaca, NY

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