Re: Penrose vs the Robot


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. There is nothing paradoxical about it.
> If Penrose can't make sense of the sentence, then a
> *consequence* of that failure is that the sentence is
> *true*---he definitely doesn't unassailably believe
> anything that he finds paradoxical or meaningless.
>
> The fact that Penrose doesn't know what to think about G
> does *not* imply that there is anything paradoxical about
> it.
>

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. I think the sentence is really quite similar to the liar
paradox.

> --
> Daryl McCullough
> Ithaca, NY

.

Relevant Pages

  • Re: Penrose vs the Robot
    ... >>Daryl McCullough wrote ... >>> The robot will never star this sentence. ... > it comes to Penrose believing his own soundness. ... the analogy with the liar paradox. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >> then Penrose cannot consistently maintain his soundness ... >This sentence leads to paradox. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... Daryl McCullough wrote: ... it applies to the robot equally well. ... even if the original theory F is sound (for arithmetic ... Penrose believes his own unassailable beliefs to ...
    (sci.logic)
  • Re: This sentence is not true
    ... Daryl McCullough wrote: ... You want to say that it is meaningless, ... and there is no paradox. ... assuming that it *doesn't* have a solution leads ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >>Daryl McCullough wrote: ... >>> be consistent. ... >>> where B is some belief predicate for Penrose. ... What he thinks is that if F is sound, ...
    (sci.logic)