Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >Daryl McCullough wrote:
>
> >The reason Penrose can't star the sentence "Penrose will never star
> >this sentence" is because self-reference is involved; Penrose's
> >behaviour involves making a prediction about Penrose's behaviour.
>
> Yes, both Penrose' statement and the robot's statement are
> self-referential, in exactly the same way. Neither Penrose
> nor the robot is able to follow the rule that he star
> each and every sentence that he unassailably believes,
> and for exactly the same reason: it is inconsistent to
> do so.
>
> >In the case of the robot, the sentence is merely a statement about
> >numbers. So it looks like we need a different sort of explanation of
> >why the robot can't star the sentence.
>
> It doesn't look that way to me.
>
> Let G_R = "The robot will never star this sentence."
> Let G_P = "Penrose will never star this sentence."
>
> The explanation for why Penrose cannot star G_P is *exactly*
> the same for the explanation for why the robot cannot star
> G_R. In both cases, the person or robot can reason: If I
> star that sentence, I will have made the sentence false.

This seems to me to be questionable in the case where the sentence is a
mathematical one. You can't make a mathematical sentence true or false,
it just is true or false, regardless of what you do.

.

Relevant Pages

  • Re: Penrose vs the Robot
    ... >>>Penrose's suggestion was that the robot could prefix a star to those ... >> Penrose will never prefix a star to this sentence. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >The reason Penrose can't star the sentence "Penrose will never star ... >In the case of the robot, the sentence is merely a statement about ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >> The robot will never star this sentence. ... it comes to Penrose believing his own soundness. ... Penrose will never star this sentence. ... Daryl McCullough ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... Penrose tries to argue it's a ... the set of sentences that the robot would ever star is ... Penrose' unassailable beliefs about pi-1 sentences are sound. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >>Daryl McCullough wrote: ... >>> the same for the explanation for why the robot cannot star ... >>> star that sentence, I will have made the sentence false. ... What's Penrose going to do then? ...
    (sci.logic)