Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >Daryl McCullough wrote:
>
> >> 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.
>
> G_R is not a mathematical statement. It is just the sentence
>
> "The robot will never star this sentence."
>
> Now, in the case of the robot, you can come up with a purely
> arithmetical statement
>
> Star(p,Phi)
>
> which holds if and only if the robot with program p will
> star sentence Phi after being told that he is program p.
> Then we can come up with a sentence
>
> G_p <-> not Star(p,G_p)
>
> Now, we tell both Penrose and the robot "You are program
> p" and ask each of them whether he unassailably believes G_p (and
> if so, to star it). What's Penrose going to do then? Is
> he going to *believe* that he is program p, just because
> we told him that? Probably not. But if not, what basis
> does he have for starring G_p?
>

But the whole point is Penrose thinks he can know he's not the program
p. And if the robot has the same sort of epistemological relationship
to reality as us, the robot can also know it's not the program p, but
that's a contradiction. Penrose concludes the robot can't have the same
sort of epistemological relationship to reality as us.
> --
> Daryl McCullough
> Ithaca, NY

.

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
    ... >> star that sentence, I will have made the sentence false. ... "The robot will never star this sentence." ... What's Penrose going to do then? ... Daryl McCullough ...
    (sci.logic)
  • 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
    ... 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)
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