Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >Daryl McCullough wrote:
>
> >> 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.
>
> But to show that he is not program p, he needs to come up with
> some behavior that Penrose can do, but that program p *cannot*
> do. What behavior is that? If he can't come up with such a behavior,
> then what reason does he have for believing that he is not program p?
>
> I thought that Penrose was claiming that he could star some sentence
> that the robot cannot. But that doesn't seem to be true.
>

Let program p' be everything program p can see to be true on the
assumption that it is program p. Penrose is claiming that he can see,
on the assumption that he is program p, that the Goedel sentence for
program p' is true. Program p can't do that.

> >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.
>
> It's just a mistake on the part of the robot. The same mistake
> Penrose is making, no doubt.
>

But we still need to identify the mistake.

> --
> Daryl McCullough
> Ithaca, NY

.

Relevant Pages

  • Re: Penrose vs the Robot
    ... > p is a simulation of Penrose. ... > on *how* the robot came to find out that it is p. ... > Human beings do not work by deduction from axioms, ... "Human beings do not work by deduction from axioms" ...
    (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)
  • Penrose vs the Robot
    ... I actually think now that Penrose' ... is some robot with a Turing machine brain that is equivalent to ... current state is a computable function of its past inputs. ... of determining what "unassailable beliefs" are implied ...
    (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)