Re: Penrose vs the Robot


Daryl McCullough wrote:
> Rupert says...
>
> >Daryl McCullough wrote:
>
> >> But you were arguing *against* making the distinction between
> >> mathematical statements and nonmathematical statements, when
> >> it comes to Penrose believing his own soundness. The statement
> >> for Penrose
> >>
> >> Penrose will never star this sentence.
> >>
> >> is just as problematic for Penrose as "The robot will never star
> >> this sentence" is for the robot. The fact that we can turn the
> >> latter sentence into a Diophantine equation doesn't seem relevant
> >> to me.
>
> >Well, at least it shows that the latter sentence is definitely
> >meaningful. We might have some doubts that the former is, in view of
> >the analogy with the liar paradox.
>
> How can you doubt the meaningfulness of the statement that
> Penrose will place a star on a particular statement? There
> is no analogy with the liar paradox. It doesn't lead to
> a contradiction for the statement to be true, and it doesn't
> lead to a contradiction for the statement to be false. So
> I don't see any analogy with the liar paradox. It's just
> an ordinary statement about the future actions of Roger
> Penrose. If there existed a complete enough theory of
> Roger Penrose, then you could use that theory to figure
> out whether the statement is true or not.
>
> --
> Daryl McCullough
> Ithaca, NY

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. 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.

.

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
    ... >>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)
  • 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 will never prefix a star to this sentence. ... > that both Penrose and the computer simulation are told the ...
    (sci.logic)
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