Re: Penrose vs the Robot


Aatu Koskensilta wrote:
> Rupert wrote:
> > Daryl McCullough wrote:
> >
> >>The problem is that what is r.e. is the set of possible
> >>*behaviors* of the robot. We don't have a foolproof means
> >>of determining what "unassailable beliefs" are implied
> >>by that behavior. So we can't go from an r.e. set of
> >>behaviors to an r.e. set of "unassailable beliefs".
> >>
> >>Or, at least I don't see any way to extract the set of
> >>unassailable beliefs from the robot's program. Without
> >>such an extraction procedure, Penrose' argument can't
> >>even get started.
> >
> > Penrose's suggestion was that the robot could prefix a star to those
> > sentences it believed unassailably.
>
> Sure. I could also prefix a star to those statements of mine I think I
> believe "unassailably". I've no reason to suppose the set of the
> statements I'll ever prefix with a star will be consistent.
>
> Unassailabality of beliefs should imply some sort of soundness
> condition, e.g. consistenty, 1-consistency, truth or some such in order
> for Penrose's argument to go trough, which putting stars before
> sentences in no way guarantees. Presumably there is in some sense an
> infinite subset of sentences I would star (what ever this means exactly)
> all of which are true - perhaps this is the set of sentences I
> "unassailably know". I've no idea whether *this* set is (would be?) r.e.
> or not.
>
> I have grave doubts about the "set of all arithmetical truths I can
> unassailably know" being definite enough a thing to say anything about
> its recursion theoretic properties.
>

How about for the hypothetical robot? Penrose tries to argue it's a
definite r.e. set. Do you think his arguments succeed?

> > Are you suggesting there might be
> > things the robot unassailably believes but doesn't prefix a star to?
>
> What reason do we have to think that the set (or the deductive closure
> of the set) of sentences the robot prefixes with stars is consistent?
>

Penrose assumes (for the sake of reductio ad absurdum) that it's a
reasonable model of the human mind, and he thinks this entails at least
pi-1-soundness.

> --
> Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
>
> "Wovon man nicht sprechen kann, daruber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

.

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
    ... >>Penrose's suggestion was that the robot could prefix a star to those ... Are you suggesting there might be ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... >Penrose's suggestion was that the robot could prefix a star to those ... Yes, I'm suggesting that. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... I've no reason to suppose the set of the statements I'll ever prefix with a star will be consistent. ... Unassailabality of beliefs should imply some sort of soundness ... But as in case of humans, e.g. myself, I see no reason to suppose a sentence being prefixed by a star to be necessarily true, or the set of them 1-consistent or whatever soundness condition Penrose needs. ...
    (sci.logic)
  • Re: Penrose vs the Robot
    ... *behaviors* of the robot. ... We don't have a foolproof means of determining what "unassailable beliefs" are implied by that behavior. ... statements I'll ever prefix with a star will be consistent. ... Unassailabality of beliefs should imply some sort of soundness ...
    (sci.logic)
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