Re: Penrose's reply to Chalmers

abo says...

>Penrose' argument used the notion of soundness - correctly or
>incorrectly, I'm leaving that to one side - but he uses it. So you
>need to be able to go from an individual recognizing a statement as
>being unassailably true to it being unassailably true. That doesn't
>work for the robot.

Why do you think it works for humans?

>> How are you planning to determine whether a human or a robot is
>> using the phrase "unassailably true" appropriately? What reason
>> do you have for saying "the human being is correct in assuming
>> that when he holds an assertion to be unassailably true, then it
>> really is"?
>
>Well first, I should say that I think this notion of "unassailably
>true" is not entirely clear to me; but one of the implications of the
>phrase would surely be: if a rational being recognized that S is
>unassailably true, then S *is* true.

But why can't I use the same definition for a robot?

>But Penrose's argument is not based on a human
>being thinking he knows that he is F. He is claiming that he *does*
>know that he is F. If you grant him this premise, then he is F.
>
>For the robot, because you have programmed the meaning of "know" (or of
>"unassailably true"), the implication "individual knows S, therefore S"
>does not hold, because the meaning of "know" has changed.

We can restrict the use of "know" for robots in the same way; we
can say that a robot only knows X if X is true. Of course, that
leads to the possibility that the robot can mistakenly believe that
he knows something. But what reason do we have for thinking that
a human can't mistakenly believe that he knows something?

>I think what you need to be disputing is that Penrose really does know
>that he is F, or really does know the Peano Axioms, or.... But I don't
>see how the introduction of a robot helps you to advance this claim.

Penrose is not arguing that he is formal system F, he is arguing
that he is *not* formal system F. It's a proof by contradiction;
Assume that he is F, and that he knows that he is F, and that he
knows that he is sound. Show that leads to a contradiction via
Godel's theorem.

My point is that I can program a robot to make the same argument,
leading to the same conclusion, that he is not system F. But in
the robot's case, the conclusion is *false*. That shows that
something is wrong with the argument.

Penrose' argument doesn't prove that Penrose isn't system
F, it just proves that *if* Penrose is system F, then either
he doesn't know he is system F, or system F is inconsistent.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Penroses reply to Chalmers
    ... >>being unassailably true to it being unassailably true. ... >>work for the robot. ... seems to be a weak point that Penrose can argue against. ... > Penrose is not arguing that he is formal system F, ...
    (sci.logic)
  • Re: Penroses reply to Chalmers
    ... >>being unassailably true to it being unassailably true. ... >>work for the robot. ... Penrose claims his axioms ... Then some of the axioms are false. ...
    (sci.logic)
  • 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
    ... > I claim that Penrose *cannot* produce such a statement. ... > arithmetic that the robot considers unassailably true. ... > be the sentence "T is consistent". ... Unless you are claiming that "considers unassailably true" is ...
    (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)
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