Re: Penrose vs the Robot

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?

--
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. ...
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  • 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 ...
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  • 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. ...
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  • Re: Penrose vs the Robot
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  • Re: Penrose vs the Robot
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    (sci.logic)
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