Re: Penrose vs the Robot

Rupert says...

>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.

Why do you think that there is a program p'? p is not a *theory*.
It is a program, one that is simulating a human being. In particular,
p is a simulation of Penrose. You can *ask* the robot running program
p "What would you do if you knew you were program p?" but if it
*doesn't* know that, then its answer would be pure speculation
(as is Penrose' answer when asked the same question). It depends
on *how* the robot came to find out that it is p. The process
of finding out may very well cause the robot to change other
beliefs.

>> >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.

He hasn't shown a statement that he can star but the
robot clearly cannot. So he hasn't proved his case.

The mistake is that Penrose is confusing formal theories
with computer programs. They aren't the same thing. There
is no single formal theory associated with a computer program
that is programmed to simulate a human being, and so it
makes no sense to ask what follows from adding the statement
"I am p" to this formal theory. There is no such theory, and
there is no way to add such a statement to it.

Human beings do not work (exclusively) by deduction from axioms,
and neither would a robot programmed to simulate a human. There
is no well-defined operation of adding a new axiom (such as "I am
P") to the set of axioms believed by Penrose, and there is no
such operation for robots, either.

--
Daryl McCullough
Ithaca, NY

.

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