Re: Can Computers Have Incomputable Concepts?

In article <1182624218.877452.22410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
LauLuna <laureanoluna@xxxxxxxx> wrote:
Now, suppose we are computers. We have the concept but we cannot
compute it. It sounds like there is something other than computing
capacity in our intellectual abilities. 'Sounds like', I say; I do not
assert it. I know very little about computation and dare not state
anything here.

I just ask how it could be.

Let me ask you this. Suppose that a computer program were written that you
could interact with in English. You could type questions, and it would
answer them. Suppose that the computer's answers seemed remarkably
intelligent, and that it was able to explain mathematics and logic and so
forth to you, far more lucidly than any human professor or teacher had ever
done. Suppose that based on the verbal interaction you had with the
computer, you would swear that it "had the concept of arithmetical truth,"
and understood it much better than you do.

Is there anything impossible about this scenario? The fact that
*arithmetical truth* is not computable doesn't mean that *generating
intelligent discourse about arithmetical truth* or *proving theorems about
arithmetical truth* are not computable.

By "having the concept of arithmetical truth," do you mean anything beyond
this? And even if you do, do you see that there is no obstacle to strong AI
here, because for all practical purposes, a computer that can publish
brilliantly original, groundbreaking papers about arithmetical truth has
achieved strong AI, even if in some sense it does not "know" what it is
doing and does not "have the concept of arithmetical truth"?
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.