Re: Can Computers Have Incomputable Concepts?

On Jun 24, 4:31 pm, A.L. <f...@xxxxxxxx> wrote:
On Sun, 24 Jun 2007 00:22:22 -0700, LauLuna <laureanol...@xxxxxxxx>
wrote:



That is exactly why I'm asking for help. I don't know what it means
for a computer to have a concept. I'm suggesting to assume we are
computers and all possible human cognitive behavior is computation.
Then, since we undoubtedly have the concept of arithmetical truth,
there are computers that have that concept. But the concept is
incomputable; how is this possible?

See this:

http://www.scottaaronson.com/democritus/lec10.5.html

A.L.

Thanks for the link.

I'm familiar with Gödel's theorem and with Lucas and Penrose's
arguments. I find Penrose argument inconclusive but they are usually
deemed weaker than they actually are.

In Shadows of the Mind Penrose argues convincingly that human
mathematical intelligence cannot be simulated by a knowably sound
algorithm.

Indeed if 'human mathematical intelligence' denotes rigidly, then
whatever it denotes cannot be a knowably sound algorithm. But it still
must be proved:

1. that that expression actually refers to some well defined object
2. that human mathematical intelligence -if it exists as such-
cannot be an unsound or a unknowably sound algorithm.

The first seems to me the hardest to prove.

Regards

.