Re: Can Computers Have Incomputable Concepts?

On Jun 23, 6:11 pm, t...@xxxxxxxxxxxxx wrote:
In article <1182610545.086255.12...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

LauLuna <laureanol...@xxxxxxxx> wrote:
Why should there be at all any computers endowed with the concept of
arithmetical truth? Well, we humans have that concept; if no computer
could have it, there would be a seemingly too easy refutation of
computationalism, mechanism or Strong AI.

It's easy to say, "we humans have that concept," but that glib-sounding
statement is the crux of the matter. Probably when you say it, you are
presupposing some commonsense view of consciousness, which you have no
difficulty attributing to human beings but which you hesitate to attribute
to computers. However, coherently articulating just what that theory of
consciousness is, and how we know that humans have it and that computers
don't, is a notoriously trickly philosophical minefield.

One can back off that minefield by saying that by "we humans have that
concept" means only that human beings are able to reason about arithmetical
truth and prove theorems about it and so forth. But computers are able to
mimic that reasoning, because one can write down axioms for the concept of
arithmetical truth. The deductions humans make from these axioms are the
usual logical deductions that are standard made in mathematics. So there is
nothing here that humans demonstrably can do and computers can't, if you
refuse to open the lid and look inside the brain. For example, computers
can't decide whether an arbitrary arithmetical statement is true, but
neither can humans.
--
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

But this is not the point. I'm not claiming here that there is
something humans can do and computers can't. I'm just proposing a
difficulty of quite another type.

We do have the concept of arithmetical truth. Otherwise we wouldn't
know what we are speaking about when we say it is not computable and
Gödel's and Tarski's theorems would mean nothing at all.

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.

Regards

.

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