Re: Cantor's diagonal proof wrong?

From: Curt Welch (curt_at_kcwc.com)
Date: 11/16/04 

Date: 16 Nov 2004 17:57:52 GMT

Russell Blackadar <russell@mdli.com> wrote:

You made multiple interesting comments, but I wanted to just answer this
for now:

> Curt Welch wrote:

> > It may be impossible to build this type of self referencing process,
> > but not impossible to describe it. And that would explain how it could
> > "exist" in the world of mathematics but does not, and can not, exist in
> > the physical world.
>
> Whoa, why are you talking about the physical world at all? If
> you need physical models for your mathematical abstractions, then
> you had better do away with *all* infinite sets.

You probably have not read all my posts because this thread is getting out
of hand. But, I'll repeat what you might have missed. I'm not working on
math. I'm working on AI. I'm an engineer exploring the problem of
building a machine that can do everything we do, including, create, and
debate, all of math.

Before I can build the machine, I have to design it. I have to use
language to describe the operation, and behavior of the machine. I'm
talking about the physical world because I have to build a physical
machine.

If this physical machine can in fact do all the things we do, and, if I
have the power to describe the design of this machine, I will in effect end
up with physical models of mathematical abstractions.

I don't need a physical model of a infinite set, but I do need a physical
model of machine that can talk about an infinite set.

So, where as a mathematician can do what you suggested:

> Why? What if they just "are"?

I can't. I have to answer the question: "why are they there?"

I have to understand why things exist for us. I have to answer the
question why a physical hunk of matter will think that things exist - why
it will think it is conscious and all the complexity that question pulls
in.

I actually believe I have that answered. And at the lower level it makes a
lot of sense, to me at least.

But there's a gap between my lower level understand (i.e., my design for an
conscious machine), and the fact that in math, we have this interesting
stuff going on with infinite sets and 1 to 1 mappings between them.

> It's *your* mystery, so maybe the way *you* use language is
> relevant.

Exactly what I'm saying. I have a contradiction in my language. And damn
it, I'm going to find the source of it and remove it. You do not have the
contradiction. I thought I was hot on the tail of the contradiction which
is why I came to this group and started this thread. But the damn thing is
slipping away from me again when everyone pointed out the flaws in my
logic.

The easy answer I was hoping for when I came here is that there were not in
fact multiple sizes of infinity, mathematicians just like to say they are.
But clearly, there's more to it than that. There is a large body of
evidence that this idea of cardinality is consistent with itself.

The contradiction is not in the large body of consistent evidence (we call
math), if it were, it would have been pointed out 100 years ago. It's
hidden somewhere else in my mind. 

-- 
Curt Welch                                            http://CurtWelch.Com/
curt@kcwc.com                                        http://NewsReader.Com/

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