Re: Cantor's Theory: Mathematical creationism
From: Curt Welch (curt_at_kcwc.com)
Date: 11/25/04
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Date: 25 Nov 2004 20:21:24 GMT
herc777@hotmail.com wrote:
> Intuitively this is a new sequence, but that is not a *property* of the
> number, its merely DEFINED AS DIFFERENT.
> This is why A still holds:
> ------------------------------------------------------------
> An infinite number of people each toss a coin infinite times, can you
> guarantee a new sequence of heads and tails?
> ------------------------------------------------------------
Look at what you have written above and think about it in terms of what
I've been posting - that math, and Cantor's proof is a poof about the
nature of language, and not a proof about the properties of the physical
world.
In the domain of language, anything you can DEFINE, is REAL (inside the
domain of language). Above you write: "DEFINED AS DIFFERENT" as if it was
no proof of existence. But inside the domain of language, existence is
defined as anything you write, or think. If you can think it, it does
exist - by definition. It's valid and real in that domain. The only thing
that's important to prove is if it's logically consistent with the rest of
math. And Cantor's proof is consistent with the rest of math.
In you counter argument, you bring into the picture, a physical process.
That's what I was doing as well. Because my personal focus is to try and
explain everything in physical terms. But the physical world is not in the
domain of math. It's pure language abstraction. You are bring in
properties of the physical world, and trying to use those properties to
argue the validity of Cantor. And that's not math. You can't bring in
facts about elephants to support an argument about airplanes. Elephants
can't fly, so clearly it's impossible to fly.
The only thing that is important in math is for the words to be consistent
with each other. And all the different words used to talk about the nature
of Cantor's work are consistent with each other - for the most part - there
are these edge issues which people continue to explore, but the core work
of set theory is all consistent with itself, and that's all that's
important.
You and I just have to understand that the nature of the physcial world is
not important when understanding the nature of the formal language of math.
-- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/
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