Re: Cantor's diagonal proof wrong?

From: num num (num_at_num.num)
Date: 11/22/04 

Date: Mon, 22 Nov 2004 00:30:41 -0500

On 14 Nov 2004 20:29:24 GMT, curt@kcwc.com (Curt Welch) wrote:

>But, is there some way to use language where we cross over from
>very-unlikely, to flat out impossible? I think there might be. I'm trying
>to understand if that point exists and how to describe it.
>
>I'm trying to understand if some fields of math might have wondered off
>into the "flat out impossible" land.

n spatial dimensions can be described in mathematics, yet there's
reason to believe only 3 spatial dimensions may be possible. There we
seem to have math (over 3D space) with no analog in nature flowing
smoothly from math with a natural analog (the 3Ds of space).

>And if they have, what it means for
>those fields of reason and how they relate to the fields of reason which
>have not left the land of the possible.

Seamlessly. If there was something distinct about the subset of
mathematics with analogs in the natural world, then you could find and
know about nature a priori by investigating mathematics, but that's
not the case. The natural world is only known by empirical means, ie,
by observation. We can only know if some subset of math has an analog
in nature a posteriori.

num num

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