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

Relevant Pages

  • Re: Cantors diagonal proof wrong?
    ... >I'm trying to understand if some fields of math might have wondered off ... reason to believe only 3 spatial dimensions may be possible. ... smoothly from math with a natural analog. ... know about nature a priori by investigating mathematics, ...
    (sci.logic)
  • Re: How many dimensions are there?
    ... explaining that way of nature through tools like ... you believe that SR and GR is physics! ... SR and GR are only math theories. ... that our reality is a physical ...
    (sci.physics.relativity)
  • Re: CORROLORY[sic]:[corollary]
    ... > larger as in an extension of PA? ... Maybe, but it's also math. ... > rudimentary logic to reason about the statement ... After the corolla of a flower. ...
    (sci.logic)
  • Re: Proposal: 6NF
    ... I have never understood what else than math could define ... It does please me that some of mathematics can be used to reason about other parts of mathematics, I guess this is beautiful for some people if not me. ... When it comes to business systems I've yet to meet an executive who isn't satisfied with division by zero resulting in zero. ... On the other hand I can't deny that it is a human trait to maintain motion/activity in a direction that has the fewest obstacles even when the returns diminish rapidly, eg., the anti-smoking movement has basically won its cause where I live but the restrictions on the aging smokers continue to increase in severity. ...
    (comp.databases.theory)
  • Re: Why a Problem?
    ... The most difficult problem I have with SR experts seems to be hid in this one concept: The separation of the models of nature that we used, ... Models of nature are on at least two different levels: just math models, where math functions and relationships are directly used to predict the results of tests, or physical models that are used, upon which math models are eventually developed. ... The understanding that comes with the physical base allows one to understand the theory one level deeper than when one only has the math. ...
    (sci.physics.relativity)