Re: 'Uncountable' doesn't exist

From: Andrew Usher (k_over_hbarc_at_yahoo.com)
Date: 07/28/04 

Date: 27 Jul 2004 22:39:02 -0700

Will Twentyman <wtwentyman@read.my.sig> wrote in message news:<41052cd6_4@newsfeed.slurp.net>...

> My experience with mathematics is that all mathematical statements
> either explicitly or implicitly assert something to be literally true or
> false *given certain axioms and definitions*.
>
> The best example I have seen of this was when I took a course in
> non-Euclidean Geometry. In Euclidean Geometry, you have such statements
> as "Given a line and a point not on the line, there is a unique line
> through the point parallel to the line," as an axiom. A consequence of
> this is that parallelograms have angle sum of 360 degree angles. If you
> change the axiom to "Given a line and a point not on the line, there is
> are at least 2 lines through the point parallel to the line," then you
> get the result that the sum of the angles in a rectangle is strictly
> less than 360 degrees.
>
> As the class went through this material, intelligent people who are
> otherwise skilled in mathematics lost their ability to cope. They could
> not let go of what they thought they knew.

This is because Euclidean geometry is literally _true_ - it uniquely
describes the properties of R^n. Trying to imagine impossible
geometries is hard, hence the less intelligent will not be able to
comprehend it.

Andrew Usher

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