Re: Geometry as Physics, and the foundations of mathematics

Jason Bode (jason_bode@hotmail.com)
Sun, 06 Jun 1999 21:25:16 PDT

> >Math has no solid basis now, in fact it is based on a set of undefined
> >terminology, determined by what you choose it to be. For just one example
>of
> >this, look at the different geometries. Enough information has been
>around
> >since at least 3000 years ago, but people made assumptions that weren't
> >correct (such as Euclid's 5th postulate) which led them off track.
>Actually Euclid's 5th postulate IS correct, for its, and non->Euclidean
>geometries are, effectively, mere extensions of Euclidean >geometry,
>because they effectively assume the introduction of >something not present
>in Euclidean geometry: Curvature of the plane (or of space). Further,
>geometry is not really a branch of >mathematics, anyway, and the failure to
>grasp this is a major source >of the confusion surrounding the status of
>mathematics. Geometry is >a "purified" and formalized branch of PHYSICS,
>which is why we use >terms like "space," "edge," "angle," "solid,"
>"surface," "plane," >and "curve," and it's why we can so DIRECTLY represent
>geometrical >figures with physical drawings.

A couple comments: noone can prove that Euclid's 5th postulate is correct.
Margin of error always leaves room for all 3 types of geometries. I agree
that it appears true in general, and I would suspect it is, but it is not
necessarily so.
Assuming "the introduction of something not present in Euclidian geometry"
is adding to it and the 5th postulate CANNOT be proven from the other
postulates. (It's never been proven, and the independence of it has been
proven; I'll give some names for backup if you wish)
And geometry most certainly IS a branch of math. Trust me, I'm a math major
and I just finished a math history class where we investigated mathematical
roots and it's development. If you wish, I'll ask my professors if geometry
is math or physics, and see what they say.

>But what I wanted to remark on, mostly, was the idea that "Math has >no
>solid basis now." This is not true. Math has a solid basis, but >many (if
>not most) people don't know what it is because of >confusions caused by bad
>philosophy, especially bad epistemology. >The basis for mathematics is
>logic and the fact that one thing is >more than no thing, or: 0 < 1. The
>rest of mathematics is the >working out of the implications of this fact.
Try reading Godel. He proved that no matter how many axioms you start with,
there will always be statements within the system governed by those axioms
that cannot be either proven or disproven. The second axiom he proved is
that the consistency of any system of axioms is one of those improvable
statements. You cannot prove math, you can only prove mathematics based on
your assumptions.

>Okay, I may exaggerate a little, but you get the idea: The >foundation of
>mathematics is no big mystery, unless it's a mystery >that one apple is
>more apples than no apples at all. That this is >true doesn't seem
>mysterious to me.
The foundation of mathematics doesn't exist. Again, read Godel, and maybe
some Hilbert to see how his quest to provide a foundation for math failed
miserably. It simply cannot be done.

If you want more information, I could refer you to my professor, who knows
the course materials far better than I (obviously). Thanks,

Jason

_______________________________________________________________
Get Free Email and Do More On The Web. Visit http://www.msn.com