Science is a human activity (was: Python syntax in Lisp and Scheme)

[Michele Dondi]

On Tue, 14 Oct 2003 17:18:34 -0500, David C. Ullrich
<ullrich at math.okstate.edu> wrote:

>Of course it's not. But it seems to me that his skepticism regarding
>whether that proof _can_ be formalized must in fact be skeptism
>regarding whether it's possible to state all the necessary axioms
>and deduce the theorem without any appeal to the way things
>look.

As I have stressed in my other post, I'm *not* skeptic about the fact
that that proof can be formalized!

I'm simply puzzled thinking of how it would be done, since IMHO it is
a proof that indeed *does* make heavily appeal to the way things look,
and in this sense it is so simple that often one can find it in
popularization books.

(BTW) Also, since you mentioned axiomatic euclidean geometry, I just
don't know anything about it[*], but I don't know wether it is
possible in its formalism to define/talk about "continuous
transformations", that are indeed the basis of that proof.

So, if I am right in my assumption above, while the object of the
proof can be reasonably defined in axiomatic euclidean geometry,
either the theorem can't be proved in that teory or there exists an
alternative proof that does not use continuity arguments.


[*] This means: "so I may well be wrong"!


Michele
-- 
> Comments should say _why_ something is being done.
Oh? My comments always say what _really_ should have happened. :)
- Tore Aursand on comp.lang.perl.misc