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

Michele Dondi bik.mido at tiscalinet.it
Wed Oct 15 16:57:11 EDT 2003 
On Mon, 13 Oct 2003 18:03:02 -0500, David C. Ullrich
<ullrich at math.okstate.edu> wrote:

>>I am not claiming that it is a counterexample, but I've always met
>>with some difficulties imagining how the usual proof of Euler's
>>theorem about the number of corners, sides and faces of a polihedron
>>(correct terminology, BTW?) could be formalized. Also, however that
>>could be done, I feel an unsatisfactory feeling about how complex it
>>would be if compared to the conceptual simplicity of the proof itself.
>
>Well it certainly _can_ be formalized. (Have you any experience
>with _axiomatic_ Euclidean geometry? Not as in Euclid - no pictures,

No, I have no experience with it. Just heard it exists: I presume
you're talking about the work of Hilbert... but then I'm not sure that
it provides a full formalization! It's clear though that it brings one
step forward towards formalization.

>nothing that depends on knowing what lines and points really are,
>everything follows strictly logically from explictly stated axioms.
>Well, I have no experience with such a thing either, but I know
>it exists.)

 :-) [should have read ahead...]

>Whether the formal version would be totally incomprehensible
>depends to a large extent on how sophisticated the formal
>system being used is - surely if one wrote out a statement
>of Euler's theorem in the language of set theory, with no
>predicates except "is an element of" it would be totally
>incomprehensible. Otoh in a better formal system, for
>example allowing definitions, it could be just as comprehensible
>as an English version. (Not that I see that this question has

In any case I'm sure too that *that particular proof* can be
formalized! But, even if I am under the impression that most proofs,
for some meaning of "most", would be affected by the concern expressed
above, somehow I feel like the effect with this one would be "one
order of magnitude" stronger, to say the least!

>any relevance to the existence of alleged philosophical
>inconsistencies that haven't been specified yet...)

In fact, it has no relevance to that matter: I thought that my
introduction should have made that clear. My comment is something I
happend to think about sometimes; your words just reminded me of it
and this seemed to be the right chance to talk about it. No more than
that, no more than a naive comment...


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
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