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

David C. Ullrich ullrich at math.okstate.edu
Sat Oct 11 11:37:33 EDT 2003 
On Sat, 11 Oct 2003 14:21:32 -0000, claird at lairds.com (Cameron Laird)
wrote:

Well, since you crossposted this to sci.math you must be hoping
for replies from that direction:

>In article <QAJhb.6667$dn6.5852 at newsread4.news.pas.earthlink.net>,
>Andrew Dalke <adalke at mindspring.com> wrote:
>>Alex Martelli:
>>> would you kindly set right the guys (such as your
>>> namesake) who (on c.l.lisp with copy to my mailbox but not to here) are
>>> currently attacking me because, and I quote,
>>> """
>>> Software is a department of mathematics.
>>> """
>>
>>And anyone who doesn't think mathematics has its own
>>culture with ideas and even mistaken preferences for what
>>is right and wrong should read
>>
>>The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind
>>
>>to see how Cantor's ideas of transfinite numbers (and other ideas,
>>as I recall, like showing there are functions which are everywhere
>>continuous and nowhere differentiable) were solidly rejected by
>>most other mathematicians of his time.
>>
>>Mathematicians are people as well.
>			.
>			.
>			.
>And let no one assume that these are mere foibles of the
>past that we moderns have overcome; mathematics remains
>stunningly incoherent in what's labeled "foundations".
>There's a wide, wide divergence between the intuitionism
>working mathematicians practice, 

Actually "inuitionism" has a certain technical meaning,
and actual intuitionism is not what most mathematicians
practice. But never mind, I believe I know what you meant.

>and the formalism they
>profess.

Far be it from me to insist we've overcome the foibles
of the past. But:

It's certainly true that mathematicians do not _write_
proofs in formal languages. But all the proofs that I'm
aware of _could_ be formalized quite easily. Are you
aware of any counterexamples to this? Things that
mathematicians accept as correct proofs which are
not clearly formalizable in, say, ZFC?

>'Good thing, too; our age enjoys the blessing of superb
>mathematicians, and I'm relieved that philosophical in-
>consistencies don't (appear to) slow them down.

What's an actual example of one of those philosophical
inconsistencies that luckily doesn't slow us down?

************************

David C. Ullrich
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