Why should a mathematician be interested in QEDemail@example.com (David McAllester)
From: firstname.lastname@example.org (David McAllester)
Date: Thu, 22 Apr 93 09:55:39 EDT
Cc: email@example.com, firstname.lastname@example.org
In-reply-to: david mumford's message of Wed, 21 Apr 93 16:04:58 EDT <9304212004.AA05327@math.harvard.edu>
Subject: Why should a mathematician be interested in QED?
I can't help responding to David Mumford's comments about Bourbaki.
The hope was that a fairly small
simple set of basic structures were the basis of most research.
This seems to express the hope that all mathematical concepts can be
made to be elaborations of a small set of very general basic concepts
(such as topology, algebra, and "structure").
These to me to be an orthogonal issue to the question of foundations.
A foundational system, such as ZFC, seems neutral on the question of
whether one should elaborate a small set of general difinitions or
make a much larger set of independent and much more concrete definitions
with abstraction coming later. A foundational system such as Ontic
can accomodate either style. The reals can be defined directly as
Dedikind cuts, or defined indirectly by adding axioms to the concept
of a topological field.