On Tue, Aug 13, 2002 at 10:08:50AM -0700, Tim May wrote:
> * Because toposes are essentially mathematical universes in which
> various bits and pieces of mathematics can be assumed. A topos in which
> Euclid's Fifth Postulate is true, and many in which it is not. A topos
> where all functions are differentiable. A topos in which the Axiom of
> Choice is assumed--and ones where it is not assumed. In other words, as
> all of the major thinkers have realized over the past 30 years, topos
> theory is the natural theory of possible worlds.
How does this compare to the situation in classical logic, where you can
have theories (and corresponding models) that assume Euclid's Fifth
Postulate as an axiom and theories that don't?