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.

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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?