Re: categorical foundations

[Charles Wells <charles@abstractmath.org>]

This is the right attitude toward doing math.

You can work away with the axioms for categories without caring about
models of the axioms, unless you try to do certain things such as for
example take a limit over all the diagrams of a certain kind in the
category.  Then you have to think about foundations.

You can check what logical constructs you have used in a mathematical
argument, and then maybe you will see you have not used the axiom of
choice or excluded middle, so your models can live in many toposes.

And so on.

This is "just in time" foundations: think about foundations when you
have to, not before.  That is really what most of us do most of the
time.

Charles Wells

On Mon, Nov 16, 2009 at 8:54 AM, Colin McLarty <colin.mclarty@case.edu> wrote:

>
> This is the Hilbert conception where axioms are not asserted as true
> but offered as implicit definition; and so they are not about any
> specific subject matter but may be applied to whatever satisfies them.


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