Dear Mitch, (01)
We seem to be more or less on the same page. (02)
> > > I was unaware that Category Theory was distinct from logic.
> It's all math. Category theory is usually considered coming out of the
> subdomain of algebra (though its primary examples are in topology;
> logic (-mathematical- logic that is) is usually considered a quite
> separate subdomain of mathematics. That said, you can make meaningful
> connections between any two subdomains (e.g. Categorical logic).
> > Category Theory is an alternative foundation.
> Yes, but that's at a different idea of foundation. Logic (and set
> theory is considered a foundation of mathematics with respect to
> truth. Category theory provides a foundation
> > You can for example describe logic in terms of category theory.
> And you can describe category theory in terms of logic. (03)
[MW] Indeed, that is what I meant by being an alternative foundation.
> I think category theory is a red herring here (as well are probably
> most of my comments). Category theory is a fascinating unifying theory
> of mathematics, and is also quite useful in its applications to
> programming language semantics, I would think that any benefit that
> you could get out of it would be way beyond the learning curve. And
> that benefit could be gotten with, well, simplifying to semantic
> networks, though I'm sure there are some nice tricks that category
> theory provides that logic (logical theories?) can use. (04)
[MW] Actually I think Category Theory may provide some useful ways to do
inferencing in a more structural way, but that is really just a hunch (or
conjecture if you want to be a bit more formal). (05)
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> Which is all to say that mathematical formalisms are pretty useful
> whether we are using something called category theory or one of the
> many varieties of logic.
> Mitch Harris
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