On Sat, Jan 24, 2009 at 1:09 PM, Matthew West <dr.matthew.west@xxxxxxxxx> wrote:
> Dear Ali,
>
> > I was unaware that Category Theory was distinct from logic. (01)
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). (02)
> Category Theory is an alternative foundation. (03)
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 (04)
> You can for example describe logic in terms of category theory. (05)
And you can describe category theory in terms of logic. (06)
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. (07)
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. (08)
--
Mitch Harris (09)
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