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)
Regards (06)
Matthew West
Information Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.matthew-west.org.uk/ (07)
This email originates from Information Junction Ltd. Registered in England
and Wales No. 6632177.
Registered office: 2 Brookside, Meadow Way, Letchworth Garden City,
Hertfordshire, SG6 3JE. (08)
>
> 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
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> (09)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (010)
|