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Re: [ontolog-forum] Ontology and Category Theory

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Mitch Harris <maharri@xxxxxxxxx>
Date: Tue, 27 Jan 2009 10:27:59 -0500
Message-id: <553db06d0901270727y3af50b1eg20accfa68456b3a4@xxxxxxxxxxxxxx>
On Tue, Jan 27, 2009 at 10:03 AM, Len Yabloko <lenya@xxxxxxxxxxxxx> wrote:
> Dear All
> Category Theory had been mentioned many times on this forum. I think this 
>subject deserves a separate thread. As usual the attitudes range widely. Some 
>of you consider CT largely irrelevant to subjects discussed on this forum 
>because it lacks both philosophical underpinning of Logic and practical 
>application of Ontology, leaving it pretty much a mathematical discipline.    (01)

 - My opinion is that it is currently irrelevant because there are no
current applications of CT to ontologies, and I don't see any
immediate applications other than loose analogies. Sure, some
application might be developed, but right now I don't see any (but
please don't that let prevent people from at least considering it).    (02)

- I don't think that CT 'lacks...philosophical underpinning of Logic'.
One can 'do' CT given a basis of logic and set theory. One can also
'do' logic/set theory given a basis of CT, but that is a great
oversimplification. CT has a quite rigorous underpinning.    (03)

- I do think that CT is 'pretty much a mathematical discipline'.
That's where most of its application lies currently. It also has great
application in programming semantics, whose real world application has
trickled down a bit to compiler design of some functional programming
languages (Haskell, ML).    (04)

> I strongly disagree. The view of the world that CT takes is indeed very 
>mathematical and may appear to non-mathematician like myself to be completely 
>abstract and void of any relevance to the real world. However, it provides the 
>discipline that is essential to any kind of information engineering and 
>practical application, which classical Logic and Ontology lack IMHO.    (05)

Classical logic and ontologies don't provide discipline? or CT
provides more? I can hardly disagree more with that.    (06)

> For example, (and please correct me if I miss something) there is no reliable 
>way in classical Logic to establish and confirm the identity of any object 
>outside of specific context. CT, on the other hand, includes identity in the 
>very definition of object. This enables what someone called here "ruthlessly 
>extensional" approach to logical inference. I believe this to be a meaning of 
>"grounding", which is admittedly absent in other semantic theories.    (07)

You get out what you put in to them. Logic can have mechanisms for
inferring identity. CT (with a logical underpinning) has axioms that
-assume- the existence of identities. Again, a great
oversimplification.    (08)

'Outside of a specific context'? The context that you specify in a
particular logical presentation would also have to be specified in
your collection of categories.    (09)

Mitch Harris    (010)

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