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[ontolog-forum] Ontology and Category Theory

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "Len Yabloko" <lenya@xxxxxxxxxxxxx>
Date: Tue, 27 Jan 2009 15:03:17 +0000
Message-id: <W6571016668327451233068597@webmail36>
Dear All    (01)

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.    (02)

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.    (03)

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.    (04)

Len Yabloko, Owner/CEO
Next Generation Software
www.ontospace.net    (05)

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