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[ontolog-forum] Fwd: Ontology and Category Theory

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "Len Yabloko" <lenya@xxxxxxxxxxxxx>
Date: Wed, 28 Jan 2009 17:21:25 +0000
Message-id: <W632611739693941233163285@webmail44>
Ed,     (01)

[EB]>Rather than discussing the philosophical and theoretical significance of 
>undefined terms, I would suggest that the proponents of Category Theory 
>for knowledge engineering identify the aspect(s) of category theory for 
>which they see a specific use in knowledge engineering.  Otherwise the 
>discussion is pointless.    (02)

I agree.    (03)

>Now, to that end, Len Yabloko wrote:
>> There is no reliable way in classical Logic to establish and confirm
>> the identity of any object outside of specific context.
>There is no universal reference scheme for 'thing' in terms of 
>properties.  The presumption of classical logic is that terms that 
>denote 'things' in the UoD do just that.  The presumption that distinct 
>terms denote different 'things' is an axiom, which a given theory may or 
>may not include.    (04)

I think the usefulness of any theory depends on what it preserves. Obviously 
axioms of any theory are preserved by that theory. Someone correctly pointed 
that CT theory itself can be stated in classical Logic. But you would have to 
create axioms for any property that you want to preserve, and such axioms may 
not be shared by different theories. The difference in using CT is that certain 
axioms, such as identity and associativity are universal.      (05)

>> CT, on the other hand, includes identity in the very definition of object.
>Citation please.  This sentence means nothing to me.    (06)

http://en.wikipedia.org/wiki/Category_theory#Categories.2C_objects_and_morphisms    (07)

>But identity is an interesting problem in logical theories, and it is 
>possible that this bit of the discussion is actually going somewhere.
>-Ed    (08)

The direction I would like it to go is actually back to the question of theory 
 which I see as the law of identity preservation. I believe that in this sense 
CT provides a natural framework for grounding.    (09)

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