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 nonmathematician 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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