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Re: [ontolog-forum] Ontology and Category Theory

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Mitch Harris <maharri@xxxxxxxxx>
Date: Fri, 30 Jan 2009 13:45:11 -0500
Message-id: <553db06d0901301045j253b6875g199208cd3b5fb979@xxxxxxxxxxxxxx>
On Fri, Jan 30, 2009 at 12:36 PM, Len Yabloko <lenya@xxxxxxxxxxxxx> wrote:    (01)

> my impression of CT remains to be as of an attempt to make abstract reasoning 
>in general (not only mathematical form of it) more precise.    (02)

If anything, the executive summaries of logic and category theory are:    (03)

logic is the study of reasoning.    (04)

category theory is the study of transformations.    (05)

Sure a gross oversimplification, but I think in the appropriate
direction for each, and it allows meaningful distinction and
comparison. It might be difficult to extract the above from wikipedia
or other easy online sources, but still it's a start.    (06)

> I believe this objective to be a paramount to making it useful beyond 
>calculation and in the real of reasoning. If I am wrong and CT is not 
>attempting to do that, then some other theory should. And my observation is 
>that neither classical Logic nor Ontology as discipline are adequate to this 
>goal if they can't "nail down' the identity.    (07)

There's all sorts of discussion within the ontology community about
identity. Whether the unique name assumption (UNA) holds, inferring
subsumption of one concept by another.    (08)

> Again, I not talking about absolute and universal identity (I don't know what 
>it is), but about sufficient level of identification required for business 
>transactions.    (09)

If you're concerned that a particular formalism might be inappropriate
for business transactions, then CT is definitely it. Even
well-educated and, separately, intelligent people have difficulties
with even boolean logic.    (010)

>>No mathematical theory, category theory or anything else, is magic.
>>You have to decide which aspects of the world to represent in the
>>mathematics:  your size and weight or your DNA and fingerprints.
> I don't see a big difference between what mathematicians and magicians do - 
>it is all matter of talent and imagination.    (011)

There's what magicians do and then there's magic. There's no magic.    (012)

Mitch Harris    (013)

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