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Re: [ontolog-forum] Ontology and Category Theory

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Len Yabloko" <lenya@xxxxxxxxxxxxx>
Date: Fri, 30 Jan 2009 21:56:10 +0000
Message-id: <W5152227891197351233352570@webmail17>
Mitch,    (01)

>On Fri, Jan 30, 2009 at 12:36 PM, Len Yabloko <lenya@xxxxxxxxxxxxx> wrote:
>> 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.
>If anything, the executive summaries of logic and category theory are:
>logic is the study of reasoning.
>category theory is the study of transformations.    (02)

Reasoning and transformations are closely related to each other, even in strict 
mathematical sense- I believe.    (03)

>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.
>    (04)

It is not that difficult to extract since 'morphisms' are at the very 
definition of Category. What is difficult is to understand what it is 
'appropriate direction' for each. I dawned on me long time ago that both 
complement each other, but I still can't figure out why everybody insists on 
keeping them separate (and seemingly as far from each other as possible). What 
am I missing?    (05)

>> 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.
>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.
>> 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.
>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.
>    (06)

I always thought that you don't need to be a specialist to apply someone else 
specialty to your work. Isn't it the job of specialist to make it possible?
It is clear that transformations are at the heart of everything, including 
identity. Why not borrow some principles and results from CT?    (07)

>>>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.
>There's what magicians do and then there's magic. There's no magic.
>    (08)

Identity should not be a matter of magic - don't you agree?    (09)

>Mitch Harris
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