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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 21:46:16 -0500
Message-id: <553db06d0901301846j34bef83clcee143f3ffc94aef@xxxxxxxxxxxxxx>
On Fri, Jan 30, 2009 at 4:56 PM, Len Yabloko <lenya@xxxxxxxxxxxxx> wrote:
> Mitch,
>>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.
> Reasoning and transformations are closely related to each other, even in 
>strict mathematical sense- I believe.    (01)

Sure. Everything is different, everything is the same. It depends on
the details and context.    (02)

>>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.
> 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?    (03)

I don't -insist-, I just don't see anything immediately useful from
category theory. It's hard to tell you that what you see isn't there,
because it very well may be there. I could see maybe some sort of
analysis of hierarchies, say mappings between trees, from a category
theory perspective, but that would be an abstract analysis of such
mappings in general, not really about the particulars of one given
hierarchy compared to another one (which is what most ontologists in
practice might care about; to be open, the particular mapping would
probably be better informed by combinatorics rather than logic, if one
really has to put a label on the methods).    (04)

>>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.
> I always thought that you don't need to be a specialist to apply someone else 
>specialty to your work.    (05)

I've always heard that you have to study ten times as much statistics
as you actually use. I guess it depends on the specialty.    (06)

> It is clear that transformations are at the heart of everything, including 
>identity. Why not borrow some principles and results from CT?    (07)

Sure, that does seem promising said that way. Since identity is an
important concept maybe some of the ideas about identity involve in CT
might be useful (but that concept of identity in CT, as others have
mentioned, is very specific, whereas in logic, you have a lot more
freedom to specify exactly what you mean by identity).    (08)

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

Sure.    (010)

Mitch Harris    (011)

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