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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Mon, 26 Jan 2009 13:03:55 -0500
Message-id: <497DFB0B.2070602@xxxxxxxx>
Matthew West wrote:    (01)

> I was unaware that Category Theory was distinct from logic.    (02)

Then you have missed the last 40 years of mathematics.
A colleague of mine once described Category Theory as the study of 
mathematical analogy.  It is about the relationships among different 
mathematical systems.  As I remember, Etienne Galois is the first 
example of a Category Theorist (although the term didn't arise until 
about 1960) -- he devised an algebra, proved certain properties of 
permutation groups, and then used those properties to prove that there 
was no closed solution to general 5th order polynomials!  In a similar 
way, the proof of Fermat's Last Theorem (which was the primary 
motivation for Category Theory in the 1960s) was based on a proof of 
equivalences between two "unrelated" mathematical theories.    (03)

While logic is the foundation for all of mathematics, it is actually a 
theory (or multiple theories) in itself.  Category theory is not 
"foundational" in the same way; it is more like an upper ontology, an 
abstraction of abstractions.    (04)

-Ed    (05)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (06)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (07)

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