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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