To: |
"[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx> |
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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) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (08) |

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