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## Re: [ontolog-forum] Ontology and Category Theory

 To: "[ontolog-forum]" "John F. Sowa" Fri, 30 Jan 2009 11:04:43 -0500 <4983251B.3060305@xxxxxxxxxxx>
 ```Len,    (01) It's important to distinguish the fundamental difference between the physical world and our mathematical theories and constructions. The world has many complex aspects, some of which are easier to represent in mathematical models than others.    (02) LY> I don't think that mathematics in CT in particular were invented > to turn ordinary notions into schizophrenic image of it. There has > to be a level at which identity is ... well identity, at least > for all involved in conversation.    (03) The mathematical notion of identity is very simple, and it's embodied in the notation 'x=y' and the axioms that apply to it:    (04) 1. Reflexivity: For all x, x=x.    (05) 2. Symmetry: For all x and y, x=y implies y=x.    (06) 3. Transitivity: For all x, y, and z, x=y and y=z, implies x=z.    (07) This is the concept of identity in mathematics, including category theory. It is indeed very clear and very simple.    (08) The difficulty results from complexity in the world. For example, is Len at age 2 "identical" with Len at age 22. From the point of view of many physical attributes, the answer is no. From others, such as DNA and fingerprints, the answer is yes. Which point of view is relevant for a particular task will determine which mathematical theory you apply.    (09) There is no "ordinary theory" of identity that can make a decision of which aspects are relevant to any given problem.    (010) 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.    (011) John Sowa    (012) _________________________________________________________________ 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    (013) ```
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