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## Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

 To: "[ontolog-forum]" "doug foxvog" Wed, 3 Feb 2010 17:12:07 -0000 (GMT) <35264.140.203.154.5.1265217127.squirrel@xxxxxxxxxxxxxx>
 Rob Freeman wrote: > > Yes, my key doubt is that "incompatible theories can be described in > terms of common, more basic elements". > > On Tue, Feb 2, 2010 at 12:02 PM, Patrick Cassidy wrote: >> ... >> ... If you doubt that incompatible >> theories can be described in terms of common, more basic elements, try >> presenting some incompatible theories (and show how they are logically >> incompatible) and I will show how it can be done.    (01) > Examples of incompatible theories: the axiomatic set theories of > mathematics.    (02) Why shouldn't these be able to be described in terms of more basic elemets?    (03) > How they are logically incompatible: Search Google on "axiomatic set > theories incompatible" for numerous proofs.    (04) > If you want to build me a FO, can you build me a FO of maths first. > Show me how all theories of maths can be derived from a single theory.    (05) The theories include more than the terms which are used to define them. Although the theories are not DERIVED from a single theory, they should be able to be DEFINED using terms less rigorously defined. Parallel lines can be defined as two straight lines in the same plane that never meet. One subtheory may state that there is exactly one parallel line to a given line through any given point outside that line. A second may state that there are none, while a third may axiomatize that there are an infinite number. None of these three subtheories can be DERIVED from the more basic one, but they can all be DEFINED using its terminology.    (06) There will be terms defined in subtheories which are not included in the more general ones. A basic theory of mathematics would not include groups, fields, transfinites, or complex numbers. The appropriate concepts would be defined in the appropriate contexts, but defined using the terminology of the more general context or using locally defined terms so defined.    (07) -- doug    (08) > -Rob    (09) ============================================================= doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org    (010) "I speak as an American to the leaders of my own nation. The great initiative in this war is ours. The initiative to stop it must be ours." - Dr. Martin Luther King Jr. =============================================================    (011) _________________________________________________________________ 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    (012)
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