ontolog-forum
[Top] [All Lists]

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

 To: "[ontolog-forum] " Christopher Menzel Thu, 4 Feb 2010 12:28:45 -0600 <666CC29D-ABB5-47AE-B658-3EB9F10EC803@xxxxxxxx>
 ```On Feb 4, 2010, at 12:07 PM, Matthew West wrote: > ... > Well I agree that anything defined by axioms is affected when those axioms >change. However, at least some primitives just are – membership would be one >of them.    (01) I don't understand what it means to say a primitive "just is". A primitive of a system is a lexical item in the basic lexicon of the language of the system. Ideally, given the axioms of the system, a primitive should not be redundant, that is, it should not be definable in terms of the other primitives. A prime example of a primitive is the membership predicate in a theory of sets -- it is obviously non-redundant since it is the only primitive in the system. A good example of a redundant primitive is found in the system PA^, which is the result of adding an exponentiation operator to the language of Peano Arithmetic (PA) (whose primitives are 0, +, •, and ' (the successor operator)) and axiomatizing it as usual. That operator is redundant since (as Gödel showed in a beautiful lemma in his proof of his incompleteness theorem) it can be defined in terms of addition and multiplication.    (02) > Are you therefore arguing that in using membership in the axioms that define >other things, that that affects the meaning of membership itself (as an >example)?    (03) I think what he's saying is simply that if you axiomatize the same primitive P with different axiom sets A1 and A2 and those axiom sets yield different theories T1 and T2, then A1 and A2 provide different, possibly incompatible, accounts of the meaning of P.    (04) > I can see that there are clearly subsets of membership that are say set >membership and type membership, but I’m not sure that that changes the meaning >of membership.    (05) What, other than the axioms you provide for a primitive, could determine its meaning (in a scientifically significant way)?    (06) -chris    (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) ```
 Current Thread Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, (continued) Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Duane Nickull Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Chris Partridge Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Chris Partridge Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel <= Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Pat Hayes [ontolog-forum] Meaning in ontologies and mathematical theories, Patrick Cassidy Re: [ontolog-forum] Meaning in ontologies and mathematical theories, Rob Freeman Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Pat Hayes Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Duane Nickull Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Rob Freeman Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Rob Freeman Re: [ontolog-forum] Foundation ontology, CYC, and Mapping -4D?, Pavithra