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## Re: [ontolog-forum] type free logic and higher order quantification

 To: "[ontolog-forum]" "[ontolog-forum]" k Goodier Fri, 19 Aug 2011 19:27:37 -0400 <1DC9F8BA-624F-42D0-94ED-3038A5C74D1F@xxxxxxxxxxx>
 ```Why do we still use analogies like "long in the tooth" which harken back to our horse trading days?    (01) Sent from my iPhone    (02) On Aug 19, 2011, at 6:53 PM, Rick Murphy wrote:    (03) > Chris, thank you. The explanation below is very helpful in answering my > question regarding predicativity in logics with FO semantics and HO > syntax. > > I enjoyed your paper [1] and recommend it highly for anyone who wants to > understand the design goals of CL. > > -- > Rick > > [1] http://cmenzel.org/Papers/Menzel-KRTheWWWAndTheEvolutionOfLogic.pdf > > On Fri, 2011-08-19 at 14:56 -0500, Christopher Menzel wrote: > >>> In CL, the statement equivalent to Russell's paradox >> >> I'd say: The sentence that *generates* Russell's paradox... >> >>> has a stable truth value: false. No paradox. >> >> Right. In more detail: the chief culprit in Russell's paradox is the >> so-called "naive" comprehension principle that, for any formula φ there >> is a set containing (or a property true of) all the things that are φ. >> In the CL dialect CLIF, this principle is expressed schematically as: >> >> NC (exists (p) (forall (q) (iff (p x) φ))). >> >> In CL, where self-predication is permitted, an instance of NC is: >> >> R (exists (p) (forall (q) (iff (p x) (not q q)))). >> >> A contradiction follows from R immediately. For let r be one of the >> things p said to exist by R: >> >> (1) (forall (q) (iff (r x) (not q q)))). >> >> But CL is type-free, so r itself is among the things being quantified >> over; so by universal instantiation: >> >> (2) (iff (r r) (not r r)), >> >> contradiction. So, as John notes, in CL, sentence R is false; more >> exactly, it is *logically* false; its negation is a theorem of CL. >> >> -chris >> >> >> >> >> >> >> >> _________________________________________________________________ >> 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 >> > > > > _________________________________________________________________ > 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    (04) _________________________________________________________________ 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    (05) ```
 Current Thread Re: [ontolog-forum] type free logic and higher order quantification, (continued) Re: [ontolog-forum] type free logic and higher order quantification, Christopher Menzel Re: [ontolog-forum] type free logic and higher order quantification, Rick Murphy Re: [ontolog-forum] type free logic and higher order quantification, John F. Sowa Re: [ontolog-forum] type free logic and higher order quantification, Pat Hayes Re: [ontolog-forum] type free logic and higher order quantification, John F. Sowa Re: [ontolog-forum] type free logic and higher order quantification, Christopher Menzel Re: [ontolog-forum] type free logic and higher order quantification, Pat Hayes Re: [ontolog-forum] type free logic and higher order quantification, Christopher Menzel Re: [ontolog-forum] type free logic and higher order quantification, Rick Murphy Re: [ontolog-forum] type free logic and higher order quantification, k Goodier <= Re: [ontolog-forum] type free logic and higher order quantification, Christopher Menzel Re: [ontolog-forum] type free logic and higher order quantification, Rick Murphy Re: [ontolog-forum] type free logic and higher order quantification, John F. Sowa