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Re: [ontolog-forum] intangibles (was RE: Why most classifications are fu

 To: "[ontolog-forum] " Christopher Menzel Mon, 8 Aug 2011 11:44:45 -0500 <44706AA2-DC90-4BEF-BDF9-6F0EB1B85937@xxxxxxxx>
 On Aug 6, 2011, at 9:14 AM, John F. Sowa wrote:...In his modal logic, CSP also distinguished five different kindsof modalities.  In his existential graphs, he used differentcolors to represent them (he had a box of colored pencils): 1. Logical possibility.  A proposition p is possible iff it is not    provably false.  Impossible means inconsistent or provably false.This won't do. Provably false in what theory? Consider the continuum hypothesis (CH) that all uncountable sets of real numbers are the same size.  By well known results of Gödel and Cohen, CH is independent of ZF set theory.  Hence, neither CH nor not-CH is provably false in ZF. So both CH and not-CH are possible according to Peirce?Clearly there is a sense of possibility that is independent of any theory. CH, in particular, is either true or false — either all uncountable sets of reals are the same size or some uncountable sets of reals are smaller than others. Hence, either CH or its negation is impossible, full stop, regardless of their consistency with our best theory of sets.If you believe, as I suspect you might, that the uncountably infinite is the villain here, note that basically the same argument can be run vis-á-vis Peano Arithmetic and its Gödel sentence (relative to some coding scheme), which we in fact know to be true in the natural numbers (hence necessarily true) but independent of PA.-chris
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 Current Thread Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), (continued) Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Obrst, Leo J. Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Simon Spero Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), Rich Cooper Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), Rich Cooper Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Rich Cooper Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Christopher Menzel <= Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), Christopher Menzel Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), Christopher Menzel Re: [ontolog-forum] intangibles (was RE: Why most classifications INare fuzzy), Christopher Menzel Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Christopher Menzel Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), Christopher Menzel Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), John F. Sowa Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy), doug foxvog