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*To*: John Cowan <cowan@LOCKE.CCIL.ORG>*Subject*: Re: more on logical issues*From*: Jim Carter <jimc@MATH.UCLA.EDU>*Date*: Wed, 22 Nov 1995 08:58:08 -0800*In-Reply-To*: Your message of "Tue, 21 Nov 95 23:16:56 CST." <9511220522.AA19419@julia.math.ucla.edu>*Reply-To*: jimc@MATH.UCLA.EDU*Sender*: Lojban list <LOJBAN@CUVMB.BITNET>

Steve Hazel <hazel@TURING.CS.STEDWARDS.EDU> writes: > While the English syntax is not flawed, the logic may be. The basic question > here, I think, is whether or not it is logical to say that a nonexistant thing > or nonexistant things ("even prime numbers greater than three") can be given > properties ("are multiples of 27"). That's the whole point of the argument (which has been running for several years on and off): when the speaker says the "all" quantifier, under what circumstances does he claim that the number of quantified items is nonzero? Certainly in mathematics it's very common to identify some set, prove two properties for all its members, then prove that the same item can't have both properties, thereby proving that the set is empty. Pragmatically, natural languages were created through the speech of workers, peasants and soldiers who never took a course in math or logic, and it's common (if not universal) for them to commingle the claim that a set is nonempty, with an iteration over all its members, as in "all unicorns drive Chevys": "there is at least one unicorn" and "unicorn[0] drives a chevy and unicorn[1] drives a chevy and ..." My own feeling on the matter is that the pan-iteration implied by the universal quantifier should be kept separate from any claims about count. Example: "All even primes are less than 3" (not by language implying that there are any), and then, if you care, "... and at least/exactly one of them exists". That may not be the historical interpretation of "all"/"omni"/etc. in natural languages, but Lojban is supposed to be _logical_, and I think we can handle a little modularity. James F. Carter Voice 310 825 2897 FAX 310 206 6673 UCLA-Mathnet; 6115 MSA; 405 Hilgard Ave.; Los Angeles, CA, USA 90095-1555 Internet: jimc@math.ucla.edu (finger for PGP key) UUCP:...!{ucsd,ames,ncar,gatech,purdue,rutgers,decvax,uunet}!math.ucla.edu!jimc

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