From @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET Fri Nov 5 05:46:27 1993 Received: from ELI.CS.YALE.EDU by NEBULA.SYSTEMSZ.CS.YALE.EDU via SMTP; Fri, 5 Nov 1993 10:54:58 -0500 Received: from YALEVM.YCC.YALE.EDU by eli.CS.YALE.EDU via SMTP; Fri, 5 Nov 1993 10:54:52 -0500 Message-Id: <199311051554.AA05037@eli.CS.YALE.EDU> Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 9885; Fri, 05 Nov 93 10:54:41 EST Received: from CUVMB.COLUMBIA.EDU by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 3434; Fri, 05 Nov 93 10:54:10 EDT Date: Fri, 5 Nov 1993 10:46:27 -0500 Reply-To: Logical Language Group Sender: Lojban list From: Logical Language Group Subject: Re: TECH: more thoughts on zi'o To: lojban@cuvmb.cc.columbia.edu In-Reply-To: <199311042100.AA17270@access.digex.net> from "Art Protin" at Nov 4, 93 03:50:00 pm Status: RO X-Status: mi'e .djan. .i la .art. protin. cusku di'e > Though, I don't understand why the most useless and counterintuitive > rules of precedence were chosen for combining the ellipsis and the > negation. I would have bound the negation tighter than the > existential quantifying. For example "not bluer-than" becomes > "there exist a y such that it is false that x is bluer-than > y". If this is supposed to be the distinction between "scalar > negation" and "logical negation", I believe that "scalar negation" > is much more useful to me. If that is the distinction between > scalar & logicial negation, I believe that what I can say with > logical negation is a proper subset of what I can say with scalar. > If that is not the difference, then I am more comfortable with > the use of logical negation but still fuzzy about the distinction. No, it isn't. Both those forms are logical negations, but as you correctly say, the scope varies. (Ey) ~bluer(a,y) is ko'a naku blanymau da It-1 ~not bluer-than some-x which goes into prenex normal form as: da naku zo'u ko'a blanymau da (Ex) ~ : it-1 bluer-than x whereas the other case is: ko'a na blanymau da which becomes naku da zo'u ko'a blanymau da ~ (Ex) : it-1 bluer-than x So by varying between "na" (which always negates the whole thing) and "naku" (which negates only what is following it) you can capture the anything/everything distinction in English. But neither of these is scalar negation. Contradictory negation expresses what is false: "ko'a na blanu" means "it is false that it-1 is blue". Scalar negation says that something OTHER THAN what is expressed is true: "ko'a na'e blanu" means "it-1 is other-than-blue/non-blue". Scalar negations cannot be manipulated logically, and are close-binding. -- John Cowan sharing account for now e'osai ko sarji la lojban.