Date: Wed, 24 Dec 1997 07:40:16 -0500 (EST) Message-Id: <199712241240.HAA26640@locke.ccil.org> Reply-To: Ashley Yakeley Sender: Lojban list From: Ashley Yakeley Subject: Re: Set Theory Woes X-To: Lojban List To: John Cowan Status: OR X-Mozilla-Status: 0011 Content-Length: 1346 X-From-Space-Date: Wed Dec 24 07:40:17 1997 X-From-Space-Address: LOJBAN@CUVMB.CC.COLUMBIA.EDU At 1997-12-24 03:38, Logical Language Group wrote: >>Worse still, "ce" is inconsistently defined in the refgram. On page 354, >>"A ce B" is defined as the set with elements A and B (or {A, B}). >>Logically, and together with the left-grouping rule, this means that "la >>frank. ce la .alis. ce la djeimyz." means {{Frank, Alice}, James}, that >>is, a set with the two members James and the set of Frank and Alice. Page >>355 inconsistenly assigns this sumti to the more useful meaning {Frank, >>Alice, James}. > >I would not think that left grouping constitutes bounding of the set. It's not left-grouping alone that bounds the set: it's the binary nature of "ce" (as defined on p354) together with left-grouping that bounds the set. The only solution is to define "A ce B ce C ce D..." as a special form where the "ce"s cannot be considered separately. It's irregular, inasmuch as "A ce B ce C" is a set with three members, and "A ce B" is a set with two members, but "A" is not typically a set with one member. >If you want to formally get into mathematical set spectification, then you >need to goi fully into Mex, where you have parenthesis to set bounds on the >set definition. Fine, but this kind of mathematical set specification may turn up in ordinary Lojban utterances. -- fe'oca'emi'e tricrfraksizeicecmu .iji'a ca'emi'e .aclin.