Date: Tue, 23 Dec 1997 18:45:21 -0500 (EST) Message-Id: <199712232345.SAA10917@locke.ccil.org> Reply-To: Ashley Yakeley Sender: Lojban list From: Ashley Yakeley Subject: Set Theory Woes X-To: Lojban List To: John Cowan Status: OR X-Mozilla-Status: 0001 Content-Length: 1604 X-From-Space-Date: Tue Dec 23 18:45:22 1997 X-From-Space-Address: LOJBAN@CUVMB.CC.COLUMBIA.EDU For a language that claims to be logical, Lojban really ought to have better words for set theory. All I can find is "ce", "jo'e", "ku'a" and "pi'u", and there do not seem to be words, even in mekso, for the empty set, the set containing a single given element (except for "X ce X") or the set difference operator (the set of objects in A but not B). 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}. The cmavo "ce'o" (but not "joi") is similarly inconsistenly defined. As for masses, it should be made clear that there is no mathematical concept that corresponds to "mass" as such, instead, one can consider sumti as sets that when speaking of individuals contain one member, and when speaking of masses contain typically more than one member. The sumti-set of a sumti that referred to a set S would then be a set with the one member S (itself a set). Therefore, the "ce" (but probably not "ce'o") problem could be solved with a set-making cmavo that when applied to a single item referred to the set containing just that item, and when applied to a mass referred to the set containing all the items in the mass. When does the baseline period end? -- fe'oca'emi'e tricrfraksizeicecmu ji'a mi'e .aclin.