Date: Fri, 26 Dec 1997 20:23:54 -0500 (EST) Message-Id: <199712270123.UAA08113@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: 2208 X-From-Space-Date: Fri Dec 26 20:23:55 1997 X-From-Space-Address: LOJBAN@CUVMB.CC.COLUMBIA.EDU At 1997-12-26 04:09, Logical Language Group wrote: >If you are referring to the one line definition in the table, then you are >reading mathematical precision into English ambiguity. The one line >definitions do NOT say that they are exclusively binary operators, Yes it does: it says all cmavo in selma'o JOI have clear defintions as sumti connectives; and it then gives those definitions as unambigously binary. In particular, the _Complete Lojban Language_ says "A ce B" is the set with elements A and B, but fails to mention what is allowable A and B. It doesn't work for e.g. either A or B is "C ce D". > and they are not. I agree, but the CLL should really say it explicitly. >>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. > >Nothing ever says that they are considered separately. The CLL gives only a binary definition. >In any event, the table definitions ARE brief and more mnemonic than >explanatory. True in fact, but the CLL claims they are 'clear definitions as sumti connectives'. >The examples following that definition include a 3 element >ce-based set, thus clarifying the wording. This needs to be put in the definition. >>>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. > >True, but it still needs to be used with the grammar of Mex to acieve >mathematical constructs in the regular grammar. "ce" operating outside of >the MEX section of the grammar does not form a mathematical object, but a >linguistic one. A set is a set, just as the number three is the number three. The same mathematical rules apply no matter what context they're in. For instance, "lu'i ti joi ta" is the set {this, that} (two things the speaker is pointing at). It's just as much a "mathematical" set as a "linguistic" one. The "mathematical" operations 'number of members', 'union', 'intersection' etc. all apply the same way. -- Ashley Yakeley, Seattle WA http://www.halcyon.com/ashleyb/