Date: Fri, 26 Dec 1997 07:17:15 -0500 (EST) Message-Id: <199712261217.HAA21934@locke.ccil.org> Reply-To: Logical Language Group Sender: Lojban list From: Logical Language Group Subject: Re: Set Theory Woes X-To: AshleyB@HALCYON.COM X-cc: lojban@cuvmb.cc.columbia.edu To: John Cowan Status: OR X-Mozilla-Status: 0011 Content-Length: 2433 X-From-Space-Date: Fri Dec 26 07:17:16 1997 X-From-Space-Address: LOJBAN@CUVMB.CC.COLUMBIA.EDU >>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. 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, and they are not. The one-liner is a definition, and not a trnaslation, and you cannot apply it by simple substitution recursively to a text. The words "the set with" do not recurse. >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. Grammatical constructs in Lojban can go on indefinitely if based on recursive grammatical constructs. It is the nature of such recursive rules in the grammar that they are "the same as" theirnon-recursive form. But "A" does not have a "ce" in it by itself, so one can make no inferences about it being a set or not. In any event, the table definitions ARE brief and more mnemonic than explanatory. The examples following that definition include a 3 element ce-based set, thus clarifying the wording. >>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. I can try to make this more clear in the cmavo list definition (which does not have quite so limited a character length as the one-line-defintiions in the book). lojbab ---- lojbab lojbab@access.digex.net Bob LeChevalier, President, The Logical Language Group, Inc. 2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273 Artificial language Loglan/Lojban: ftp.access.digex.net /pub/access/lojbab or see Lojban WWW Server: href="http://xiron.pc.helsinki.fi/lojban/" Order _The Complete Lojban Language_ - see our Web pages or ask me.