It sounds like time for a stroll through all the va= rious descriptors and what they might mean nowadays. I'm not going to do th= at because my views are probably eccentric, but it does seem useful to take= care of a few things. {lo}, {le} and {la} ex[ressions all refer to things = (in Lojban's generous sense), things that are (somehow) or are called or ar= e named by what comes after. Sentences involving them say that these = things (including one thing but not no thing) somehow have the property asc= ribed to them. Parallel to these are two other sets, one adding -i an= d one adding -'i, for the "mass" and the (C-)set of the things referred to = by the bare forms. I assume C-sets are not a problem, except that a C= -set of things can have 0 members, in which case it does no longer correspond to a bare form. = "Mass" is a horrible word in Logjam history, having meant untold numbers of= things over the years. At the this point, the most useful thing to b= e done with it is to take it as the guaranteed collective sense of {lo}, et= c. Maybe someday a useful notion of mass will get specified and we wi= ll work with it, but it hasn't happened so far.

The point of "half a= can of oranges" is that it means "half of the oranges in the can" (however= many they are), and that is simply (assuming veridicality) {pi mu lo [oran= ges in a can]}, a no problematic expression, unlike the suggestion {lo pi m= u [oranges in a can]}.

Unless you're really good at fuzziness, it is= best not to draw anything from it for ordinary Lojban (which does have fuz= zy numbers when needed). "This can of oranges is in the set of cans o= f oranges to value 0.5" doesn't halve the can nor the oranges, it at most says this is not an absolutely perfect specimen of a can of oranges (= by whatever criteria are in use) -- and making the 0.5 fuzzy doesn't help a= bit.

It is probably worth noting that the discussion of i9nt= ernal quantifiers in CLL is at least misleading. It is not the case t= hat the internal quantifier says how many broda there are altogether, but o= nly the number of those who are of current interest. This is cl= earest with {le}, which relies overtly on a selection, and hardest to see i= n the case of {lo'i}, but applies across the board.

The word I forgo= t last time around is {zo'u}

From: Michael Turniansky <mturniansky@gmail.com>
To: lojban@googlegroups.com
= Sent: Fri, May 20, 2011 2:16:= 50 PM
Subject: Re: [loj= ban] "lo no"

Well, my canned oranges are fuzzy, then!= (I probably should have used them before the sell-by date. They= 'd've been less fuzzy).

&nbs= p; :-D

On Fri, May 20, 2011 at 3:10 PM, Ian Johnson <blindbravado= @gmail.com> wrote:

Yes, except if broda is "x1 is a can= of oranges", I don't think {lo se pi mu mei broda} is a fuzzy set at all. = Half a can of oranges is another can of oranges with its contents cut in ha= lf, so it forms {lo se pa mei broda}. (On the other hand this may ultimatel= y be malgli/malrarbau, which would beg the question of how to reasonably br= iefly express "half a can of oranges" in non-malgli/malrarbau terms.)

You're right, though, that {se te pi mu mei} does make formal sense, it= just has no similarity to its natlang counterpart whatsoever. Consequently= (assuming {mei} still maintains all its places) {pi mu mei} also has no si= milarity to its natlang counterpart whatsoever.

Good catch though.=20

mu'o mi'e .latros.

On Fri, May 20, 2011 at 2:10 PM, Michael Turnian= sky <mturnia= nsky@gmail.com> wrote:

Actually, in fuzzy logic, a member can indeed be only "half in"= a set. Therefore cardinalities of other-than-non-negative integers h= as a place in set theory. No reason why lojbaniss shouldn't be able to talk= about it.

&nbs= p; --gejyspa

On Fri, May 20, 2011 at 2:03 PM, Ian Johnson <blindbravado@gmail.com> wrote:

On the discussion about pi PA mei: ignore x3s and consider the predica= te:
se te pi mu mei
This is "x1 is a set whose 1/2 members are x2". T= his makes no sense; you can't have a set with cardinality 1/2. I think part= of the problem here is that we've never resolved the issue of masses (here= these are not technically masses, but we are considering one object and re= moving some of its components, leaving behind something that resembles the = original object in some clear sense) with respect to set theory. (At least = as far as I know, maybe this was handled at some point.) The ad hoc solutio= n would be to remove the relation to sets from mei altogether; set {lo se m= ei} to be zi'o in all cases and leave it at that. The better solution would= be to figure out, in a formal sense, what exactly about "a can of oranges"= causes it to make sense to say "half of a can of oranges", and more import= antly what makes "a half a person" make only figurative (or, I suppose, cannibalistic, if you're into that sort of thing) sense.

This really has rather little to do with {lo no}, though.

mu'o m= i'e .latros.

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