From pycyn@aol.com Wed Mar 1 07:05:24 2000
X-Digest-Num: 380
Message-ID: <44114.380.2108.959273826@eGroups.com>
Date: Wed, 1 Mar 2000 10:05:24 EST
From: pycyn@aol.com
Subject: Sets etc.

"Wherefore all this strife there be / 'twixt Tweedle Dumm and Tweedle Dee?"
A class is any collection of things conceived as together. Usually we think 
of it as all the things satisfying some formula: is a cow, is a root of 
equation..., etc., but in the full horrors of mathematics there are provably 
classes for which there is not formula (denumerably many formulae, 
non-denumerably many classes). A set is a class satisfying certain further 
conditions, amounting to its being able to be a member of other sets (though 
not so circularly -- actually recursively -- defined). A mass (in the Lojban 
sense) is a class considered in a certain way, additively rather than 
collectively or distributively. Almost all Lojban descriptors, LE, are about 
classes; they differ in how the properties ascribed to the class are related 
to the properties of the individuals that make it up. In the simplest cases, 
le and the like, the property of the class is that of some or all of its 
members (which is specified by the quantifier, explicit or implicit, used). 
For masses, the property is the sum (in some often quite inexplicit, even 
metaphorical, sense) of those of the members: the weight of a mass is 
literally the sum of the weights of the members, the triumph of the mass is 
the result of the combined efforts of the members (even including
some that had a negative impact on that triumph -- the crowd stormed the 
Bastille despite some who ran away and some who aided the Ancien Regime), the 
performance of the school is some kind of average of the performances of the 
students, and so on (you have quite a bit of freedom here, but need to be 
able to explain if push comes to shove). And at some point, the whole can 
come down to the proeprty of one member, the logical summation of an "or," 
and thus collapse back toward the first sort of usage. Finally, a class may 
be viewed collectively, and then the properties attributed to it have little 
to do with the properties of the individual but rather with matters like how 
many there are of them or (more related to their proerties) what toher 
classes they belong to -- cardinality, inclusion, and the like -- set 
theoretic properties, in short, which only rarely have value in ordinary 
discourse.
For the most part, then, the use of the set markers is, like all of MEX, in 
the system
because someday we may want to talk mathematics, the most recognizable special
language system within our (and every) language. so far we haven't been 
inclined to try that, but we should not be prevented from it for lack in the 
language (and, of course, we should not have help up the development of the 
language just to get it in -- and Lojban did not hold up....much). 
As for JCB's lo -- it was a muddle and everyone -- even JCB -- knew it was a 
muddle of half a dozen different ideas floating around in his head. I think 
we now have most of them sorted out in Lojban, though we still seem to get 
into fights over a few from time to time (and pretty generally, having 
forgetten how we solved it the last time, come up with the opposite solution 
the next).
pc