I haven't quite figured out yet how C-sets and L-sets can b= e combined in one theory, aside from just running both, with different symb= ols, say. But then I don't see what the interaction between them woul= d be. I'll work on this.
Of course the point of the masses I have = looked at so far is that they are not continuous but ultimately discrete, a= s most masses are. Thus, there is nothing odd about a gold ring being= at the same time a ring-shaped thing and a chunk of gold or of a pond bein= g a bunch of water molecules. There do seem to be a few problem cases= still, though.
What you are calling gnomic aspect I am calling statisti= cal predication, more or less. Since we have no way to express any of this in Lojban that I can find, just what we call it is not importa= nt. But I am unsure about just what you now mean by kinds and generics.&nbs= p; I don't find either "Dogs are mammals" or "Man walked on the Moon" in an= y way odd. But I do worry about introducing intensions into all this.= To be sure, looking for a unicorn clearly takes out of the present d= omain of discourse to another and that move may be inherently intensional, = the -- by fiat, to be sure -- the intensional part falls into {tu'a} and th= e like, not into the {lo}expression. In short, kinds -- if that is wh= at is involved here and in cases like extinction or creation -- seem to me = to be exactly about extensions, just maybe not this extesnsion.

From: maikxlx <maikxlx@gmail.com>
To: lojban@googlegroups.com
<= span style=3D"font-weight:bold;">Sent: Wed, November 16, 2011 6:= 52:44 PM
Subject: Re: [l= ojban] Lions and levels and the like

On Wed, Nov 16, 2011 at 8:30 AM, John E = Clifford <kali= 9putra@yahoo.com> wrote:

As I noted, in L-sets, membership and subsets are not distinct= , i.e. every member is a subset and under certain interpretations, ever sub= set is a member, though some members are more basic, having no members but = themselves. So, a bunch of things also contains all the combinations = of them. From this point of view, then, a mass is just the bunch of i= ts lowest level (what it is a bunch of, say): gold is the maximal bunch of = gold atoms, lion is the maximal bunch of lion cells and so on. More f= amiliar object arise in the intersection of bunches: lions are in the inter= section of lion and living organisms and so. And every gold thing is = in the intersection of gold and its particular form. The only Lojbani= c thing I see in all of this at the moment is that that maximal bunch ought to be given a separate gadri.

<= br>Well, subsetship (more generally, partship) and membership seem to work = a little differently in Bunt's system. As I learned from reading here (unfortunately severa= l preview pages missing) it turns out that ensembles are essentially C-sets= and L-sets generalized under one theory and reducible to either by excludi= ng the other; you get set theory from ensemble theory by excluding L-sets, = and mereology by excluding C-sets. (IMHO this seems ideal.) As far as intersections as in= "golden ring", I believe that the "overlapped" ensemble of "continuous" ma= sses like gold and "discrete" collections like rings would necessarily be e= mpty, but I am not 100% sure on this point. I need better documentati= on. At worst, I am sure you could construct a mixed ensemble that wou= ld merge all continuous masses of gold and all discrete things made of gold= to get the needed result for your intersection. So maybe, just maybe= , Lojban is doing the Right Thing by having predicates generally ignore the= count/mass distinction.

There do remain a number of cases to which this general notion does not see= m to apply. Your case of the real line is one, letters seem to be ano= ther. Here the approach seems to be to start at the top, work down an= d then back up, I think, but I don't know just how that goes. Even wi= th cases that fit this pattern pretty well, water, for excample, there are = some problems, as you note. Water molecules don't display the charact= eristic behavior of water (as do not also ice and steam), since they don't = flow, etc. But then, gold atoms don't shine and are not malleable, so= this seems a minor problem. And for generic cases, they probably are= not significant, since the far more numerous and visible sub bunches will = take over the "statistics".

I find you idea of an aspect difference among the various uses of kinds= (max. bunches) interesting, though I still tend to think of them in terms of different connections to predicates, a relic of the early= days of plural reference. And, indeed, even with aspects, some of th= is will still come into play with regular bunches, that is to say, bunches = which do not claim to take in all the possible "atoms" (I am used to your u= sage here).

I kinda like this result, since it leaves basic things basic but covers= kinds and masses economically from them. Until some real snag comes = along.

Is there a problem with modeling th= e extensions of predicates like "water"? What is clear to me is that = no purely discrete system like set theory is up to the job of modeling wate= r (though some have tried to work within sets by treating "quantities of wa= ter" as atoms), but that's where Lesniewski and Bunt step in. I am al= so not too worried about generics; as I indicated I think that they a= re mere appearances calculated from the extension under predication involvi= ng some sort of gnomic verb aspect. They give you all sorts of perple= xing results for sure, ranging from "lo gerku cu mabru" to "lo remna cu cad= zu le lunra", but the basic idea seems to be combing over extension-intrins= ic properties, either ignoring time and space or collapsing them. Then there are kinds, which generally seem to invoke intension= -intrinsic properties (as in searching for a unicorn) or episodic events pa= radoxically affecting the extension (as in dodos going extinct) without inv= oking it -- either way, pure kind-predication does not seem to involve dire= ctly any atom or part of the extension.

I am sure there will be controversy in some of these areas at least unt= il Lojban's semantics are much more rigorously formalized.

-Mike
=

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