Re: [lojban] Lions and levels and the like

As I noted, in L-sets, membership and subsets are not distinct, i.e. every member is a subset and under certain interpretations, ever subset 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 its 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 familiar object arise in the intersection of bunches: lions are in the intersection of lion and living organisms and so. And every gold thing is in the intersection of gold and its particular form. The only Lojbanic thing I see in all of this at the moment is that that maximal bunch ought to be given a separate gadri.

There do remain a number of cases to which this general notion does not seem to apply. Your case of the real line is one, letters seem to be another. Here the approach seems to be to start at the top, work down and then back up, I think, but I don't know just how that goes. Even with cases that fit this pattern pretty well, water, for excample, there are some problems, as you note. Water molecules don't display the characteristic 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 this 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 usage 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.

From: maikxlx <maikxlx@gmail.com>
To: lojban@googlegroups.com
Sent: Tue, November 15, 2011 4:49:16 PM
Subject: Re: [lojban] Lions and levels and the like

Okay, that's pretty close to Bunt's ensembles, as I might as expected. The most primitive notion in these mereological systems is the "part-of" relationship, which effectively replaces "subset-of" (although it re-uses the same rounded "less than or equal" symbol to represent it). In C-sets, membership is most primitive and subset is derived from membership i.e. "A is-subset-a-of B" is shorthand for "if x is-member-of A then x is-member-a-of B". In ensembles "partship" comes first and members (atoms) are defined as the contents of ensembles that happen not to have parts and therefore are effectively singletons, which seems different from what you call an "individualizing principle" (although that sounds like an intriguing concept). Either way, I suspect that you can get everything you need from there.

To be clear about one thing, when I said "atoms" previously I only meant "individuals" and not the things that compose molecules. In fact, masses in ensembles are a bit weird in the sense that there is absolutely no necessary commitment whatsoever to the notion of "smallest things" (except exactly when you need them). There are good reasons for this, both theoretical and practical. In the real number line, there is an infinite number of line segments and none of them are smallest. In the case of, say, water (defined as a liquid), it's really impossible to say what a smallest part actually is. A single molecule is not water, though a small group may be, obviously overlapping with other potentially smallest groups before dissolving into its surroundings. But since we're dealing with natural language semantics, there is never a practical need for "water" to encode these vanishingly small quantities, and there are other predicates to do the job.

On Tue, Nov 15, 2011 at 2:11 PM, John E Clifford <kali9putra@yahoo.com> wrote:

A so des! Sorry to be so slow.. A mass is a kind extended to be closed under "part of", a kind is the intersection of a mass and an individualizing principle (say "viable organism" for lions from lion). But the relations are formally the same, the jest of mereology (member/subset -- they fall together). Or, from my on the ground view, kinds grow upward from individuals to bunches and masses grow downward, from individuals to physical parts to ultimate atoms, the smallest things that are still of the sort (atoms, molecules, cells, etc.).
I'm not at all sure what this says about Lojban and {lo} expressions or about levels, come to that. But at least I am, I think finally near the page you all have been on for awhile.

From: maikxlx <maikxlx@gmail.com>
To: lojban@googlegroups.com
Sent: Mon, November 14, 2011 6:55:26 PM

Subject: Re: [lojban] Lions and levels and the like

Ah, you jarred my memory. Having studied Bunt, I think that I can make some sense of your earlier writings about Leśniewskian sets (L-sets) and Cantorian or classical sets (C-sets) e.g. http://pckipo.blogspot.com/2009/09/c-sets-and-l-sets-draft.html I take it that your "bunches" are basically L-sets as there described then? I am not quite sure how L-sets work differently than C-sets, other than they can't be nested and {a} = a. C-sets clearly handle individuals efficiently and masses poorly; how do L-sets handle masses and individuals? Or is there a difference?

FWIW, Bunt's "ensembles" which I mentioned are a bit different than your L-sets. Ensembles are a set-like structure in which mass is the basic concept, and atomic individuals are derived or secondary. Any non-empty ensemble may contain or atomic members (essentially a count ensemble), or for lack of a better word non-atomic "stuff" (mass ensemble). It could also contain both atoms and non-atomic stuff. Count and mass ensembles may combine in predicate relationships freely as in "The five rings were gold". So they seem pretty useful for capturing human language semantics.

On Mon, Nov 14, 2011 at 4:16 PM, John E. Clifford <kali9putra@yahoo.com> wrote:

Hmmm! Nice case! Of course, some first transistor must have been invented that all the others copied and improved upon, but that doesn't really dodge your point. At the moment, I don't know what to suggest, except to hope that Lojban still has a word for kinds. Bunches are, inter alia, Lesniewski's wholes (but xorxes doesn't like this kind of objectifying, preferring plural reference, which works the same way formally). I don't take 1a to be about kinds, but just about some unspecified bunch of lions (at least in Lojban, lo cinfo). Kinds don't seem to be the sort of things that ruin gardens, though their exemplars may. The factual situation, as far as transistors, etc. are concerned, is about genealogy, all transistors descend from something invented by Shockley. But that is at least as hard to express as types, so I wait a while on it.

Sent from my iPad

On Nov 14, 2011, at 2:24 PM, maikxlx <maikxlx@gmail.com> wrote:

I can understand the appeal of your concept of bunches -- if I understand them correctly as being something like subsets of the extensions consisting of mundanes/atoms (perhaps generalized to something like Bunt's ensemble, derivative of Leśniewski 's mereology, to cover masses). E.g.:

- (1a) Lions are ruining my garden.

- (1b) There exist some lions that are ruining my garden.

where (1a) invokes a kind and (1b) invokes a bunch or somesuch, and yet both sentences seem to have the same truth conditions or almost the same.

But yesterday as I was reading random online materials (this one - http://amor.cms.hu-berlin.de/%7Eh2816i3x/Talks/GenericitySeattle.ho.pdf ), I found what I think is a good bunch-resisting, kind-example:

- (2a) Transistors were invented by Shockley.

One can't get the same result by referring to any bunch:

- (2b) *There exist some transistors that were invented by Shockley.

Nor does taking the biggest possible bunch of transistors help:

- (2c) *All transistors were invented by Shockley.

It seems that though transistors as a kind of thing were invented, no mundane transistor nor any extension, ensemble, or bunch of them was invented. In (2a) there does seem to be some sort of "transistor kind" (dare I say "form") above the mundane, even taking into consideration the possible worlds that Montague would have in his model.

On Mon, Nov 14, 2011 at 11:45 AM, John E Clifford <kali9putra@yahoo.com> wrote:
>
> Here we have the advantage of taking kinds and the like as bunches (without
> ontological commitment of things called "bunches"): {su'o lo stuci) has
> essentially the same result under either interpretation, a subbunch of lo
> stuci. It may, of course, not correspond to the bunches put in as kinds of
> teachers, but it produces a kind of its own. Of course, there remains the issue
> of how this bunch talks to all the students, but, as I have noted elsewhere, it
> all works out to there being some teachers (mundanes) who talk to all the
> students, even if no one teacher does.
>
>
>
> ----- Original Message ----
> From: Jorge Llambías <jjllambias@gmail.com>
> To: lojban@googlegroups.com
> Sent: Sun, November 13, 2011 7:10:17 AM
> Subject: Re: [lojban] Lions and levels and the like
>
> On Sat, Nov 12, 2011 at 2:39 PM, Martin Bays <mbays@sdf.org> wrote:
> >
> > What I mean by this (i.e. by "really"): if B hears A say {su'o ctuca cu
> > tavla ro le tadni}, and B wants to understand what A means to say about
> > actual teachers and actual students, and if {ctuca} and {tadni} do not
> > specify levels, then B has to guess which levels A intends them to refer
> > to. If, for example, B guesses that A is talking about kinds of teacher
> > and about actual students, all B can deduce about actual teachers and
> > students is that every student was talked to by some teacher.
>
> You have some hidden assumptions there, for example that there are
> actual teachers of the kind that talks to every student.
>
> And B can deduce more: that there is some kind of teacher such that
> every student was talked to by some teacher of that kind.
>
> mu'o mi'e xorxes
>
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