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Date: Fri, 3 Mar 2000 13:20:01 -0000
From: "And Rosta" <a.rosta@pmail.net>
Subject: [lojban] RE: Sets etc.
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From: "And Rosta" <a.rosta@pmail.net>

Bastard Onelist unsubbed me for a fortnight, but wading through the archives
I found this very interesting messsage from pc.

> 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.

It strikes me that the victory/defeat of a sports team is a collective
rather than additive or distributive property, yet is not what I would
think of as a set-theoretic property.

I am wondering whether it is possible to find additive:collective contrasts
for a given predicate. That is, are additive:collective two aspects of
the same thing, which contrasts with distributive? Or are they different?
If same, then cardinality -- being a collective property -- would be a
property of masses (because collective is equivalent to additive, and additive
properties are masses'), and sets proper would be redundant. If not, then sets
proper (lo'i etc.) are useful, because they'd be used for collective rather
than additive properties.

I expect to be disagreed with, but I look forward to reading the reasons
why I'm wrong.

I also forget whether there's a significant difference between pi ro loi
and pi su'o loi. And if so, is pc failing to take it into account? Jorge?

> 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).

I inferred from Jorge's recent description that Loglan lo is used for
Mr Rabbit; what I in bygone times called a 'myopic singularizer'. I think
that's a Good Thing, although, as with masses, the logical properties are
a bit hard to work out.

The conceptual basis for the myopic singularizer is that a category is
viewed as an individual, and members of the category are merely aspects
of the individual. Just as we think of the suns that appear in the sky
on different days as all the same individual -- the same sun returning each
day -- so we can think of lots of rabbits as Mr Rabbit popping up all
over the place. When you start to analyse this logically, it looks very
similar to masses, but at least one difference is that the pi ro/pi su'o
distinction makes no sense for myopic singulars, just as pi ro/su'o la
djan kau,n makes no sense (if la djan kau,n denotes John Cowan rather
than merely his corporeal substance). A further difference from masses
is that whereas heterogeneous individuals can be massified, they can't
be myopically singularized.

I also agree with Jorge that Lojban lo'e is probably the thing for this (and
also le'e for its **nonveridical** counterpart). [Emphasis because le/lo and
lei/loi is primarily a specificity difference, whereas lo'e and le'e is only a
veridicality difference.]

Canonical Lojban has not solved the Mr Rabbit issue, though; only Llambian/
Llambiasian Lojban has. -- As in so many other respects too, of course.

--And.


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