Subject: Re: le ga'irfanta

From: "Jorge Llambias" <[email-masked]>
Date: Thu, 25 May 2000 17:32:15 -0000

la pycyn cusku di'e

> O Drat! Is it time for the semiannual go'round about the relation 
between 
> the properties of masses and the properties of the members of the 
underlying 
> classes? I haven't written the last one up yet!
> Well, I won't start it. I find your argument convincing until I 
try to 
> formulate the general principle and then it does not seem to work. 
So, I'll 
> stick with "le or piro lei would have been safer."

I think it may be worth trying to separate two things in the
discussion. One is the question of how masses interact 
logically with the other sumti in a given bridi, this has to 
do with the quantifiers, and a different question is how 
the properties of the mass relate to the properties of the 
underlying components.

As to the first question, the beauty of masses is that they
are single referents. {lei so'i broda} refers to a plurality,
but as a single referent. This is a very nice thing, because
single referents are the easiest to deal with in terms of
scopes of quantifiers and such. Just like {le pa broda} and
names, {[piro] lei broda} can be moved around past quantified
variables and the meaning doesn't change. You don't have to
worry about order of quantifiers because they essentially
behave as constants. Thus:

la djan e lo drata ba'o tcidu [piro] lei cukta
John and someone else have read the books.

makes the same claim as:

[piro] lei cukta ba'o se tcidu la djan e lo drata
The books have been read by John and someone else.

The order of the arguments doesn't affect anything.
But if we change {piro} to {pisu'o}, the two claims become
different. In the first case we would claim that John
and someone else each read some fraction of the books,
not necessarily the same fraction each. In the second case,
we would be saying that there is some fraction that they
both read. {pisu'o lei cukta} does not have a singular 
referent, it is an existential, like {lo cukta} that 
refers to at least one of all the possible fractions of
{piro lei cukta}, and the order in which it shows up 
matters.

I think this is a very strong reason for why the implicit
quantifier of {lei} has to be {piro}. The simplest posiible 
reference is to a singular referent, we can't throw that
away and make {lei broda} a rather more complicated 
reference by giving it an existential quantifier.

A different question to deal with is the relation 
between the properties of a mass and the properties 
of the underlying components. I think the formula
that the properties of the mass are some kind of
sum of the properties of the components works in general,
but I'm not sure it does so always.

In some cases it is clearly the arithmetic sum: the
weight of a mass of books is the sum of the weights 
of the component books. In other cases it is more like
a logical sum: let's say a playing card covers one 
percent of the surface of a table. Then a deck of
40 cards may cover from one to forty percent of that
surface, depending on how the cards are arranged
on the table. It is a kind of sum, but the overlapping 
parts only count once. So sometimes the whole is less
than the sum of the parts.

But there are cases where the whole is more than the 
sum of the parts, when there are group synergies, or
emergent properties, and in those cases it may be hard
to see the properties of the mass as a sum of properties
of the components. Suppose I see a flock of birds flying
by and I say {lei cipni cu melbi}. I don't really know
if each or any of the birds is beautiful, I can't really 
see them to tell, but I do like the patterns and movements 
of the flock. That is an emergent property that I can't 
really think of as a sum of properties of each bird.

So although I think that the relation between the mass
and the component properties is an interesting thing to
consider, I don't think we can give an absolutely general 
rule, there may be classes of properties that behave one
way or another, but I doubt there is a rule that applies
equally to all properties. And we don't really need any
such rule, because when we understand the meaning of a
predicate, say P(x1,x2,x3), we understand it as a 
relationship between three singular entities. Some of 
those singular entities may be pluralities, but the 
relationship applies to the three singular objects, not 
to the components that may make up any of the three 
objects. 

co'o mi'e xorxes