Re: quantifiers:masses

[jorge@PHYAST.PITT.EDU]

pc:
>         The non-participants in the set do not get left out of the mass.  The
> team analogy shows this, for even the non-players that day are
> components of the team.

I'm not sure what this shows. If something is true of the team that doesn't
mean that it has to be true of each component. If the team scored three
goals, that doesn't mean that each player scored three goals.

So, if x is a component of mass X, P(X) does not entail P(x).

Similarly, if one player scores exactly three goals, that doesn't mean
that the team scored exactly three goals.

So P(x) does not entail P(X).

In general, the properties of components and the properties of masses
are independent of each other. There is a semantic connection, but
what it is will depend on the semantics of the property.

> Similarly, if one says (to start a war in
> Scandanavia or Minnesota) that Swedes eat more herring than Norwegians
> and mean the mass interpretation (not the "average" interpretation, mass
> divided by cardinality), then we sum up quantities from all of each eth,
> including those who contribute 0 herring to the total.

Yes, certainly, The amount that a mass of people eat is the sum of the
amounts that each member of the mass eats. This works for eating.

But for example, the price of a mass of apples need not be the sum of the
prices of each component. Someone may sell one apple for 10 cents, a dozen
for a dollar. Then you can't say that the price of the mass is the sum
of the prices of the components.

And of course, if you consider other properties you get other rules. For
example the temperature of a mass of apples is not the sum of temperatures
of each component apple. If they are all at the same temperature, then the
mass is also at that temperature.

So, we have three different rules for eats( , ), price( , ) and
temperature( , ). I'm sure one can think of many other predicates
that don't work with any of these rules. For example mother( , ).
The mother(s) of a mass of people is one person if the people
are all siblings. If not, then the mothers will be the mass
composed of the mothers of each one.

I don't see any underlying rule for all cases.

You could say that, for a mass X, of components x, y, z.

P(x,a) & P(y,b) & P(z,c) --> P(X,a+b+c)

where a+b+c is defined as whatever is right for the given P.

If P is ...eats amount..., then + is the sum of amounts.
If P is ...has price..., then + is the sum of prices minus any discount
                                 that applies for buying large quantities.
If P is ...has temperature..., then + is, if all temperatures are the same,
                                  then that temperature, otherwise it may
                                  be undefined.
If P is ...has mother..., then + is the usual massification with {joi}.

and so on for every predicate. Do we gain anything by calling that function
a sum? Maybe, but it certainly has to be individually defined for each
predicate in each context. I don't see a general rule. In many cases it
is probably not well defined. If x is blue, y is red and z is yellow, what
color is the mass? It probably is tricolor.

>         There is a difference between the mass of the whole and the whole
> of the mass.  I think that (thank you, dn) that one blue marble is enough to
> make the mass of the whole set of marbles blue.

I don't think that is enough. The mass would have a blue component, and if
the component is preponderant enough we may say that the mass is blue, but
not in general. Just like we don't say that someone is blue just because
they have blue eyes.

> But the whole of the
> mass of the set of marbles is not blue, but rather blotchy with the green
> and the yellow and the red and the white and the clear and...-- or else it is
> no color at all.  I am not sure which.

That's what I would say of the mass. But then I don't see the difference
between the mass and the whole of the mass.

> I am inclined to think that something
> about this is involved in the difference between _loi broda_, a referring
> expression (so without external quantifiers) for the mass of the whole of
> the set of brodas (which I thought xorxes and I had gotten to a month ago
> or so but, given our skill at cross talk, will not insist on)

Since I still don't see why {piro loi broda} can't be a referring expression,
I can't argue this point.

> and something
> about the whole of that mass, presumably _piro loi broda_, something else
> (but what?) derived from the first in a way like the new masses _pisu'o loi
> broda_ are derived.

Well, as long as you don't say what is that something else, we can't disagree
about it.

I understand {pisu'o loi broda} as a mass whose components are broda
(not necessarily all the broda there are), and {piro loi broda} as
the mass whose components are all the broda there are.

Furthemore, I think {loi broda} is more useful as an abbreviation of
{pisu'o loi broda} rather than of {piro loi broda}.

Jorge