Message-Id: <m0sxds7-0000ZOC@xiron.pc.helsinki.fi>
Date:         Tue, 26 Sep 1995 08:09:04 -0700
Reply-To:     "John E. Clifford" <pcliffje@CRL.COM>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         "John E. Clifford" <pcliffje@CRL.COM>
Subject:      quantifiers:masses
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 2843
Lines: 41

        On the mass mess, I am not much "forrider."  A few thoughts, set
out without commitment nor confidence.
        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.  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.  We could, of course,
say that herring-eating Swedes eat more herring than herring-eating
Norskies, but that is clearly a different claim (about the mass of a different
set), even if the numbers were the same (but the averages would be
different and might even go the opposite way).
        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.  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.  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) 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.   And thus, I may have bought loi plise for five dollars
even though I surely did not buy piro loi plise at all, let alone for such a
low price.  This is hopelessly vague and in many ways unsatisfying, but it
also seems to catch something right (though maybe not in the apple-
buying case, which is particularly fuzzy -- like an old-man cactus, i.e.
prickly as well -- right now).  Comments eagerly sought.  Clearly the
property being projected and the class on whihc it is originally applied are
important but the relevant classifications of these and the rules that they
generate are not at all clear.
        As the reply about _piro loi pavyseljirna_ shows, the empty mass is
up for grabs at the moment.  I think the advice to wait until the regular
masses are dealt with is a good one; even mathematicians usually -- the
case of the empty set being perhaps an contrary case -- generalize from the
simple cases to the odd ones.  I think there is less reason for argument this
time, but I do not expect that there will not be an argument.
pc>|83