[lojban] Re: A Proposed Explanation of {gunma}

[John E Clifford <lojban-out@lojban.org>]

The talk about the place structure of {gunma} and
the subsequent expansions on that got me
wondering just what a gunma, a "mass," is. Since
this is Lojban, ordinary usage and ordinary
technical jargon are not reliable guides, though
they cannot be ignored.  So we go back to the
last definitive answer on this question, CLL 6.3
& 4. There several rather different -- though
perhaps interrelated -- things are said about
masses.  Masses differ from sets in that, while
they do encompass pluralities, they have
properties that depend upon the properties of the
individuals encompassed, while sets do not (this
is only true of pure set theory, not applied, but
the point is clear).  Secondly they differ from
simple pluralities of individuals (in CLL the
nebulous way of dealing with plurals and
singulars without overt distinction) in that
masses have properties that depend upon the
collaboration of the members, not just upon the
properties of each individually --- they have
collective, not merely distributive or
individual, predication.  Third, masses inherit
all the properties of their members; the
collective properties are over and above these. 
Finally, masses are like the referents of what
linguists call mass nouns, substances that
override (or underlie) their individual
manifestations: water, as opposed to drops of
water (as in "Water covers 3/4 of the world") or
cow (As in after an accident "There was cow all
over the road").

Although I have at one time or another argued for
most of these positions and tried to interrelate
them, I now think that some of them are seriously
flawed and that a couple of errors pervade the
list above.  I think that the first two points 
-- that masses differ from (pure) sets in that
they have properties that depend upon the
properties of the members and that masses differ
from individuals or plurals in that they take
collective predication rather than distributive
(or individual individual predication).   I also
think that the fourth point -- that (some) masses
do the work of mass nouns is correct but that
that description of this role -- in Lojban -- is
incorrect as given above. The third
characteristic -- that a mass inherits all the
properties of its members (I used to call it a
logical sum) -- I now think rests upon some
interlocking errors.

I take it that it is obvious that masses are what
{lVi} decriptions refer to and so discussions of
these also are discussion of masses.  Yet the
various such descriptions seem to be radically
different: {lei broda} refers apparently to a
fixed mass composed of the things I have in mind
and call brodas.  It remains the same mass on
several different occurrences (or, if my 
consideration shifts to other things I call
brodas, I am under conventional obligation to
note the shift with {bi'u} ir such).  But {loi
broda} -- in CLL -- contains an implicit
particular quantifier so that separate
occurrences of the same expression may have
different referents (or satisfiers).  Yet we tend
to think of all {lVi} expressions in the same way
-- like {lei}, generally.  And this leads to the
peculiar notion that a mass inherits all the
properties of its members -- a position that does
not fit well with the notion that a mass has
collective properties. Reconstructed, the steps
seem to go like this.  Suppose there is a bald
man and a man with long hair.  Then there is a
submass of the mass of men (or a massification of
some men) which is bald, namely the mass
comprised of the bald man.  Since the
characterization of this case is exactly what is
required for CLL {(pisu'o) loi (ro) nanmu cu
krecau}, loi namu is bald (collectvely, even). 
Similarly, loi nanmu is long-haired, taking
another submass into consideration.  But if we
take {loi nanmu} to be like {lei} descriptions, a
fixed reference, then it follows that loi nanmu
is both bald and long-haired.  But the move from 
sP & sQ to s(P & Q), which is legitimate when s
has a fixed reference, like {lei broda}, is
invalid when s involves a particular quantifier,
as here.  Take away that illegitmate step  -- and
the understanding of {loi broda} that makes irt
seem to have a fixed reference -- and there is no
obvious reason to hold that a mass inherits the
properties of each of its members. 

Another mistake underlying this reasoning seems
to be the notion -- probably inevitable in a
language like Lojban -- that a collective
predication must come directly from the
individual predications of the member of the
collective and thus that for a collective
predication to hold all the individuall
predications must as well.  It may even be that a
collective predication is taken just to *be* the
cooccurrence of those individual predications. A
century and more of attempts at reductionism has
shown that this is not the case, that a
collective predication cannot be defined or even
causally related to the actions of the members of
the collection -- without remainder.  That is,
even the most minute explication of the actions
of the participants will rarely, if ever, either
define or entail a collective predication  (there
are typically references to predications of
things not in the collective and to
generalizations not overt in the collective
predication).  Thus, even the more speculative
need for inheritance of individual properties is
not required

The problem with masses as referents of English
mass nouns, as the Urgoo to be divided up into
bits as needed, that it is backwards of what
Lojban actually does.  loi djacu, "water," is not
the name of a substance, from which isolated
quantities of water (glasses, lakes, etc.) are
carved out by determiners of some sort.  Rather,
loi djacu is a collecting of several isolated
quantities of water and and considering what can
be predicated of this collection.  That is, as
always in Lojban, the delimited isolated
continuous individuals are primary and the
"substance" is built up from them. (The "cow"
mentioned earlier is not, of course, a collection
of cows, since when this usage is appropriate the
cows have been deconstructed, but rather a
collective of cow bits, loi bakni spisa or so.)

All this is about CLL explanations, of course,
and many flaws have been noted in these and many
"corrections" have been proposed.  Pretty much
all these proposals reject the reading of of {loi
broda} as {pisu'o loi ro broda}.  One thread
takes {loi broda} to be more like {lei broda}
(and that more like {le broda}) to have a fixed
reference in context, several unspecified  
brodas who collectively have the property
mentioned and who continue to be the referents of
{loi broda} throughout the context.  If
quantifiers are mentioned at all, they would be
{piro} on the outside and {su'o} on the in ({loi}
having also shifted that way).  While this does
give {loi broda} a fixed reference in a context,
the argument does not go through, because that
referent does not collectively have the
properties of one of its members, since it does
not generally reduce to one of its members.  

The other major line is to take it that the
referent of {loi broda} is always the same (in a
given domain at least), namely Mr. Broda, who is
conceptually like the Urgoo in the sense that
individuals, if they are relevant at all, have
properties derivatively from the substance (and
the substance may have properties that none of
its subsumed individuals does, even
collectively).  This position accepts that loi
broda inherits the properties of the individuals
-- or rather that if a subsumed individual
displays a property, the substance must already
have that property in. Because this notion is not
built up from individuals as is usual in Logic
and Lojban, this notion requires a secondary
semantics where substances receive properties in
the same way as ordinary individuals do elsewhere
in the system and these properties of substances
are then to be tied incidentally to properties of
underlying individuals.  But the underlying
individuals need play no actual role in the
discussion.

I prefer the first version as seeming to me to be
more in accord with the Sprachgeist of Lojban and
also simpler, requiring nothing not needed
elsewhere.  In the version I particularly like, a
mass is nothing in itself but is simply the way
of showing the collective predication of a bunch
of things, contrasting with {lV} referents for
distributive predication.  (This way of showing
the type of predication involved is theoretically
inadequate but has been used for half a century
without a serious problem arising.) The mass is
then simply the bunch (as is the referent of {lV}
expressions) and its members can be given as a
list or a {joi} string or just about anything but
{e} strings, assuming the list has to be complete
(it doesn't for sets; why the difference here?). 
I tend, therefore, to think that {gunma} means
"bunch," a less confusing term than "mass" and
closer to what we want in ordinary language.

I do, by the way, agree with xorxes that sets are
basically useless or at least misleading or
unnecessarilyy complicating in most real
situations.  The work can usually be done with
bunches (which may mean, remember, just plural
reference/quantification). Of course, bunches may
just be sets in applied set theory, but then it
is their bunchiness noit their settiness that
plays a role.


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