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[cowan (John Cowan)]

co> = John Cowan
ca> = Jim Carter
bo> = Dave Bowen

co> In the second sentence, I am making an assertion about something which I
co> assert to be a bear.  You probably haven't heard anything about this bear
co> before.  So I call it "lo cribe".  I could also say "da poi cribe" = "some
co> x1 such-that [it] is-a-bear"; the only difference between "lo" and "da poi"
co> is that "lo" is meaningful even if no bears exist.

ca> This is the aspect of "veridical" that puzzles me: why is "lo cribe"
ca> different from "da poi cribe"?  With "da noi cribe" I make a supplementary
ca> assertion "something (which by the way is a bear, so I say)".   Whereas,
ca> with "da poi cribe" the referent set of the sumti (before implicit
ca> quantification to "at least one") is restricted from "everything" to only
ca> those everythings that actually are bears.  Then it is run through the
ca> bridi with the other arguments.  If no N-tuples of thus-related
ca> referent set members survive (the first of each is one of the alleged bears)
ca> then with the existential quantification the assertion ends up false.
ca> Isn't this just what "lo cribe" does -- not approximately but exactly,
ca> so that "lo cribe" should be considered an abbreviation for "da poi cribe"?


No.  The error here lies in the notion that "da" means "everything" before
quantification.  "da" in fact means "something"; it is existentially quantified
from the beginning.  In the case of "noda" and "roda" the existential
quantification is overridden by a universal quantification, negative and
positive respectively; but "da poi cribe" does not mean "everything that is
a bear" but rather "something that is a bear".  The "something" must exist.

"lo cribe", OTOH, has the property that you believe "da poi cribe" has.
It means "(at least one of) the individuals of the set of (all) bears", where
the two quantifications can be overridden.  If there are no bears, it
causes the embedding bridi to be true rather than false, because every
predicate is true of the non-existent.  So

	da poi pavjirnydanlu cu blabi
	some x1 such-that it-is-a-one-horn-beast is-white
	A unicorn is white

is false, whereas

	lo pavjirnydanlu cu blabi
	at-least-one-of-the-members-of-the-set-of-all one-horn-beasts is-white
	Unicorns are white

is true.

co> It is the function of the mass articles ("lai", "lei", "loi") to refer
co> to the individuals aggregated together, and of the set articles
co> ("la'i", "le'i", "lo'i") to refer to the sets composed of the individuals.
co> If you say "The letters of the alphabet are of Roman origin", you can say
co> "le lerfu", because it is true of each of them.  If you say "The letters
co> of the alphabet are ultimately of Phoenician origin", you must use "lei"
co> because it is true only of the letters considered >en masse<; some are not
co> of Phoenician origin but were invented later.  If you say "The letters of
co> the alphabet number 26", you must use "le'i", because no single letter
co> "numbers 26", whatever that would mean.

ca> For me, "mass" has been even more slippery than "veridical sumti".  When
ca> the team (mass) carries the log, I have a lot of trouble to distinguish this
ca> from how the set carries the log.  OK, a set has no arms, but neither does a
ca> team, only the members of the (team, set) have arms.  Similarly, in a sports
ca> team each member has a different job, but equally in a traditional set such
ca> as the ring of integers, particular members like 0 and 1 have specialized
ca> roles. In short, I don't see much need to distinguish between sets and
ca> masses.  

To blur the distinction between sets and masses, in favor of sets, is to
extend all sorts of properties to sets that are not generally given them.
For example, suppose that some rats (lo ratcu) are gray.  The we may say
of the mass-of-rats-in-general (loi ratcu) that it is gray as well.  But
to say that the-set-of-rats (lo'i ratcu) is gray is to allow the predicate
"is-gray" to be applied to sets.  Traditionally, sets have properties like
cardinality and finiteness, and relations like equivalence and subset.

Consider elephants (lo xanto).  Most elephants are large (barda)
compared to other animals, but some elephants are pygmies.  So

	loi xanto cu barda
	Elephants considered-as-a-mass have-the-property-of-largeness.
	Elephants are large

is true.  On the other hand,

	lo'i xanto cu barda
	The-set-of elephants has-the-property-of-largeness
	The set of elephants is large

is false, at least compared with other sets of animals.  We have here a
small set, but a large mass.

bo> If my memory isn't failing me (and I'm sure someone will correct me if it
bo> is) the distinction is in the way the operation is carried out.  To continue
bo> Jim's sports analogy a bit further, a mass individual is something like an
bo> 8-person crew, in which all eight members are jointly involved in getting
bo> their boat from start to finish.  The set would be more like those members
bo> of a track team competing in a given event, say a 100 meter dash.  Each
bo> member of the set individually runs the 100 meters.  In many cases this is
bo> hair-splitting.  The cases where it isn't are those where one person by
bo> himself is unable to perform the task.  For example, the claim "The mass
bo> individual composed of ten men carried the Volkswagen beetle accross the
bo> street", is one we might believe.  The claim "Each of those ten men carried
bo> the Volkswagen beetle across the street, by themselves", is less likely to
bo> be believed, even if all ten look like members of the Soviet weightlifting
bo> team.  That last comment suggests an even better sports analogy. If I say,
bo> "The Michigan State offensive line can bench press 150 kilos", presumably
bo> I mean that each individual in the MSU offensive line can bench press 150
bo> kilos, not that the five together can collectively lift 150 kilos.

This is the distinction between masses and individuals rather than between
masses and sets.  The set of rowers does not row, and the set of runners
does not run.  Again, sets have properties like cardinality (how many?) and
finiteness, not like "is-a-rower" or "is-a-runner".  The property of
rowing the boat is a mass property, whereas the property of running the
100 meters is a property of individuals.

We don't often make claims in English that are explicitly about sets, unless
numbering is involved.  "The letters of the alphabet number 26" is a claim
about "lo'i lerfu".  But otherwise English usually paraphrases.  "Lo'i ratcu
cu barda" comes out "There are a lot of rats (in the world)".  

--
cowan@snark.thyrsus.com		...!uunet!cbmvax!snark!cowan
		e'osai ko sarji la lojban