What is a lojbanmass? Quantification

[Nick Nicholas <opoudjis@optushome.com.au>]

I now see why And judges loi as redundant to substance/individual: 
individuals are things quantified by natural numbers, masses are 
things quantified by [0,1]. But collectives are also things 
quantified by [0,1]: you have half a collective, even though you also 
have 2 ppl out of the collective. And you certainly can have pisu'o a 
collective.

I think the deal is

for n \elem N* (0, 1, 2, 3...)
for q \elem [0,1]

lo broda = n lo broda (n people)
loi broda = q lo broda (e.g. 1/2 the group of people; 1/2 the goo of a person)

q lo broda =def q loi pa lo broda
(1/2 of an individual is by definition half the substance of that 
individual: fractional quantification of individuals forces a 
substance interpretation. Not a collective interpretation: an 
individual of broda cannot consist of a collective of broda)

n loi broda =def n lo piro loi broda
(2 lojbanmasses of individuals are by definition two lojbanmasses 
converted to individuals: integer quantification forces an individual 
interpretation)

Where loi broda is a collective,
pa lo piro loi broda is an individual collective
re lo piro loi broda is two individual collectives

Where loi broda is a substance
pa lo piro loi broda is the individual of all the substance
re lo piro loi broda is meaningless

Where broda is inherently-substance (e.g. djacu)
pa lo djacu = pa lo pisu'o loi tu'o djacu

Where broda is not inherently-substance

pa lo tu'o remna = pa lo pisu'o loi tu'o remna = pa lo pisu'o loi 
su'opa lo remna
(Take at least one individual human. Universal-grinder them. Take a 
scoop of that. That's your scoop of humanity.)

I'm petering out here, but the point is:
the lo/loi distinction is wholly redundant to the piro/ro 
distinction, but signals it in the absence of overt quantification: 
it indicates the potential domain of quantification.
The outer quantifiers when omitted have default values, which are 
either defeasible or not. I suspect they are defeasible. But in 
formally speaking of lojbanmasses, we must supply them; we leave 
omitting them until we get to speakability.
Both collectives and substances are quantified by piro. So loi isn't 
freed up at all to do collective work, if loi indicates "this is 
fractionally quantified".
An explicit outer quantifier forces a conversion from lo to loi or loi to lo.

The matrix (omitting forced conversions) is:

OUTER GADRI INNER
ro lo ro Individual
piro loi ro Collective
piroi loi tu'o Substance
ro lo tu'o Substance individuated (Substance -> Individual)

loi tu'o and lo tu'o both indicate substance. lo tu'o heads to 
countable amounts of substances (re lo pisu'o djacu; pa lo piro 
djacu), loi tu'o presumably to generic substances.

I'm sure there are holes in this you told me about 2 months ago that 
I didn't get. Remind me what they are.
--
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* Dr Nick Nicholas, French & Italian Studies nickn@unimelb.edu.au *
University of Melbourne, Australia http://www.opoudjis.net
* "Eschewing obfuscatory verbosity of locutional rendering, the *
circumscriptional appelations are excised." --- W. Mann & S. Thompson,
* _Rhetorical Structure Theory: A Theory of Text Organisation_, 1987. *
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