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A second reply now I understand what Nick was up to:
> 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].
Substance is a thing with cardinality tu'o.
Generalized-collective1 is a thing with cardinality ro.
Collective is a thing with cardinality za'u.
Individual is a thing with cardinality pa.
ro quantifies over something with cardinality ro.
If piro quantifies over something with cardinality ro, it means
"every member of".
If piro quantifies over something with cardinality tu'o, it means
"every bit of".
> 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)
I don't agree that the q is necessary there.
> 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)
This should be:
n loi broda = n lo pi su'o loi broda
-- "n lo piro" is nonsensical.
> Where loi broda is a collective,
> pa lo piro loi broda is an individual collective
> re lo piro loi broda is two individual collectives
This is a radical change from SL. {loi broda} is the mass of
all broda, {piro loi broda{ is every constituent of that
mass. So {re lo piro loi broda} must mean "re lo brodo be
piro loi broda", "two brodo of every constituent of the mass
of all broda". I don't know what the value of brodo could
be, but it's hard to see how the whole phrase in SL could
end up meaning 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
How can you tell that there is pa rather than re? Substance is
uncountable. I can see how by your definition it would
be an individual, but again countability is the key
criterion, not least because the quantifiers are doing counting.
> 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 presume this stuff describes what we'd glork, not what is
prescribed?
> I'm petering out here, but the point is:
> the lo/loi distinction is wholly redundant to the piro/ro
> distinction,
How do you say "half of all men have only one functioning testicle"?
piro quantifies also over individuals.
--And.