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la nitcion cusku di'e
We have a Jorge-cube. We can speak of the bit of it that forms the center eighth; that is a pisu'o-substance of Jorge-cube(x), but it's a substance. We take the Jorge-cube itself; it is a substance. We take the collective of all Jorge-cubes in the world; they are a substance.
I gave the cube as an example of something that is a Nick-substance but does not map to what I understand as Substance. To me, a solid cube is as much a countable individual as anything. The set of all solid cubes has aleph-one cardinality, but that is not what determines what a substance is.
I realise I still have a confusion: I am making piro loi broda be every single possible portion, and that's not true; piro is the entire substance. So I need to modify my interpretation of fractional quantification; it is not over bits of the substance, but over the substance.
I used to understand {piro} as "the largest possible bit" = "the
whole" too, but And persuaded me that "every bit" makes more sense,
given no default quantifiers for "the whole". It seemed that
Lojbab too was in favour of the "every bit" interpretation.
A collective of all humanity is piro loi ji'i6ki'oki'oki'o remna, ok?
Not according to my current understanding of {piro}. In both
SL and XS4, the collective would just be {loi ji'i6ki'oki'oki'o remna}.
In SL, if you add {piro} then you have "each bit of the collective
of 6G humans", i.e. just "each human" in this case.
What's the cardinality of humanities? I mean, there are 6G humans, so a human being is one out of 6G. How many all-of-humanities is this an all-of-humanity of?
Quantifying over "all-of-humanities" is like quantifying over the number two. We don't really want a quantifier there.
The question's meaningless, right? There is only one all-of-humanity, just as there is only one all-of-water. As you say, no individuals within the all-of-water to quantify.
Right.
If there is only one all-of-humanity, what's the 6G doing in there (or for that matter the ro?)
That's because {remna} does not mean "is an all-of-humanity".
{remna} means "is an atom of humanity", and the 6G is the cardinality
of the atoms of humanity.
The inner quantifier isn't telling you the cardinality of groups, the way lo 6ki'oki'o tells you the cardinality of individual humans. No, the inner quantifier tells you how many possible atomic bits there are to quantify over, using the fractional quantifier.
Exactly.
So the inner quantifier of a lojbanmass gives you not the cardinality of the mass, but of the bits of the mass. In a collective, the inner quantifier tells you there are cisinfinite bits over which the fractional quantifier quantifies. piro means you are picking, not all possible fractions of the collective, but the fraction of the collective which contains all the individual bits.
That's the tricky bit. I used to understand it as you say, but
now I prefer the other understanding. To get the fraction as a
whole we need to collectivize the selected bits again:
In SL {loi piso'i loi ro remna}: take the jbomass of all humanity,
select many atoms of it, take those many atoms as a whole.
In XS4 {loi so'i remna}: take many atoms as a whole. (The inner
quantifier is not forced to be "all" in XS4.)
The inner quantifer of a substance is aleph-1. piro means you are picking, not all possible bits of the substance, but the bit of the substance which contains all the possible bits --- the entirety.
That's one understanding of {piro}, the one I had been defending
when I thought "default quantifiers" were not real quantifiers
but were really default. Now I think "default quantifiers" are
real quantifiers but are not really default, so I prefer {piro}
as "every bit".
Ergo, there are only two possible halves of all water, if I define them as Western Hemisphere and Eastern Hemisphere water; but there are transinfinitely many halves of water defined by an arbitrary great circle on the globe. Yet both are described as pimu loi ro ci'ipa djacu. pimu, because it's the size of the portion, not how many portions are defined, that counts; roci'ipa, because there are transinfinitely many such possible portions --- whereas for a collective, there are at most 2 ** aleph-0:
I think how the portions are taken in the case of {djacu} and
other "amount of" predicates will have to be left to context.
You will have to interpret {pimu loi djacu} as "for a given
partition I have in mind", or better "for a reasonable partition
in which every bit is of equal size and sufficiently small"
rather than "for any possible partition". The latter is
clearly useless.
pimu loi vo prenrbitlzi (keeping them intact --- half the Beatles is people, not people goo) is a subgroup, of cardinality 4*3 = 12: there are 12 ways you can form a duo out of the four members. But the inner quantifier isn't counting Beatles. It's counting atomic bits of Beatles, which you're using to form the subgroup. And the outer quantifier isn't counting portions. It's describing size of portion.
In SL (according to the Lojbab/And/Jorge recent understanding)
{pimu loi vo prenrbitlzi} is not a collective of two bits, but
two bits out of the four. You'd need {loi pimu loi vo prenrbitlzi}
to get the collective reading.
In XSL you can just say {loi pimu prenrbitlzi} for the same meaning,
if you don't need to mention the total number.
... Ergo, if it is legitimate to have the inner quantifier of a collective to be the count of members of the collective (loi vo prenrbitlzi), it is legitimate for the inner quantifier of a substance to be the count of bits of the substance (loi ci'ipa djacu).
It is legitimate to do that. I just wouldn't call it a substance. It is a collective of bits of water. mu'o mi'e xorxes _________________________________________________________________The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail