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cu'u la xorxes.
la nitcion cusku di'e >xod said in English "if only you guys hadn't hijacked tu'o to mean >Unique, we could use it to indicate the inner quantifier of >substances." And immediately said "good idea." I now think it isn't. They are both cases where the grammar provides a slot to be filled with a number, but where no number will do.
Maybe so; but the number 'won't do' for different reasons. And if Kinds end up inner quantifiers (quantifying over subkinds), tu'o becomes ambiguous between Kind (uncounted) and Substance (uncountable).
In XS4 there is a use for quantifiers to quantify over subkinds,
though. So if there is a gadri for Kind, we can find a way to
interpret a quantifier in front of it. When I proposed tu'o
for Unique we were working under the assumption that there is
always a default quantifier, so something like tu'o was needed
to cancel it. If there is no default quantifier, there is no
reason to assume that {lo broda} is quantified.
But tu'o lo broda is an explicit signal that there is no quantification. XS says by default, lo broda = [tu'o] lo broda, rather than [su'o] lo broda. So even if there isn't a semantic quantifier, there is still a syntactic quantifier.
I'd rather have an explicit mark for "this is not quantified"; and tu'o does so admirably.
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 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.
Damn. I want to indicate somewhere that there are aleph-null bits to the substance, but that's not quite what piro = whole of means. And piromei is, in fact, an atomic property (though pisu'o mei is not.) Aargh. Back to drawing board on this, too.
... No, hang on, I've got it. A collective of all humanity is piro loi ji'i6ki'oki'oki'o remna, ok?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?
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.
If there is only one all-of-humanity, what's the 6G doing in there (or for that matter the ro?) 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.
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.
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.
So, for w being the maximum amount of substance of water,{piro loi djacu cu broda} means not AzAnAy : memzilfendi(w,n,y,z) => broda(w)
It means: AzEy : memzilfendi(w,1,y,z) => broda(y) i.e. broda(w) pimu loi (ci'ipa) djacu cu broda means: EzEy : memzilfendi(w,2,y,z) => broda(y)There are ci'ipa memzilfendi of all-the-water. pimu can also pick out ci'ipa memzilfendi, since the cardinality of z (which picks out a 3D space) is ci'ipa.
It can also pick out exactly two halves, if z is fixed.So though the portions selected from is transinfinite, the portion selected can be finite. If this truly was pisu'omei, we could say
piromei = 1 lo ci'ipa boi pisu'omei pimumei = 2 lo ci'ipa boi pisu'omei (cut only one way) pimumei = ci'ipa lo ci'ipa boi pisu'omei (cut arbitrarily)But in lojbanmasses, the outer quantifier is not how many portions are selected; it's how big the portion is. And the inner quantifier is not how many lojbanmasses there are; it's how many possible portions can be chopped out of it.
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:
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.
... 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).
--Dr Nick Nicholas, French & Italian, Uni. Melb. nickn@hidden.email
http://www.opoudjis.net "Must I, then, be the only one to be beheaded now?" "Why, did you wanteverybody to be beheaded for your consolation?" Epictetus, Discourses 1.1.