RE: [jboske] Transfinites

["And Rosta" <a.rosta@lycos.co.uk>]

Nick:
> 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) 

As I say in another message, both Kind and Sunstance are uncounted
-- I would say they both have cardinality tu'o, along with everything
else that there is only ever one of. Bit of Substance is fractionally 
quantifiable, and I would agree that it always has cardinality
ci'ipa.

> > 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 

I'm with xorxes on this. We all hate zi'o because it makes us 
indicate the absence of something by means of marking it with
a presence. So a KS could insist on always using a zi'o, but
then it would genuinely be kludgesome.

> 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 

Good -- another respect in which we are converging. Me and xorxes
say that you don't quantify over the substance. You need a
gadri expression equivalent to "da poi broda-stuff" where poi
is not read as restricted quantification -- i.e. where it is
logically equivalent to "da broda-stuff".

> 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 

Good news, then.

> .... No, hang on, I've got it 
> 
> A collective of all humanity is piro loi ji'i6ki'oki'oki'o remna, ok?

Do we have to agree? You can stipulate that this is what it means,
but as a compositionalist I think it *should* mean "1 in every 1
member of the collective of c. 6bn humans". The way I think the
collective *should* be expressed is {(tu'o) loi ji'i6ki'oki'oki'o 
remna}. Or {(tu'o) lu'o ji'i6ki'oki'oki'o remna}.

Clearly this would not be SL-conformant, but SL is a balls-up.

> 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. 

Right. But the same is true of sets. {lo'i ci broda} doesn't tell
you how many sets of broda there are; it tells you how many broda
there are.

> In a collective, the inner 
> quantifier tells you there are cisinfinite bits over which the 
> fractional quantifier quantifies. 

yes

> piro means you are picking, not all 
> possible fractions of the collective, but the fraction of the 
> collective which contains all the individual bits 

Yes. So really it's functioning as an inner quantifier and
means "lu'o ro fi'u ro".

--And.