Re: loi includes Kind

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

--- In jboske@yahoogroups.com, "Jorge Llambias" <jjllambias@h...> wrote:

> >This denotes any collective of doctors, of cardinality n. (Yes, I said
> >'any' on purpose.) But there is more than one possible such collective.
> >In fact, there are n C ro (n out of ro combinations.) So there are 12
> >possible duos in the Beatles. 
> Actually there are 6 possible duos: {John, Paul} and {Paul, John}
> is the same duo. 

Because I've forgotten how to calculate Combinations as distinct from 
Permutations.

> >When we claim that ny fi'u ro loi ro mikce cu broda, we are saying that
> >broda holds of at least one of the possible subcollectives of doctor,
> >of cardinality n.
> "At least one" is not the same as any. If we say that it holds
> of at least one, that's ordinary quantification, not over the
> set of all doctors but over the set of all subcollectives of n
> doctors.

At least one is not the same as any, in that at least one is extensional/de re. 
My contention is, we also use fractional quantifiers de dicto.

> >We are not, however, supplying an overt outer quantifier; so we are not
> >saying just how many such subcollectives broda holds of (other than
> >it's not zero.)
> 
> That's an implicit {su'o}, isn't it?

Yes. And this is actually the crucial difference I'd missed. Mr Human has 
avatars in this world, Mr Hobbit does not. loi broda refers only to thinks with 
'Manifestations' in the real world.

> >And the outer quantifier could also be... tu'o: the non-quantifier
> >corresponding to 'any' in English. 
> Then you're saying that {fi'u ro loi broda} is ambiguous
> between "at least one fraction of broda" and
> "Mr Fraction of Broda".

Yes. Or rather, Mr Fraction of Broda-In-This-World.

> >Under this interpretation, there isn't necessarily anything to go to a
> >prenex when you see pimu loi or fi'u ro loi. In (1), what would have to
> >go to a prenex as an overt outer quantifier is pa da. In (2), it is ro
> >da. In (3), nothing goes to the (outermost, extensional) prenex at all:
> >it is tu'o da.

> Now you seem to be saying that it is not ambiguous, but it
> is always intensional, so that {pa fi'u ro loi broda} =
> {tu'o lo broda}, is that right?

Not quite. Mr Broda-In-This-World subsumes any avatar of Broda in this 
World, but not beyond. You go beyond only in intensional contexts. 

So: I eat half an apple: there exists an apple half such that I eat it.
I want half an apple: I want any of the apples halves (in this world): I want Mr 
Apple Half In This World
I draw half an apple: I draw a particular half of Mr Apple (I think)

> >Therefore, the Lojban lojbanmass loi broda (which is always implicitly
> >quantified) includes in its denotation Mr broda. In particular, fi'u ro
> >loi broda can mean Mr Single Broda, and pisu'o broda means Mr Any
> >Number of Broda = Mr Broda (since pisu'o >= fi'u ro).
> 
> And how do you refer to extensional collectives then?
> {su'o lo pisu'o loi broda}?

... yes, I guess.

> >This is why the lojbanmass was proposed as a rendering of Mr Shark, and
> >why the definition insists on "if one of us, then all of us", and the
> >pisu'o outer quantifier --- both somewhat odd for extensional
> >collectives.
> If fractionals entail intension, can we also say {piro lo tanxe}
> for one box, unquantified, i.e. Mr Box?

Only as a Manifestation of Mr Box, I *think*.

> >But of course, little thought had ever been paid to
> >disambiguating the manifold possible senses of the lojbanmass. And for
> >(bits of) substances, this probably doesn't work: you'd need
> >collectives of bits of substances, really, since loi is ambiguous
> >between finite collective (intensional or extensional) of wholes, and
> >transfinite collective of stuff.
> >
> >But for individuals, loi broda can be used to mean Mr broda. This is a
> >concealed ambiguity of the lojbanmass, and now it is unearthed. This is
> >why fractional quantifiers are not real outer quantifiers.
> 
> I don't get why there is a distinction here. It would seem that
> whatever applies to Mr Box will also apply to Mr Amount of Water.

... yes...

> It is true that {loi} has been proposed before to cover intensional
> cases, but shoving intensionality into the fractional quantifiers
> does not seem to be a nice move.

Well, I don't want that to be their default meaning, or the solution to how to 
render intensionality. I've observed that mi djica pimu lo plise is intensional 
with respect to which of the halves; but if this is really just the intensionality of 
mi djica tu'a lo pimu lo plise (no different than the intensionality of mi djica tu'a 
lo plise), then the observation is bogus. Well, bogus-ish...