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la nitcion cusku di'e
For consider a word with a total of {ro} doctors (where ro is a finite
number.) Fractionally quantify the collective of all doctors, as
ny fi'u ro loi ro mikce
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.
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.
In particular, for n = 1, pa fi'u ro loi ro mikce cu broda means that broda holds of at least one of the possible subcollectives of doctor, of cardinality 1. That is, of course, at least one individual doctor.
So: {pa fi'u ro loi ro mikce} = {su'o lo ro mikce}.
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?
For example, it could be just the one: (1) fi'u vo loi prenrbitlzi cu se cmene zo djordj And that is true; only one quarter of the Beatles is called George: pa lo fi'u ro loi prenrbitlzi cu se cmene zo djordj pa lo prenrbitlzi cu se cmene zo djordj
Ok.
But it could also be all of the subcollectives of that size: (2) fi'u vo loi prenrbitlzi cu ki'ogra li su'e 100 And that is true: at least one quarter of the Beatles weighs less than 100 kg. In fact, all the quarters do (did): pa lo fi'u ro loi prenrbitlzi cu ki'ogra li su'e 100 pa lo prenrbitlzi cu se ki'ogra li su'e 100
Those should be: su'opa lo fi'u ro loi prenrbitlzi cu ki'ogra li su'e 100 su'opa lo prenrbitlzi cu se ki'ogra li su'e 100 Or: vo lo fi'u ro loi prenrbitlzi cu ki'ogra li su'e 100 vo lo prenrbitlzi cu se ki'ogra li su'e 100 Or: ro lo pa fi'u ro loi prenrbitlzi cu ki'ogra li su'e 100 ro lo prenrbitlzi cu se ki'ogra li su'e 100
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".
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?
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}?
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?
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.
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.
mu'o mi'e xorxes
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