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loi includes Kind



It is clear why loi mikce in Standard Lojban is necessarily true of Mr Doctor.

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.

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. 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.

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.) 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

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

And the outer quantifier could also be... tu'o: the non-quantifier corresponding to 'any' in English.

(3) mi djica lenu mi tavla fi'u vo loi prenrbitlzi

i.e.

mi djica lenu mi tavla tu'o lo fi'u ro loi prenrbitlzi
mi djica lenu mi tavla tu'o lo prenrbitlzi

This is in line with the fact that fractional quantification of masses being either intensional or extensional. If you drink half the water, there is a specific half of the water such that you drink it: you could put that half on the outer prenex --- su'o do poi xadba lei djacu. But if you need half the water, you don't need any particular half; any of the possible halves will do: top half, bottom half, whichever.

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.

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).

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. 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.

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Dr Nick Nicholas. Unimelb, Aus. nickn@unimelb.edu.au; www.opoudjis.net
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