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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.`

`--------------------
=================================----------------------`

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

"Electronic editors have to live in hope: hope that the long-awaited

standards for encoding texts for the computer will arrive; hope that
they

will be workable; hope that software will appear to handle these texts;

hope that all the scholars of the world will have computers which can

drive the software (which does not yet exist) to handle the texts (which

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yet been devised). To hope for all this requires a considerable belief
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the inevitability of progress and in the essential goodness of mankind."

(Peter M.W.
Robinson)