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Nick:
> (Resend)
>
> And posits an XS4.1, which I'll digest later, and which he knows I'll
> reject. Under the Yuletide Accord of 2002, this is an honourable
> outcome: I kludge as much of a solution together that does things XS
> does without violating basic precepts of SL; this results in M$
> Lojban rather than McD Lojban; And can use M$ Lojban or stick with AL
> as he chooses
Yes, of course. But I'm hoping that consistency and compositionality
are as much basic precepts of SL as CLL-conformity is, though.
> Instead, let me do my own take of what I think piro means
>
> piro lo'i broda is not all possible bits (= subset) of a set. It is
> one particular subset of the set: the entirety of it. If lo'i broda =
> {a, b, c, d}, piro lo'i broda = {a, b, c, d}, since {a, b, c, d} is a
> subset of lo'i broda
>
> pimu lo'i broda is any set which is a subset of {a, b, c, d}, and of
> cardinality 2. There are 12 such possible subsets
Agreed that this is what CLL says they mean.
> How do we quantify over those possibilities? My contention, piro is
> not a 'real qantifier', it is a description of a portion, and it
> makes only an existential cllaim as far as real quantification. piro
> lo'i = there exists a subset of the set, and it encompasses the whole
> set. pimu lo'i there exists at least one subset of the set, and it
> encompasses half the set
Is "1 in every 2 broda" {pi mu lo broda}, {pa fi'u re lo broda}?
What does {re fi'u ro lo broda} mean? How about {re fi'u pa lo
broda} and {re pi no lo broda}?
If piro is not a quantifier here, then either you have to come
up with a comprehensive and consistent account of what is and
is not a possible quantifier, such that piPA isn't a possible
quantifier, or else you have to treat piPA as idiomatic in
these examples.
It seems plain that piPA could be an ordinary quantifier, quantifying
over bits and members, if there were an outer gadri or LAhE that
could glom them togther again. Is there no way of analysing
{piPA lVi broda} and {piPA lV'i broda} as an elliptized version
of {loi piPA lVi broda} and {lo'i piPA lV'i broda}? You might
say that this runs up against CLL saying that the default outer
Q of loi is always pisu'o, so you get infinite recursion --
loi pisu'o loi pisu'o loi pisu'o loi pisu'o loi pisu'o -- but
CLL does say somewhere that its defaults are merely an indication
of what the pragmatically most likely value will be. That can
be taken as simply an erroneous guess, not as a prescription.
And then you could take the outer quantifier to be su'o
"at least one set/jbomass". That is not proscribed by CLL
afaik.
As for the existential claim, I read this as meaning that there
is an existential quantifier in the logical formula expressed
by the sentence, but that it is vacuous because all sets exist.
> Do you want to universally, rather than existentially, quantify piro
> lo'i and pimu lo'i? We have two different tasks
>
> 1. All the bits of lo'i = all the subsets of lo'i
>
> That is, all the sets consisting of at least one member of the given set
>
> The members of the set lo'i broda are
>
> lu'a piro lo'i broda
ro lu'a [su'o] piPA
= "every x such that there is a set that contains x"
-- which is not the meaning you want. You need to override the
default scope rules, so as to get "there is a set such that each
of its members...".
> At least one member of the set lo'i broda is:
>
> su'o lu'a piro lo'i broda
>
> A set consisting of at least one member of the set lo'i broda is:
>
> lu'i su'o lu'a piro lo'i broda
>
> All sets consisting of at least one member of the set lo'i broda is:
>
> ro lu'i su'o lu'a piro lo'i broda
>
> piro lo'i broda is only one of the possible subsets of lo'i broda ---
> the one that isn't a proper subset. So it is
>
> pa lu'i su'o lu'a piro lo'i broda
>
> So much for "the whole of" vs. "all bits of". To speak of "all"
> anything, including "all bits of", I need an explicit {ro}
>
> Now, "half the set of", for a set of cardinality 4, means any subset
> of cardinality 2. There are 12 such subsets
>
> Of any such subset ({a,b}, {c,d}, {a,c}...), it can be said that it
> is an instance of {pimu lo'i broda}. (They are in fact different
> avatars of the kind tu'o lo pimu lo'i broda, but let's not go there
> today.)
>
> If you want to say "all halves of a set", you end up saying
>
> ro lu'i ro fi'u re lu'a piro lo'i broda
How does {ro fi'u re} work? What number is ro equal to, here?
And {ro lu'i}? I'm getting lost here.
> which is
>
> ro lu'i ro pi'i pimu lu'a piro lo'i broda
>
> But if any given set is half a set, it is
>
> pa lu'i ro pi'i pimu lu'a piro lo'i broda
>
> This is kinda kludgy, and I may yet make it more elegant. I was doing
> lots of type shifts with lo ro loi... in the KS1, I may end up doing
> so for sets and individuals. Or I may not
>
> By the by, I deem that lu'a working on individuals gives you the
> individuals back; lu'a working on collectives and sets gives you any
> member of the collective/set (so the lu'i in the KS1 should be
> replaced by lu'a.)
>
> Similarly, lu'i of individuals gives the set of individuals; lu'i of
> a set gives a set of sets. So lu'i .abu .e by (lu'i re broda} = {a,
> b}; lu'i .abu ce by (lu'i le'i re broda) = { {a,b} }
>
> I will naughtily and jboskeily define lu'a with respect to a
> substance as a portion of substance. So
>
> lo djacu = a physically distinct expanse of water (something that is
> intuitively an individual); a spisa
>
> lu'a loi djacu = any amount of the substance, physically distinct or not
>
> In that case, every possible portion of the substance is
>
> ro lo ro lu'a pisu'o loi ci'ipa djacu
>
> All out of all the possible portions of at least some of the mass of
> all water
>
> This can be abbreviated to
>
> ro lu'a loi djacu
>
> But "the whole of water", the universal of the substance, is
>
> pa lo ro lu'a pisu'o loi ci'ipa djacu
> pa lu'a loi djacu
So {pa lu'a loi} = {piro loi}?
> In particular, the piromei of water:
>
> su'osu'epa lu'a loi djacu poi ro lu'a loi djacu cu se vasru ke'a
>
> Half of all the water there is is:
>
> pi mu loi ci'ipa djacu
>
> All the possible halves of all the water there is are:
>
> ro lo ro dunlysimxu te memzilfendi be piro loi ci'ipa djacu bei li re
>
> This too is prolix
>
> But you know what? I'm not that fussed about this. Talking about half
> a glass of water --- any half --- is a lot more useful than talking
> about all possible halves. The quantification of fractional bits of
> substance will be almost always unique. (In fact, the fractional
> quantifier is arguably a Unique: "top half,bottom half, left half,
> right half, it's all half a glass.")
>
> I've got no problem with pimu loi djacu being any half of water,
Eh? I thought you'd been saying it means "half of all water"?
> rather than... what, one out of every two possible bits of water? No,
> it's not that. Fractional quantifiers specify the size of the
> portion. They don't say anything about how many such portions are
> possible (an inner quantifier), nor how many such portions you're
> actually talking about (because, uh, you don't care, because it's a
> Unique.)
Given what you said earlier, it would mean "the glom of 1 in every
2 bits of water", no? -- "A part that contains 1 in every 2
bits of water".
--And.