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Nick:
> If a is an individual with respect to property ^\lx.P(x),
> then kairselci(a, ^\lx.P(x)) =>
> \An\Ay~\Az: n > 1 & memzilfendi(a,n,y,z) & P(a) -> P(y)
>
> This means a is a true *individ*ual: however you cut it up --- into
> 2nds, 3rds, 4ths..., vertically, horizontally, diagonally... if the
> property P holds of a, it cannot also hold of all of the fractions of a
Surely this is too strong. In Lojban, if we way "each sheet of paper
is white" then we are talking about individuals, yet whiteness holds
of all fractions of the paper. Perhaps you mean the criterion to
hold only of the individuating property (the te memzilfendi), so that
for this example, not every fraction of each sheet of paper is itself
a sheet of paper? This does seem to be your intention, give the rest
of what you said.
> A collective is anything that is neither an individual nor a substance.
> It is something with individual components: that is, it does have
> fractions for which the property still holds, but below a certain
> threshold you can divide it up no further
You mean the property by virtue of which the collective is a collective --
the te memzilfendi.
> If a is a collective with respect to property ^\lx.P(x),
> then kairgirzu(a, ^\lx.P(x)) =>
> \E!n\Ez\Ay: ( n > 1 & memzilfendi(a,n,y,z) & P(a) -> P(y) )
> & (~\Am>n: memzilfendi(a,n,y,z) & P(a) -> P(y) )
What does "E!n" mean?
> Now it is intended that the three types are mutually exclusive. (If
> I've got the logic wrong, they aren't, but that's the intent.) No x can
> be both a substance and an individual, or both a collective and a
> substance, with regard to a given property:
AFAICS the ideas are sound, though I haven't battled through the
notation.
> As {ce'u blanyselbartu gi'enai xunryselbartu} shows, not all properties
> have the same ontological type hold of all their members. Contrary to
> founder intent though, it is clear that some properties *do* have
> intrinsic type. It is intrinsic to the definition of {citka} that, when
> the property {pizrolcitka ce'u} is claimed of a foodstuff, that
> property holds of all the fractions of the foodstuff. (You betcha I'm
> not going to get into pisu'o vs. piro yet; right now, I'm assuming a
> piro default, though.) If I eat an entire apple, I do eat both halves
> of it, the four quarters of it, the 16 16ths of it, and so on
I'm not clear how this makes a point about te memzilfendi. Are you
saying that, for example, {pizrolcitka ce'u} can be te memzilfendi
only for a substance. That seems right, but I construe the founder
intent as entailing that using {pizrolcitka ce'u} as an indivuating
te memzilfendi would coerce (in the technical linguistic sense of
'coercion') an interpretation of {pizrolcitka ce'u} that is different
from its dictionary meaning. I don't see a conflict between founder
intent and what you're saying.
> I haven't read Link's paper on Masses and Collectives properly yet, but
> one of the things he points out very early on is that spatial
> properties are intrinsically substance-related. If the apple is in
> London, every conceivable fraction of it is in London
I think that's untrue. "The car is in the garage" doesn't mean the
bumper can't be outside, and "The British Council is in Paris"
doesn't mean it isn't also in Bombay.
> For my next instalment, I need to formalise collective vs. distributive
> predicates, just as I've just done for {pizrolcikta ce'u} and
> substances. Collective properties will be collectives relative to
> particular individual properties: the Beatles are a group of guys, not
> (just) a group of human limbs and offcuts; a library is a collective of
> books, not (just) of book covers and book pages
>
> Then I need to work out how to convert between substances and
> individuals (a glass of water), between individuals and substances
> ("sailor goo"), between individuals and collectives (a bunch of people)
> and between collectives and individuals (the members of the bunch).
> Substance to collective and vice versa go via individual (5 trays of
> glasses of water.)
This is an admirable enterprise, excellent in its first instalment.
If you can do as nicely with SL as you've done here, then I'll bow
down to you in awe.
> Once we can securely convert any type to any other type, we can obey
> the Lojban dictate that everything is both countable and uncountable,
> which underlies the lojbanmass notion, and the Cowan dictum that the
> mass/count distinction is culture-specific. (I dispute this is always
> true --- one does not eat indivisible individuals, even if they are
> indivisible relative to other properties --- but it is enough that it
> be occasionally true.) Then, I'll need to work out how the three types
> apply to abstractions. (I know what an individual event is; what I'm
> not sure about is whether wanting an any-event is a lojbanmass, a
> collective, or an intension of individuals. A substance it clearly
> isn't, because events are as indivisible as anything.) Once I have a
> handle on the ontology, I'm going to start trying to match its
> parameters to the lojbanmass, and see for myself how the
> quantifications work
>
> So yeah, I am merely doing what X and & (to use pc's charming
> abbreviation of the revisionists) did three months ago; I'm just trying
> to take it slowly. Let me know, those who can judge, whether this is
> acceptable so far..
Yes. You are doing what we did three months ago, only more nicely.
But I'm eager to see you hit actual Lojban!
> (And then I gotta do intensionals, and *then* work out if Kinds do the
> same thing, and how prototypes work. I doubt I will see this all the
> way through; but like I said, it's Rubicon time: I cannot continue to
> do anything with Lojban until I understand its gadri.)
Very admirable, but you're cleverer or dafter than me if you think
that understanding logic will make you understand SL... But hopefully
you will either come up with an unmonstrous gadri scheme that the
BF will adopt, or you will become a convert to my proposal.
--And.