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Nick:
> This is in many ways meta-stupid. And has a highflying Excellent
> Solution that is (I think) intensional (in that it makes lo a Kind
> rather than an individual), and I'm basically crawling around even
> getting collectives and substances defined
>
> But even though I look at John revering Quine and think "that's so old
> hat", I cannot accept an intensionalist model. Even if it's more
> realistic cognitively (and it may well be --- we start with Kinds, and
> go to individuals as avatars of Kinds.) Lojban was begotten of the
> prenex --- and extensionalism --- and I want it to stay there. As in,
> to the extent of defection or schism. :-( Sorry
I'm not sure quite what you mean. You can probably formulate
ExSol 4.0 in such a way that Kinds aren't treated as more basic,
and ExSol is essentially neutral wrt extensionalism/intensionalism.
So if you're saying that you want it to be possible to do everything
purely extensionally, I have no problem with that. But if you're
saying you want to make it impossible to do things intensionally
(except when using {nu}!) then I don't understand why. I still
opine that Lojban strives to avoid bias and undue limitations on
speakers' choices, and there is definitely a sense in which
Lojban aspires to make everything sayable.
> Lots of repetition in the following. I want each version of the
> Ontology to be self-contained, and I would like for And's Excellent
> Solutions to be the same
I think they are.
> ****
>
> 1. Ontological types: Definition
>
> I define the following predicates
> (A1) A hole is defined as:
> (A2) A perfect atom is defined as:
> (A3) A chipped atom is defined as:
> (A4) An atom is defined as a perfect or chipped atom
> (A5) A pisu'o-substance is defined as
> (A6) A piro-substance is defined as:
> (A6a) Jorge-cube(a) => AnEzAy: ( n>1 & memzilfendi(a,z,n,y) ) =>
> (A7) A substance is defined as a pisu'o-substance. All piro-substances
> (A8) A partial_group is defined as
> partial_group(a, ^\lx.P(x)) <=>
> EnEzEy : ( n>1 & memzilfendi(a,z,n,y) ) => atom(y, ^\lx.P(x))
> & EnEzEy : ( n>1 & memzilfendi(a,z,n,y) ) => P(y))
> & ~atom(a)
> (A9) A full-group is defined as
Where is all this leading? Are we going to have gadrioids (i.e.
LAhE, gadri, quantifier combos) for each of rhese?
> As an example of demergence, all human beings (atoms of humanity) have
> the property "weighs less than a ton". Any group of more than 1000
> people, though, will have that property fail
If I'm part of the group, then 990 people will suffice.
> Fractional quantifiers presumably quantify over Goo(P), not P, to
> answers And's well-placed critique
I can't remember what my well-placed critique was, but surely
we can fractionally quantify over sets or groups too? Instead
of taking a percentage of bits of goo, you take a percentage
of members.
> 4. Countability
>
> We have atoms and groups and substances; but we don't have countabilty
>
> To fix that, I will introduce some geometry
[...]
> An individual a is a physically separate bit of b with respect to P
I didn't really understand what you're after here. Obviously not
every individual is a physically separate thing in 3d space. So
is space being treated abstractly, i.e. a Langackerian concept-space?
> 5. Interpretation
>
> Gods, later; but I think this is getting clearer:
>
> the inner quantifier, tu'o vs. ro, identifies the reference as
> substance or atom/group
>
> the outer quantifier being an integer (and concomitantly the gadri
> being lo) indicate the referent is an individual
>
> the outer quantifier being a fractional (and concomitantly the gadri
> being lo)
lo? or loi?
> indicate the referent is an uncountable: it is not being
> considered an individual of anything. This includes substances which
> may or may not be physically contiguous. It also includes the entirety
> of a group, rather than any individuals of the group (atomic or
> subgroups.)
>
> A group has multiple possible cardinalities of individuals, depending
> on the ve memzilfendi, lo forces the maximum possible cardinality, that
> of atoms. Thus, re broda is a group of two atoms of broda, expressed in
> atomic cardinality
>
> One might also construe lo as indicating the referent has a fixed
> cardinality (individuals of substance, individuals of atoms, atomic
> individuals of groups), and loi as indicating the referent does not
> have a fixed cardinality (non-individuals of substance: infinitely many
> bits, uncountable as they need not be physically differentiated as
> individuals; non-individuals of atoms: undefined; non-individuals of
> groups: no extraction of the atoms or subgroups of the group.) When a
> non-individual is spoken of, the property predicated is not identified
> with any countable individual of the entity, though it is identified
> with the entity (as a piro-substance, a pisu'o-substance, a full-group
> or a partial-group.)
Sorry -- my head is boggling. I'm afraid I have taken in only piso'u
of what you've said. I realize that you are to some extent thinking
aloud, working stuff out for yourself. I'll probably understand it
more once you get to an actual proposal concerning how to say stuff
and what stuff means.
By the way, I take it that all the explicitness and precision is
mainly for your own benefit? The rest of us are, i think, perfectly
happy to work on a somewhat more intuitive basis (taking the
formalization as given).
--And.