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And:
> 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.
And, I am not John. :-) I want to do everything extensionally, because I believe that is Lojban nature (we are bound to the prenex). But I also agree that the intension must be possible, and would rather kludge that by just switching the damn quantification off.
But the ontologies work at a much more basic level than that: they are nowhere near intensions yet, but are fully extensionalist.
> 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.
Sorry; like I said, I couldn't understand XS4.
> 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?
Not necessarily. But: the ontological type determines the cardinality of the inner quantifier: atoms are countable, groups are countable and countably subdividable, substances are uncountable and uncountably subdividable.
> 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.
You are correct, and I use this in KS1. I will adjust this in KS1. What I'm saying here is, fractional quantification of atoms is actually fractional quantification over atom-goo. Fractional quant' of substances is bits of substances (which are still substances). Fractional quant' of groups is subgroups. (It is potential group-goo, but that needs to be marked.)
> 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?
No, concretely. This far, I'm really only considering spatial entities. Non-spatial entities, I haven't deal with yet. If all non-spatial entities were atomic, I'd be fine. But time is a substance. So I will have to abstract things further; but that will be when I incorporate abstract entities into this.
> the outer quantifier being a fractional (and concomitantly the gadri > being lo) lo? or loi?
loi
> indicate the referent is an uncountable: it is not being > considered an individual of anything.
Sorry -- my head is boggling. I'm afraid I have taken in only piso'u of what you've said.
Now you know how I've been feeling. ;-)
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).
Oh, I've learned stuff by doing this formalisation, so I think it is necessary. And it is ultimately motivated by Jordan, who kept saying "what the hell is a collective, why isn't a jbomass good enough." If you're sure you know what a collective is, then carry on.
-- κι έγειρε αργά τα στήθια τα θλιμμένα·#Nick Nicholas, French/Italian, σαν αηδόνι που σε νυχτιά ανοιξιάτα #University of Melbourne την ώρα που κελάηδα επνίχτη, ωιμένα! # nickn@hidden.email στις μυρωδιές και στ' ανθισμένα βάτα.# http://www.opoudjis.net-- Ν. Καζαντζάκης, Τερτσίνες: Χριστός#