WikiDiscuss

A> I think I have managed — with a little more fiddling. The non-importing versions have not been shown necessary.

B>Aesthetics; it is a neater system with only one universal quantifier. Also, the lambda quantifer gives anomolous cases (that is, universal claims that are not covered by thatuniversal quantifier) and getting rid of them is surely a good idea (although pointing them out is also useful for the study of English, say).

C> Because there are sometimes (i.e., with noncumulative F) no "the Fs" yet the proportional quantifiers need a whole to work off of.
Yes, I should separate the proportional ones from the others, since the whole reference to the Fs is unneccesary there,

D> The second part gets that only F's are in (each hsa to be in some group that Fs), while the first gets them all in. It should read "[EK:"

E> Yes, I seem to have actually defined the stronger notion which deal with all the FGs, not merely the locally interesting group. Of course you need this fuller form to do a bang-up job when Q = "all", but by inference even that can make do with only an "E" and without the "the F' G's." Nice, since the steps for "the" are messy in detail. Thanks.
This should amount to the same thing when "the F and G" are well-defined, but it covers (is meant to, anyhow) the remaining cases as well in a single formula.

F> Yes; even McKay has to do "no" separately, since it involves the denial of some or all of those E's he has built in. I aam less sure about the dual of E, which does seem to work out — but my score with working things out is low right now. I don't see the problem with "at most" unless you mean it to cover the "no" case — and if you do, then it is just "not at least" which is admittedly another new pattern. But McKay has to deal with all those, too, so I seem to be one up on him (and he does not even describe how he will do the other proportional quantifiers with noncumulative predicates). Does he reduce the dual of E other than by using the dual formula?

Jorge Llambías <jjllambias2000@yahoo.com.ar> wrote:

pc:
> A> Well, I am being dense here, but this looks like the first case ("I is an
> individual")If there are n+a zillion things among I, then there will be n
> things among I and an individual among I but not among those those n things,
> indeed, a zillion such. The formula works for "at least n+1" but that is not
> what was sought.

You're right, you do need the "all" there.

> C> One of the points here was to get rid of all these "all"s.

A>I don't think we can get rid of them. There are two "all"s that
differ significantly (each of them can have an existential and
a non-existential variant, but that is generally irrelevant).

The two different "all"s are the one used in "all students
surround the building" and the one used in "all companies that
compete share common interests". "Any" can substitute for it
in this second case "any companies that compete share common
interests".

B>But I don't see how the point can be to get rid of them. Both
have clear and distinct uses.

> All this
> going around has helped me sort through a mess of stuff (making public
> mistakes along the way), but this last bit puts the finishing touches on one
> more try: [QX:Fx]GX depends upon the notion of *the* Fs or rather the F's,
> where F' is the distributive correlate of F, "is involved in F".

C>I'm not sure why you need F'. Anyway, "the Fs" are needed for proportional
quantifiers. Non-proportional ones are meaningful even when "the Fs" is
not well defined.

> Then, if a are the F's iff ~[EI:I are F] ~I among a & ~[EJ: J among a & J
> individual] ~[K:K are F] J among K.

D>What's the second part for? What's the quantifier that binds K? I would
have thought that a are the Fs iff ~[EI:I are F] ~I among a. Is that not
enough?

> And some existence things I need to sneak
> in there somehow — or just move over to normal universals. Then the
> quantified sentence above is just [EI: I are the F & G)'s][EJ: J are the F's]
> I is Q of J. Some fuzzy stuff here still, so plese knock this doen so it
> comes into focus.

E>Why not simply [EI: I are G][EJ: J are the Fs] I are Q of J, which is
what McKay gives for proportional quantifiers? I think it amounts to the
same thing when "the F&Gs" is well defined.

F>Either way, it won't work for {no}, for {su'eci}, or for A (the dual of E).
But as McKay shows these are definable in terms of the others.

mu'o mi'e xorxes

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