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The "need" for the two lambdas comes about because he thinks that "All the students in my class who are Italian are chemistry majors" follows from "All the students in my class are chemistry majors," even when none of the students are Italian. And there is a sense in which it does, but not what he seems to think. That is, he wants "Ax:x is a student in my class and an Italianx is a chemistry major" to follow from "Ax: x is a student in my class x is a chemistry major." But, with importing A, you can expand the subject only when the expanded expression has an instance, so not in this case. On the other hand, it always works to go from "Ax:Fx Gx" to "Ax:Fx if Hx then Gx" (indeed, expanding the subject moves through this as an intermediate step), and this can be read as "All fs which are H are G" or so as well as the earlier version.

The lambda, even as importing is curiously defined, taking acoount of the anomolous cases rather than eliminating them from the get-go. If it were just what we would write in unrestricted quantifiers as "~Ex(Fx & ~Gx) & ExFx" (or, at the end, "Ex(Fx & Gx)") it does not appear that the anomolous cases would arise. Further, all the cases could be handled using importing quantifiers.

Having said that, I should note that, while this solves the problem for "all," it does not do so for the "proportional quantifiers" (other than "all" if you want to include it in this class). They still seem to require a totality that is not available with non-cumulative predicates. At this point it seems to me that McKay should take heed of what singularists do with non-dstributive predicates, namely turn them into relations and consider the pluralities involved pairwise. Thus, "I are shipmates" becomes (roughly) "for all j, k among I, j is a shipmate of k and k of j." The the non-cumulative cases (and in deed the non-distributive ones generally) become, taking "most" as an example, "most x that engage in F (with someone) are G (with someone or with someone — or all or most or whatever fits --they F with). I think that is what he is shooting for but is hampered from getting there by his presuppositions about how proportional quantifiers work (though that pattern could be made
to work with this reading and a bit of work-- the sortal has been distributed).

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

pc:
> A>I don't get your point then.

My point is that:

pa da broda ijo ge su'o de broda gi ro di poi broda cu du de

is true when the da's are singular variables, but false when they
are plural variables (taking ro as McKay's lambda quantifier).

In other words, assuming there are broda, {su'o da poi broda
cu du ro de poi broda} is always true with plural variables, but
normally not true with singular variables.

[McKay's system has two (or three) "all"s.]
> C> I only count two (and note he is mistakena about the need for
> non-importing regular lambda "all" since he screwed up an example.

Count again. He represents one of them with an inverted A, that's
the dual of inverted E. The other two are represented with capital
lambda, one with and one without a superscript that indicates
existential import. But this latter distinction is not that
interesting, the two interesting cases are the inverted A versus
the lambda.

mu'o mi'e xorxes