Well, since you keep mentioning ."known identities", I felt free to introduce one myself -- especially one from Montague. It is not a new quantifier, only a new manner of writing an old one, an afterthought quantifier, if you will. With forethought, I could lay out all the constants I was going to use in my narration and list them at the beginning (what initially took & to be suggesting). But I don't generally know before hand, so I introduce them as they turn up -- but they have the same scope as they would have had were they introduced initially. In effect, I am advocating the particular version of "any", hardly a novel idea. As for proof, I note that, translating back to standard notation and assuming there is no context, both sides of your equivalence are simply sa Ra na Pa.
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On Sun, Sep 9, 2012 at 10:50 PM, John E Clifford <kali9putra@hidden.email> wrote:
These communications get rather out of synch. So, to sum up; 'lV' is a particular quantifier (an sV but for one peculiar property) which, wherever it occurs, has scope over the entire discourse and thus is immune to influence from local matters like rV or other sV or na or je. This does mean that somethings which I would have called lVs on analogy with {lo} are, in fact, sVs, since they have only local scope and are affected by negations and other local quantifiers. In particular, the definition of o'e turns out to require an initial sV, not lV..
Okay, am I to understand correctly that you've simply invented a novel
quantifier and plopped it into FOL? Or, is it possible to define your
"lo/lV" more precisely in terms of pure FOL? Can you for example prove
that:
na la Ra Pa <=> la Ra na Pa
... i.e. can you
demonstrate that in your system each side is a logically equivalent transformation of
the other? Or do you simply declare that that identity is so? What
about the other known identities I have mentioned? I want to give your
ideas due consideration, but I need to see things a little better defined
than this.
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