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Re: [engelang] Xorban: Semantics of "l-" (and "s-" and "r-")

I agree there's a need for a maximal scope existential quantifier, for the woodcutter, tho I'll address in another msg the question of how to do it in xorban. With regard to your wish to make this the meaning of l, how would you address the point that when you have a category known to have exactly one member, the choice of quantifier for it is redundant, and it is insensitive to scope relative to negation. This is what the (ando)xorxesian singulating quantifier was for, and it covered "everyone loves their own mother" cases too. Is it that you want to get rid of this singulating quantifier completely? if so, what's so wrong with it?

On Sep 10, 2012 2:39 PM, "John E. Clifford" <kali9putra@hidden.email> wrote:


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.

Sent from my iPad

On Sep 9, 2012, at 11:20 PM, "Mike S." <maikxlx@gmail.com> wrote:

 


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.