On Mon, Sep 10, 2012 at 10:01 AM, John E. Clifford
<kali9putra@hidden.email> wrote:
Well, since you keep mentioning ."known identities", I felt free to introduce one myself
The known identities that I mentioned are logical equivalences that I _observed_ in post-xorlo Lojban & Xorban, not something that I personally introduced on a whim. It seems desirable, IMHO, to account for these identities using the least exotic method that can be found.
-- especially one from Montague.
Montague's system is like Xorban in that it has three basic quantifiers. Two of them are exactly equivalent to "s-" and "r-". The third is Bertrand Russell's formalization of English "the" i.e. the "definite description". (Just thought it might be helpful to point this out.)
As a minor side note, I am not too keen on Russell's DDs (my only beef with Montague), but if you can demonstrate they work, I'd be genuinely curious to look at that.
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.
Well, definite descriptions don't seem like "any" so I honestly haven't a clue what you're on about. I don't wish to be disrespectful, but I think we do need to move out of this bowl-of-oatmeal mode of discourse. All I ask is to please give me a (roughly speaking, doesn't have to be perfect) _formal_ definition of your "l-" and show me how it works wrt FOL "s-" & "r-".
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.