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On Mon, Sep 10, 2012 at 10:01 AM, John E. Clifford <kali9putra@hidden.email> wrote:
, mWell, 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.
I don't see how you observed any of these in Lojban, since they don't hold there. I can't speak of Xorban, since it is still a bit amorphous. But it is inherently unlikely they hold there either, since the would work only if every predicate had a unit extension.
-- 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.)
Which Montague system are you referring to, Elements or Proper Treatment (etc.)? While I haven't looked at my class notes in years, my memory is that Elements uses Frege's description operator (primitive, not defined) and Proper Treatment has some nice discussions about where quantifiers are in surface grammar and logical structure (a large part of the point).
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
See above. I'd just as soon do without either of them as far as possible.
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-".
To say it yet again, lV is just sV with it's scope extending from way to the left (beginning of discourse, beginning of the sentence, wherever) to as far right as needed. It has essentially nothing to do with definite descriptions. It works in this system much like "any" does in English, except that "any" is a universal quantifier over the sentence in which it occurs and lV is particular.
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.
Well, (leaving aside a minor quibble) that is what is _meant_ to be proved, equivalence.
But this equivalence, between na laRa Pa and laRa na Pa, is very different from those between la RaPa and ra Ra Pa or sa Ra Pa, both of which are generally false. |