On Mon, Sep 10, 2012 at 5:58 PM, John E. Clifford
<kali9putra@hidden.email> wrote:
I assume then that you would hold that "na la Ra Pa" and "la Ra na Pa" are equivalent, same as Xorban?
For the second time in this note and the I don't know how manyth time in this conversation, of course they are. Can we move on from this never disputed point?
Well, sorry about that, but you didn't seem to like my identities, most of which are
uncontroversial ones. I realize now that the only one you object to is
the putative one-way transformation "(s|r)a Ra Pa => la Ra Pa" which I admit
is at best uncertain. So perhaps we are less in disagreement than I had thought.
As a side note, could we think of something other than "long-scope s-" to describe "l-"? Call it anything you
like, but please leave the well understood and uncontroversial parts of our system out of it. It's not really "s-" if it is long-scope.
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.
I hold that "na la Ra Pa" and "la Ra na Pa" are generally equivalent i.e. always interchangeable. It's worth noting that "la Ra (s|r)e Re" and "(s|r)e Re la Ra" (keeping s/r the same) are also equivalent. The exact relationship between "la Ra Pa" and "(s|r)a Ra Pa" is a trickier matter, but suffice to say that it's clear that they are not generally equivalent.
Again, no problem. These follow from the nature of l as always leftmost in fact regardless of where it is in the text. I am sorry if I have attributed to you what is apparently &'s claim about the equivalence of l and s and r. As you say, they are not generally equivalent, though the implication chain does run r > l > s.
I would hold that la Ra <=> sa [[R]]a <=> ra [[R]]a but I would deny the equivalence with [[R]] replaced with R. I have a rather longish essay in the works that will suggest a means of separating the syntax from the semantics of [[R]], in order to allow "l-" to work in FOL as we want it while sidestepping (a large part of) the semantic controversy over [[R]] i.e. "myopic singularization".
/