Subject: Re: [lojban] Re: zo'e =? su'o de (was Re: What the heck is this crap?)

From: [email-masked]
Date: Wed, 6 Nov 2002 10:15:59 EST

In a message dated 11/5/2002 11:00:54 PM Central Standard Time, 
[email-masked] writes:
<<
> As I say above, I think it does import. It's not a settled question.
> >>
At the risk of muddying the water yet further, let me suggest that some of 
these problems arise from failing to note that Lojban quantifiers function in 
two (at least) different systems. The purest case of one system is 
schematized as Qxg Fx gi Gx (g being usually either {ganai} -- with Q = {ro} 
-- or {ge} -- with Q = {su'o}). This has as primitive Qs only {ro} and 
{su'o} and the rest are variously defined -- more or less accurately -- in 
terms of these. These Qs obey the simple Q-DeMorgan laws. With them, {no 
da broda gi'e brode} = {naku su'o ... } is non-importing for broda (nor for 
{brode}). (It does import, of course, for the range of {da}, the universal 
class, but that fact is rarely interesting.) 
The second system is the Aristotelian one, schematized by Q broda cu brode, 
with Q ranging immediately over the whole set of PA (well, I am always unsure 
about {tu'o} and maybe a few others) For the usual logical cases, the rules 
with negations are the rules of the square of opposition. Within that 
square, given that {ro} and {su'o} import for broda, the status of their 
denials, {no} and {me'i[ro]}, is uncertain. For a variety of reason, the 
historical position has been (however poorly expressed and often apparently 
contradicted) that these latter two do not import for broda. On the other 
hand, given the Lojban system with internal quantifiers, it does seem that 
they must. I take this more as a criticism of internal quantifiers than 
anything else, but I am less clear about what the ultimate ramifications may 
be here.
The {Q da poi broda cu brode} forms lie somewhere in between -- using the 
variables of the first system but apparently restricting their range in a way 
differreent from that used in the first and, thus, closer to that in the 
second. It is just not clear what rules apply to these. One of the 
advantages of &'s device to make predicates of {poi}s was exactly to shift 
these unequivocally into the {Q broda cu brode} system, where I think they 
belong. The other direction requires that {poi broda} takes on a different 
meanings when the quantifier is {ro}. And, of course, these expressions may 
be sui generis in some as yet unworked out way.