Subject: Re: [lojban] More about quantifiers

From: [email-masked]
Date: Mon, 11 Mar 2002 10:43:41 EST

In a message dated 3/10/2002 6:51:28 PM Central Standard Time, 
[email-masked] writes:

> >I should note, though, in case, the idiosyncrasies of this
> >quantification system is given any as an argument for a particular 
> >position,
> >that there are equally tidy ways to do everything in terms of {lo ro 
> broda}
> >and of a set involving the Aristotelian A+E-I+ O-.
> 
> Yes, as long as you stay in the {lo ro broda} form they are
> equally tidy. The mess shows up when you try converting between
> the three forms: prenex, da poi and lo broda, or when you try
> to make a quantifier conversion.
> 

As I said, the closer your modified system is to the one you take as basic, 
the easier everything will look without any particular significance over all. 
If we do the basics in the Aristotelian system, for example, then the prenex 
forms are really hideous and ones based on them at least as bad. To be sure, 
in Lojban, the Aristotelian quantifiers are not an option, since we didn't 
have them until last week in any very real sense (well, we lacked O). So, in 
that sense at least, the systems that goes back to the prenex forms is more 
Lojbanic. But, of course, all the systems go back to those forms, since we 
have taken them as basic (if they can't be so defined, then they can't be a 
Lojban quantifier system at all). And then, the one that departs least from 
the basic system will, of course, be easiest to return to that system. But, 
of course, the less a system departs from the basics, the harder it is to 
build into it the import distinction. It is possible to hold that that is a 
Good Thing, that making that distinction ought to be difficult. But it does 
surface, and, as soon as it does, we need a device for dealing with it at a 
basic level, since once it is in it turns up in even the simplest situations, 
by virtue of negations.

But, amusing as all these combinations and reductions may be, they have led 
us away from the basic question, how should the difference between + and - be 
represented in Lojban -- for we have decided to represent it, I take it. The 
choice at the moment is between xorxes' system and mine. After a number of 
modifications and restatements, xorxes' system has gotten a bit cloudy to me, 
so I will leave it to him to give the definitive version. Mine, also with a 
few modifications, runs as follows:

A+ ro broda cu brode
A- ro da poi broda cu brode
E+ no broda cu brode
E- no da poi broda cu brode
I+ [suo /lo /su'o lo] broda cu brode
I- (su'o) da poi broda cu brode
O+ me'iro broda cu brode
O- me'iro da poi broda cu brode

The Aristotelian quantifiers are in place, with the right readings, the + and 
- are clearly marked (Q broda v Q da poi), all the transformations are 
entirely regular and all the forms are unmucky (mainly, to be sure, because 
we have hidden the muck, but that is what definitions are meant to do). And, 
as seems proper given their less frequent significant occurrence, the - forms 
are slightly longer.