From pycyn@aol.com Mon Mar 11 07:44:37 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 11 Mar 2002 15:44:37 -0000 Received: (qmail 14580 invoked from network); 11 Mar 2002 15:43:47 -0000 Received: from unknown (216.115.97.167) by m9.grp.snv.yahoo.com with QMQP; 11 Mar 2002 15:43:47 -0000 Received: from unknown (HELO imo-d09.mx.aol.com) (205.188.157.41) by mta1.grp.snv.yahoo.com with SMTP; 11 Mar 2002 15:43:47 -0000 Received: from Pycyn@aol.com by imo-d09.mx.aol.com (mail_out_v32.5.) id r.171.a14e09d (4324) for ; Mon, 11 Mar 2002 10:43:41 -0500 (EST) Message-ID: <171.a14e09d.29be2aad@aol.com> Date: Mon, 11 Mar 2002 10:43:41 EST Subject: Re: [lojban] More about quantifiers To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_171.a14e09d.29be2aad_boundary" X-Mailer: AOL 7.0 for Windows US sub 118 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra X-Yahoo-Message-Num: 13604 --part1_171.a14e09d.29be2aad_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/10/2002 6:51:28 PM Central Standard Time, jjllambias@hotmail.com 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. --part1_171.a14e09d.29be2aad_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/10/2002 6:51:28 PM Central Standard Time, jjllambias@hotmail.com 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.
--part1_171.a14e09d.29be2aad_boundary--