From pycyn@aol.com Wed Nov 06 07:16:07 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 6 Nov 2002 15:16:04 -0000 Received: (qmail 65009 invoked from network); 6 Nov 2002 15:16:04 -0000 Received: from unknown (66.218.66.216) by m9.grp.scd.yahoo.com with QMQP; 6 Nov 2002 15:16:04 -0000 Received: from unknown (HELO imo-m10.mx.aol.com) (64.12.136.165) by mta1.grp.scd.yahoo.com with SMTP; 6 Nov 2002 15:16:07 -0000 Received: from Pycyn@aol.com by imo-m10.mx.aol.com (mail_out_v34.13.) id r.181.11658eef (4012) for ; Wed, 6 Nov 2002 10:16:00 -0500 (EST) Message-ID: <181.11658eef.2afa8c2f@aol.com> Date: Wed, 6 Nov 2002 10:15:59 EST Subject: Re: [lojban] Re: zo'e =? su'o de (was Re: What the heck is this crap?) To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_181.11658eef.2afa8c2f_boundary" X-Mailer: AOL 8.0 for Windows US sub 230 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_181.11658eef.2afa8c2f_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 11/5/2002 11:00:54 PM Central Standard Time, a.rosta@lycos.co.uk 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. --part1_181.11658eef.2afa8c2f_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 11/5/2002 11:00:54 PM Central Standard Time, a.rosta@lycos.co.uk 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.

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