From jjllambias@hotmail.com Sat Mar 09 09:42:51 2002 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 9 Mar 2002 17:42:51 -0000 Received: (qmail 4312 invoked from network); 9 Mar 2002 17:42:50 -0000 Received: from unknown (216.115.97.167) by m9.grp.snv.yahoo.com with QMQP; 9 Mar 2002 17:42:50 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.72) by mta1.grp.snv.yahoo.com with SMTP; 9 Mar 2002 17:42:50 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Sat, 9 Mar 2002 09:42:50 -0800 Received: from 200.69.2.52 by lw8fd.law8.hotmail.msn.com with HTTP; Sat, 09 Mar 2002 17:42:50 GMT To: lojban@yahoogroups.com Bcc: Subject: The quantifiers that Aristotle forgot Date: Sat, 09 Mar 2002 17:42:50 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 09 Mar 2002 17:42:50.0562 (UTC) FILETIME=[D5494A20:01C1C791] From: "Jorge Llambias" X-Originating-IP: [200.69.2.52] X-Yahoo-Group-Post: member; u=6071566 X-Yahoo-Profile: jjllambias2000 I was thinking about the quantifier {su'ono} that came up during the discussion. There probably was no such simple word in Greek for that, but if Aristotle had been a Lojbanist, he might have added this "tautological" quantifier to his list: U- su'ono broda cu brode U+ su'ono lo su'o broda cu brode U- is always true. U+ is true when there are broda. Now fortunately Lojban provides a sixth vowel for the corresponding contradictories: Y+ naku su'ono broda cu brode Y- naku su'ono lo su'o broda cu brode Y+ is always false, Y- is true only when there are no broda. We don't need any more vowels because each of them is its own complementary, and the contradictories are the duals. We can write Y+ also as: Y+ za'uro broda cu brode Or we could use {me'ino} instead of {za'uro}. I can't think of any simple quantifier that would give us Y-, so like I- and O- we just use naku plus its contradictory. Why do we say that Y+ has existential import? Because it requires there to be broda in order to be true (though it is not enough that there be broda, as it is never true). On the other hand, Y- can be true in the absence of broda. Indeed it is always true in the absence of broda, but the - indicates that it can be true. To see how this fits with the whole system, we might write it in terms of sets: A- SP = S E- SP = 0 I+ SP /= 0 O+ SP /= S U- S = S Y- S = 0 U+ S /= 0 Y+ S /= S Notice that the last four are the first four where P is the universal set. A+ SP = S AND S /= 0 E+ SP = 0 AND S /= 0 I- SP /= 0 OR S = 0 O- SP /= S OR S = 0 U+ S = S AND S /= 0 Y+ S = 0 AND S /= 0 U- S /= 0 OR S = 0 Y- S /= S OR S = 0 Again the last four are the first four where P is the universal set. They collapse to the same four we had before. To represent the universal set in Lojban, we need a brode which is always true. One such brode might be {davdu'o}, from {du be da}: "x1 is something". {lo'i davdu'o} would be the universal set. mu'o mi'e xorxes _________________________________________________________________ Join the world’s largest e-mail service with MSN Hotmail. http://www.hotmail.com