From pycyn@aol.com Sat May 06 15:43:28 2000 Return-Path: Received: (qmail 582 invoked from network); 6 May 2000 22:43:28 -0000 Received: from unknown (10.1.10.26) by m4.onelist.org with QMQP; 6 May 2000 22:43:28 -0000 Received: from unknown (HELO imo-r20.mail.aol.com) (152.163.225.162) by mta1 with SMTP; 6 May 2000 22:43:28 -0000 Received: from Pycyn@aol.com by imo-r20.mx.aol.com (mail_out_v26.7.) id a.7a.4e3c88c (3995) for ; Sat, 6 May 2000 18:43:23 -0400 (EDT) Message-ID: <7a.4e3c88c.2645fa0b@aol.com> Date: Sat, 6 May 2000 18:43:23 EDT Subject: RECORD: Quantifier Scope, 1999 To: lojban@egroups.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 4.0 for Windows sub 33 From: pycyn@aol.com Note: Lojban is a logical language because its basic grammar is first order predicate logic, not because it satisfies someone's (anyone's) definition of the English word "logical". So, in particular, The scope of quantifiers that occur in Lojban sentences is determined by the order of their first appearance, left to right. This means that {ro da prami de} "Everybody loves somebody" expands to "a loves somebody and b loves somebody and c loves somebody....," possibly a different somebody for each everybody. But {de se prami ro da} means "Somebody is loved by everybody" and expands to "a is loved by everybody or b is...," that there is a single somebody that everybody loves. This appears to violate the symmetry of {se} conversion, but is, in fact not a case of {se} conversion. The problem is that for speaking convenience we shave shortened the basic sentence down somewhat, the first from {ro da de zo'u da prami de}, the second from {de ro da zo'u de se prami da}. Clearly in addition to {se} conversion there has also be reordering of the quantifiers here, so the paradox disappears. Note that {ro da de zo'u de se prami da}, a simple {se} conversion, still means the same as the first sentence. If you think that prenex reordering ought to always work just as much as {se} conversion, I can only report that for most kinds of quantifiers, it just doesn't, if the variables bound by the quantifiers occur in the same bridi. It does however work with strings of all universals or all particulars (and in a few other really weird cases). It happens that, given second order logic, we can define quantifiers that are independent of one another, and, since all second order logic can be mirrored somehow in Lojban, we can introduce these -- not exactly as quantifiers usually (the mirror distorts a bit). The case that started this run through this point, {ci gerku cu batci re nanmu} ordinarily means that each of the three dogs bit some two men, that there are between 2 and 6 dog-bit men involved. To get the "symmetrical" case, three dogs each biting two men, resulting in two men each with bites from three different dogs, we need only use {le ci gerku cu batchi le re nanmu, the quantifiers are now all universal and, so, reorderable. A reorderable case for {ro da prami de} is harder to come up with, since it is a bit harder to imagine what is wanted, but maybe {ro lo prenu cu prami le pa prenu} would do -- though it says a bit more than may strictly be needed.