From pycyn@aol.com Sat Mar 09 14:18:53 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 9 Mar 2002 22:18:53 -0000 Received: (qmail 56901 invoked from network); 9 Mar 2002 22:18:52 -0000 Received: from unknown (216.115.97.167) by m12.grp.snv.yahoo.com with QMQP; 9 Mar 2002 22:18:52 -0000 Received: from unknown (HELO imo-d05.mx.aol.com) (205.188.157.37) by mta1.grp.snv.yahoo.com with SMTP; 9 Mar 2002 22:18:52 -0000 Received: from Pycyn@aol.com by imo-d05.mx.aol.com (mail_out_v32.5.) id r.a3.24e403c5 (17378) for ; Sat, 9 Mar 2002 17:18:47 -0500 (EST) Message-ID: Date: Sat, 9 Mar 2002 17:18:46 EST Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_a3.24e403c5.29bbe446_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 --part1_a3.24e403c5.29bbe446_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/9/2002 2:57:35 PM Central Standard Time, edward.cherlin.sy.67@aya.yale.edu writes: > There is no universal set in any consistent set theory, since the set > of subsets of a given set is larger (has strictly greater > cardinality) than the original set. Is there a Lojban term for > 'class' as the term is currently used in set theory? (Crudely, a > collection of sets must be a class rather than a set if > contradictions would arise from it being a set. For precision, see > any of the axiom sets for successful set theories of this kind.) Thanks for the reminder; we get so involved in the give and take that we forget to check on basics from time to time. Yes, it is a universal class that is wanted and just which one is very hard to say. It is easier in a formal language when the types are all in a row, but Lojban reduces everything to one type, as it were (but so do most natural languages), so what all can be quantified over is not at all clear. Everything that can be successfully referred to in Lojban is clearly in and a lot more besides (all of set theory and hence of mathematics is in, for example). In any case, it is unlikely to be a recognizable class from some organized theory, though the classes from a number of theories probably get into it (it may not be formally coherent, though presumably non-contraditory, since it is the stuff of reality). --part1_a3.24e403c5.29bbe446_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/9/2002 2:57:35 PM Central Standard Time, edward.cherlin.sy.67@aya.yale.edu writes:


There is no universal set in any consistent set theory, since the set
of subsets of a given set is larger (has strictly greater
cardinality) than the original set. Is there a Lojban term for
'class' as the term is currently used in set theory? (Crudely, a
collection of sets must be a class rather than a set if
contradictions would arise from it being a set. For precision, see
any of the axiom sets for successful set theories of this kind.)


Thanks for the reminder; we get so involved in the give and take that we forget to check on basics from time to time.  Yes, it is a universal class that is wanted and just which one is very hard to say. It is easier in a formal language when the types are all in a row, but Lojban reduces everything to one type, as it were (but so do most natural languages), so what all can be quantified over is not at all clear.  Everything that can be successfully referred to in Lojban is clearly in and a lot more besides (all of set theory and hence of mathematics is in, for example).  In any case, it is unlikely to be a recognizable class from some organized theory, though the classes from a number of theories probably get into it (it may not be formally coherent, though presumably non-contraditory, since it is the stuff of reality). --part1_a3.24e403c5.29bbe446_boundary--