From pycyn@aol.com Tue Aug 21 15:38:03 2001 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 21 Aug 2001 22:38:02 -0000 Received: (qmail 61766 invoked from network); 21 Aug 2001 22:35:02 -0000 Received: from unknown (10.1.10.142) by l7.egroups.com with QMQP; 21 Aug 2001 22:35:02 -0000 Received: from unknown (HELO imo-r03.mx.aol.com) (152.163.225.99) by mta3 with SMTP; 21 Aug 2001 22:35:02 -0000 Received: from Pycyn@aol.com by imo-r03.mx.aol.com (mail_out_v31_r1.4.) id r.81.f01d9de (3927) for ; Tue, 21 Aug 2001 18:34:50 -0400 (EDT) Message-ID: <81.f01d9de.28b43c0e@aol.com> Date: Tue, 21 Aug 2001 18:34:54 EDT Subject: Iota To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_81.f01d9de.28b43c0e_boundary" X-Mailer: AOL 6.0 for Windows US sub 10531 From: pycyn@aol.com --part1_81.f01d9de.28b43c0e_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Strictly there is no iota in Russell; the formula FixGx (you get the idea) is merely an abbreviation for Ex(Ay(Gy <=> y=x) & Fx), "there is exactly one G and it is F." This creates some problems -- in symbolism at least -- when there are no (or more than one) Gs. The basic sentence is false of course, but then you need to mark the basic sentence, escpecially with negations: (~F)ixGx vs. ~(FixGx). For other folk around Russell's occupation, the idea of having a name (or what looked like one) which doesn't refer was abhorrent, so they found something for ixGx to stand for when the uniqueness condition is not met. Others had different solutions for the matter depending on whether there were too many or too few Gs. JCB was of this non-Russellian solution persuasion, deciding that when there was no G, you take something plausibly Gish, and if there is more than one you take a select one (in the earliest versions) or as many as you need (later) or some number of Gish things (later still). There are any number of other solutions around (I suspect that there are some notes about this in the archives somewhere). --part1_81.f01d9de.28b43c0e_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit Strictly there is no iota in Russell; the formula FixGx (you get the idea) is
merely an abbreviation for Ex(Ay(Gy <=> y=x) & Fx), "there is exactly one G
and it is F."  This creates some problems -- in symbolism at least -- when
there are no (or more than one) Gs.  The basic sentence is false of course,
but then you need to mark the basic sentence, escpecially with negations:
(~F)ixGx vs. ~(FixGx).  For other folk around Russell's occupation, the idea
of having a name (or what looked like one) which doesn't refer was abhorrent,
so they found something for ixGx to stand for when the uniqueness condition
is not met.  Others had different solutions for the matter depending on
whether there were too many or too few Gs.  JCB was of this non-Russellian
solution persuasion, deciding that when there was no G, you take something
plausibly Gish, and if there is more than one you take a select one (in the
earliest versions) or as many as you need (later) or some number of Gish
things (later still).  There are any number of other solutions around (I
suspect that there are some notes about this in the archives somewhere). --part1_81.f01d9de.28b43c0e_boundary--