From pycyn@aol.com Thu Mar 07 01:13:50 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 7 Mar 2002 09:13:49 -0000 Received: (qmail 40427 invoked from network); 6 Mar 2002 19:32:36 -0000 Received: from unknown (216.115.97.171) by m5.grp.snv.yahoo.com with QMQP; 6 Mar 2002 19:32:36 -0000 Received: from unknown (HELO imo-r05.mx.aol.com) (152.163.225.101) by mta3.grp.snv.yahoo.com with SMTP; 6 Mar 2002 19:32:36 -0000 Received: from Pycyn@aol.com by imo-r05.mx.aol.com (mail_out_v32.5.) id r.159.a0ec78d (3925) for ; Wed, 6 Mar 2002 14:32:25 -0500 (EST) Message-ID: <159.a0ec78d.29b7c8c9@aol.com> Date: Wed, 6 Mar 2002 14:32:25 EST Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_159.a0ec78d.29b7c8c9_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_159.a0ec78d.29b7c8c9_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/6/2002 12:46:11 PM Central Standard Time, cowan@ccil.org writes: > All S is P (A): SP = S > Some S is P (I): SP /= 0 > No S is P (E): SP = 0 > Some S is not P (O): SP /= S > > Then existential import is simply the assertion that S /= 0, and we can > understand I- as asserting that S, which may be null, has a non-null > intersection with P. But plainly no set P can have a non-null intersection > with 0, and so from SP /= 0 we can deduce that S /= 0. Therefore I- > is false if S = 0, and to assert anything useful we need I+. > I- is "SP/=0 OR S=0" on this reading, so, while, when S=0 the SP part drops out, when SP/=0 (and hence a fortiori S/=0) then an number (1 or greater) of Ss may be Ps. So, I- is compatible with any number (0 or greater) of Ss being Ps. To be sure, the useful part is I+, but that can't be derived from "not both SP=0 and S/=0". You might expect E+ to be pretty useless, too, but it seems quite normal. --part1_159.a0ec78d.29b7c8c9_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 3/6/2002 12:46:11 PM Central Standard Time, cowan@ccil.org writes:


All S is P (A):        SP = S
Some S is P (I):    SP /= 0
No S is P (E):        SP = 0
Some S is not P (O):    SP /= S

Then existential import is simply the assertion that S /= 0, and we can
understand I- as asserting that S, which may be null, has a non-null
intersection with P.  But plainly no set P can have a non-null intersection
with 0, and so from SP /= 0 we can deduce that S /= 0.  Therefore I-
is false if S = 0, and to assert anything useful we need I+.

I- is "SP/=0 OR S=0"  on this reading, so, while, when S=0 the SP part drops out, when SP/=0 (and hence a fortiori S/=0) then an number (1 or greater) of Ss may be Ps.  So, I- is compatible with any number (0 or greater) of Ss being Ps.  To be sure, the useful part is I+, but that can't be derived from "not both SP=0 and S/=0".  You might expect E+ to be pretty useless, too, but it seems quite normal. --part1_159.a0ec78d.29b7c8c9_boundary--