From cowan@ccil.org Mon Feb 18 16:08:58 2002 Return-Path: X-Sender: cowan@mercury.ccil.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_2); 19 Feb 2002 00:08:58 -0000 Received: (qmail 10932 invoked from network); 19 Feb 2002 00:08:57 -0000 Received: from unknown (216.115.97.167) by m11.grp.snv.yahoo.com with QMQP; 19 Feb 2002 00:08:57 -0000 Received: from unknown (HELO mercury.ccil.org) (192.190.237.100) by mta1.grp.snv.yahoo.com with SMTP; 19 Feb 2002 00:08:57 -0000 Received: from cowan by mercury.ccil.org with local (Exim 3.12 #1 (Debian)) id 16cxqB-00033r-00; Mon, 18 Feb 2002 19:09:03 -0500 Subject: Re: [loglanists] Sets In-Reply-To: <3C712477.18628919@attglobal.net> from "John W. Kennedy" at "Feb 18, 2002 10:57:43 am" To: "John W. Kennedy" Date: Mon, 18 Feb 2002 19:09:03 -0500 (EST) Cc: "loglanists@ucsd.edu" , lojban@yahoogroups.com X-Mailer: ELM [version 2.4ME+ PL66 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: X-eGroups-From: John Cowan From: John Cowan X-Yahoo-Group-Post: member; u=212516 X-Yahoo-Profile: johnwcowan John W. Kennedy scripsit: > This seems to involve the > late-19th-century dispute over whether "all" statements and "some" > statements have existential import. Classicists claimed they did. > Modernists claimed they did not. Nobody has ever claimed that existential ("some") statements did not have existential import. The whole point of saying "Some swans are white" is to assert that there *are*, indeed, swans that are white. The question is about universal statements and how to map them. Traditionally, "All swans are white" (used by Aristotle, but now known to be empirically false) was read as having existential import, as you say. Modernists mapped this to "For all X, if X is a swan then X is white" which does not have existential import about swans (it has existential import about X, but that is no problem unless we are considering a purely empty universe, which can be dismissed). It merely says that *if* there are any swans then they are white. This clash can be resolved in one of two ways: decide that "All swans are white" has no existential import either, or decide that "For all X etc." is not a fully adequate mapping of "All swans etc." Lojban takes the second view, since both forms can be expressed: one using number + predicate directly (= "All swans"), the other using a bound variable and a relative clause ("All X such that"). > Lewis Carroll, as I recall, tried to > compromise by giving existential import to "some" statements, but not to > "all" statements (so that, by his scheme, "All unicorns are white" is > acceptable, but "Some unicorns have halitosis" is not). Carroll took the traditional view: both have existential import. -- John Cowan http://www.ccil.org/~cowan cowan@ccil.org To say that Bilbo's breath was taken away is no description at all. There are no words left to express his staggerment, since Men changed the language that they learned of elves in the days when all the world was wonderful. --_The Hobbit_