From lojban-out@lojban.org Wed Apr 06 17:21:01 2005 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 94713 invoked from network); 7 Apr 2005 00:21:01 -0000 Received: from unknown (66.218.66.218) by m14.grp.scd.yahoo.com with QMQP; 7 Apr 2005 00:21:01 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.81.49.134) by mta3.grp.scd.yahoo.com with SMTP; 7 Apr 2005 00:21:00 -0000 Received: from lojban-out by chain.digitalkingdom.org with local (Exim 4.44) id 1DJKlY-00086O-99 for lojban@yahoogroups.com; Wed, 06 Apr 2005 17:21:00 -0700 Received: from chain.digitalkingdom.org ([64.81.49.134]) by chain.digitalkingdom.org with esmtp (Exim 4.44) id 1DJKlD-00085y-3a; Wed, 06 Apr 2005 17:20:42 -0700 Received: with ECARTIS (v1.0.0; list lojban-list); Wed, 06 Apr 2005 17:20:35 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.44) id 1DJKl2-00085n-0D for lojban-list-real@lojban.org; Wed, 06 Apr 2005 17:20:28 -0700 Received: from web81310.mail.yahoo.com ([206.190.37.85]) by chain.digitalkingdom.org with smtp (Exim 4.44) id 1DJKkz-000852-6y for lojban-list@lojban.org; Wed, 06 Apr 2005 17:20:27 -0700 Message-ID: <20050407001954.80327.qmail@web81310.mail.yahoo.com> Received: from [65.69.48.37] by web81310.mail.yahoo.com via HTTP; Wed, 06 Apr 2005 17:19:54 PDT Date: Wed, 6 Apr 2005 17:19:54 -0700 (PDT) In-Reply-To: 6667 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Spam-Score: -2.6 (--) X-archive-position: 9776 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net X-list: lojban-list X-Spam-Score: -2.6 (--) To: lojban@yahoogroups.com X-Originating-IP: 64.81.49.134 X-eGroups-Msg-Info: 1:12:0 X-eGroups-From: John E Clifford From: John E Clifford Reply-To: clifford-j@sbcglobal.net Subject: [lojban] Re: Hintikka on Quantifier Scope X-Yahoo-Group-Post: member; u=116389790 X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 24132 --- 2 = 3 wrote: > "Here we are beginning to see the whole horror > of Frege's mistake. > The notation he introduced (like the later > notation of Russell and > Whitehead) arbitrarily rules out certain > perfectly possible patterns of > dependence and independence between quantifiers > or between connectives > and quantifiers." > > http://www.hf.uio.no/filosofi/njpl/vol1no2/revolution/revolution.pdf Oh, that Jaako! What a card! He is technically right, of course, but he also points out most of the reasons why little will come of it -- for a while at least. As for its role in Lojbanery, his notation does suggest a partial solution for the problem of quantifiers not getting comfortably where they are needed (sentences about dogs biting men seem to play quite arole here). I suppose the relaization here would be something like {pe} attaching a list of binding (or of nonbinding) variables to a variable that was out of place linearly. I seem to recall something like this was proposed once a long while ago using modified Skolem functions in place of particular quantifiers (and eventually groups -- bunches -- for value to make the numeric cases work). It died for now forgotten reasons, but the {pe}-like critter might survive. There has been less discussion of problems with connectives and quantifiers, though it should be easy to get up a few specimens. Alas, it is less easy to see how to apply Hintikka's notation to the connective cases (and especially how to get workarounds for connectives other than OR -- we can't expect everything to be in normal form). This probably deserves another look-at sometime along the line. > If it rained, it did not rain hard. > It did rain hard. > Therefore it did not rain. So the first premise if false, it rained and rained hard. (strictly requires that raining hard entails raining -- not a problematic addition, but it reduces then to a contradiction.)