From nobody@digitalkingdom.org Fri Apr 08 16:53:07 2005 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 08 Apr 2005 16:53:08 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.44) id 1DK3HY-000070-Eg for lojban-list-real@lojban.org; Fri, 08 Apr 2005 16:53:00 -0700 Received: from web81302.mail.yahoo.com ([206.190.37.77]) by chain.digitalkingdom.org with smtp (Exim 4.44) id 1DK3HX-00006q-4G for lojban-list@lojban.org; Fri, 08 Apr 2005 16:53:00 -0700 Message-ID: <20050408235228.14433.qmail@web81302.mail.yahoo.com> Received: from [65.69.48.37] by web81302.mail.yahoo.com via HTTP; Fri, 08 Apr 2005 16:52:28 PDT Date: Fri, 8 Apr 2005 16:52:28 -0700 (PDT) From: John E Clifford Subject: [lojban] Re: ATTN: McIvor (was: Re: Re: Hintikka on Quantifier Scope To: lojban-list@lojban.org In-Reply-To: 6667 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Spam-Score: -2.6 (--) X-archive-position: 9798 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 Precedence: bulk Reply-to: lojban-list@lojban.org X-list: lojban-list > What is your take on IF Logic? Can it express > ideas not expressible > without it? Is it simply a disguise for 2-order > logic? > Yes to the first: there is an infamous quantifier expression that is impossible in standard logic but easy in IF. Unfortunately, getting stuff like that in means that all the properties that make standard logic fruitful to study go out the window once you get that kind of strength (more than first order logic, less than full second order -- no quantification over predicates, though there are work-arounds that come close, I gather). On the further goings on, the fact that IF logic is not recursively enumerable (finitely axiomatizable) means that Goedel's theorems don't go through and so, in principle at least, arithmetic might be completed. But, since it would involve deductively unsubstantiated proof procedures, this may not be much of a triumph. None of the other things that IF does in what I've looked over this week seems to me to be useful enough (or, indeed, obviously to involve IF) to switch allegiance from standard logic. On the other (now about fourth) hand, Hintikka is a hard man to ignore, so there is something there worth at least looking at some more.