From lojban-out@lojban.org Fri Jul 14 17:37:22 2006 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 50691 invoked from network); 15 Jul 2006 00:29:23 -0000 Received: from unknown (66.218.66.167) by m34.grp.scd.yahoo.com with QMQP; 15 Jul 2006 00:29:23 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.81.49.134) by mta6.grp.scd.yahoo.com with SMTP; 15 Jul 2006 00:29:23 -0000 Received: from lojban-out by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1Y25-0000WN-Gm for lojban@yahoogroups.com; Fri, 14 Jul 2006 17:29:21 -0700 Received: from chain.digitalkingdom.org ([64.81.49.134]) by chain.digitalkingdom.org with esmtp (Exim 4.62) (envelope-from ) id 1G1Y0u-0000UW-I2; Fri, 14 Jul 2006 17:28:10 -0700 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 14 Jul 2006 17:28:00 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1Y0U-0000UN-59 for lojban-list-real@lojban.org; Fri, 14 Jul 2006 17:27:42 -0700 Received: from py-out-1112.google.com ([64.233.166.180]) by chain.digitalkingdom.org with esmtp (Exim 4.62) (envelope-from ) id 1G1Y0R-0000UF-7f for lojban-list@lojban.org; Fri, 14 Jul 2006 17:27:40 -0700 Received: by py-out-1112.google.com with SMTP id x31so1009729pye for ; Fri, 14 Jul 2006 17:27:36 -0700 (PDT) Received: by 10.35.27.1 with SMTP id e1mr181359pyj; Fri, 14 Jul 2006 17:27:36 -0700 (PDT) Received: by 10.35.39.7 with HTTP; Fri, 14 Jul 2006 17:27:35 -0700 (PDT) Message-ID: Date: Fri, 14 Jul 2006 18:27:35 -0600 In-Reply-To: <20060714160714.51031.qmail@web81310.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=WINDOWS-1252; format=flowed Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by Ecartis Content-Disposition: inline References: <20060713211125.79798.qmail@web81315.mail.mud.yahoo.com> <20060714160714.51031.qmail@web81310.mail.mud.yahoo.com> X-Spam-Score: -2.4 (--) X-archive-position: 12208 X-ecartis-version: Ecartis v1.0.0 Errors-to: lojban-list-bounce@lojban.org X-original-sender: maxim.katcharov@gmail.com X-list: lojban-list X-Spam-Score: -2.4 (--) To: lojban@yahoogroups.com X-Originating-IP: 64.81.49.134 X-eGroups-Msg-Info: 1:0:0:0 X-eGroups-From: "Maxim Katcharov" From: "Maxim Katcharov" Reply-To: maxim.katcharov@gmail.com Subject: [lojban] Re: A (rather long) discussion of {all} X-Yahoo-Group-Post: member; u=116389790; y=JyU3DnoH7lObEop0Caw5RAT7rXVMJu-7VHEf2HfVhQ0xBeMgUw X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 26635 Could you expand the definitions with some examples or brief descriptions? > I send this along for corrections and questions before using it (in its revised form) to answer > Maxim's questions. > > Singular v. Plural Semantics > > Language: > > Variables: What's a variable? > Names: What's a name? > Predicates: > Relation: Y What's the difference between a predicate and a relation? > Sentential connectives: ~, & (others by usual definitions) > Quantifiers: E Putting quantifiers up here will lead to a limited version/understanding of my position. A quantifier is just a certain type of relation. Given an identity "the students", a quantifier is (roughly) "['the students'] is [students] of number [zo'e]". > Descriptor: t What's a descriptor? > > Terms: a variable is a term, a name is a term, if F is a formula containing free variable > x, then txF is a term. What's a free variable? > Formula: A predicate followed by a term is a formula, A followed by two terms is a > formula, a formula preceded by ~ is a formula, two formulas preceded by & is a > formula, a formula preceded by a variable preceded by E is a formula So a predicate is an abstraction, while a formula is an instance of this? "Runs" would be a predicate, and "Alice runs" (or "runs(alice)") would be a formula? What's a relation? > A formula contains a free variable x just in case there is an occurrence of x in that formula > which is not in any subformula which begins Ex nor in a term which begins tx I don't understand what you mean here. > > A sentence is a formula which contains no free variables. > > A singularist model: > > Domain D: a non-empty set What is a set? > Masses M: Power D – 0. the set of all non-empty subsets of D A mass is a set of all non-empty subsets of D? No. A mass is a certain type of identity. > Concepts: > > Interpretation: a function, I that assigns to: > Each concept an object from M, with at least one concept for each singleton in M Object from M? What is an object? Singleton? > Each name a concept Each name is (probably) not a concept. A name refers to an identity. While an identity may be a special case of a concept, I avoid this position because it fails to explain the sharp distinction between instances and abstractions (identities and concepts; Alice and human), and my urge to treat a perfect clone of X as Y (instead of thinking them both X until they differentiate). > Each predicate a function from concepts into {0, 1} Relation, predicate, function, formula. How are these different? > I(Y) is the function from pairs of concepts such that I(A)(c1,c2) = 1 iff I(c1) is included in > I(c2) > > A is an assignment iff A is a function from variables to concepts What is an assignment? What is A (regardless of being an assignment or not)? So variables are identities, and concepts are abstractions? What else, if not a concept, would a certain variable be 'functioned' to? > A(c/x) is an assignment just like A except that it assigns the concept c to variable x instead > of A(x). Example? > > If a is a term, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, R(a) is a concept c > such that F is true for I and A(c/x), if a = txF What is R? > > i is an individual just in case i is in M and is a subset of each of its subsets (is identical > with each of its subsets, has only one member, i is a singleton). > If I understand you correctly, my clarification is that a mass is an identity. This opposes the pluralist view in that the pluralist mass is not an identity. > Where P is a predicate and a a term, Pa is d-true for I and A iff for every individual i > included in I(R(a)) and for every concept c s.t. I(c) = i, I(P)(c) = 1 > I don't understand what "d-true" means. > Where P is a predicate and a a term, Pa is c-true for I and A iff I(P)(R(a)) = 1 > Nor "c-true" > A Pluralist model > > Domain: Some things > Concepts > > C is a relation between concepts and items in D, such that for every d in D, there is at least > once c such that c is related by C only to d [We designate a selected such concept C/d, for each > d] > > > An interpretation I is a function which assigns > To each name a concept > To each predicate a function from concepts into {0,1} > To Y the function from pairs of concepts into {0,1} such that I(A)(c1,c2)) = 1 iff > for every thing d such that c1Cd holds, c2Cd holds > > An assignment A is a function from variable to concepts > A(c/x) is an assignment just like A except for assigning c to x in place of A(x). > > For term a, R(a) = I(a) if a is a name, R(a) = A(a) if a is a variable, is a concept c such > that F is true for C,I and A(c/x) if a = txF > > Pa is d-true for C,I and A iff for every d such that R(a)Cd, I(P)(C/d) = 1 > Pa is c-true for C,I and A iff I(P)(R(a)) = 1 > > In either case, > > A formula F is true for [C,]I and A > > If it is Pa, for some predicate P and some term a and either Pa is d-true for [C,]I and A or Pa > > is c-true for [C,]I and A > > If it is Yab and I(Y)(R(a) R(b)) =1 > > If it is ~S for some formula S and S is not true for [C,]I and A > > It is &GH for some formulae G and H and both G and H are true for [C,] I and A > > It is ExG for some variable x and some formula G and for some concept c, G is true for [C,] I > and > A(c/x) > > Otherwise not. > To unsubscribe from this list, send mail to lojban-list-request@lojban.org with the subject unsubscribe, or go to http://www.lojban.org/lsg2/, or if you're really stuck, send mail to secretary@lojban.org for help.