From lojban-out@lojban.org Fri Jul 14 18:30:44 2006 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (qmail 54446 invoked from network); 15 Jul 2006 01:27:41 -0000 Received: from unknown (66.218.66.217) by m38.grp.scd.yahoo.com with QMQP; 15 Jul 2006 01:27:40 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.81.49.134) by mta2.grp.scd.yahoo.com with SMTP; 15 Jul 2006 01:27:37 -0000 Received: from lojban-out by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1Yrr-0001K2-7n for lojban@yahoogroups.com; Fri, 14 Jul 2006 18:22:51 -0700 Received: from chain.digitalkingdom.org ([64.81.49.134]) by chain.digitalkingdom.org with esmtp (Exim 4.62) (envelope-from ) id 1G1YrG-0001Jg-LC; Fri, 14 Jul 2006 18:22:15 -0700 Received: with ECARTIS (v1.0.0; list lojban-list); Fri, 14 Jul 2006 18:22:06 -0700 (PDT) Received: from nobody by chain.digitalkingdom.org with local (Exim 4.62) (envelope-from ) id 1G1Yqm-0001JN-GZ for lojban-list-real@lojban.org; Fri, 14 Jul 2006 18:21:44 -0700 Received: from web81305.mail.mud.yahoo.com ([68.142.199.121]) by chain.digitalkingdom.org with smtp (Exim 4.62) (envelope-from ) id 1G1YqM-0001JA-VZ for lojban-list@lojban.org; Fri, 14 Jul 2006 18:21:44 -0700 Received: (qmail 90938 invoked by uid 60001); 15 Jul 2006 01:21:12 -0000 Message-ID: <20060715012112.90934.qmail@web81305.mail.mud.yahoo.com> Received: from [70.230.150.12] by web81305.mail.mud.yahoo.com via HTTP; Fri, 14 Jul 2006 18:21:11 PDT Date: Fri, 14 Jul 2006 18:21:11 -0700 (PDT) In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Spam-Score: -1.6 (-) X-archive-position: 12209 X-ecartis-version: Ecartis v1.0.0 Errors-to: lojban-list-bounce@lojban.org X-original-sender: clifford-j@sbcglobal.net X-list: lojban-list X-Spam-Score: -0.6 (/) To: lojban@yahoogroups.com X-Originating-IP: 64.81.49.134 X-eGroups-Msg-Info: 1:0:0:0 X-eGroups-From: John E Clifford From: John E Clifford Reply-To: clifford-j@sbcglobal.net Subject: [lojban] Re: A (rather long) discussion of {all} X-Yahoo-Group-Post: member; u=116389790; y=OZGKwHqd7gxKBptWH3Lo99V9oVvYbvU1dG3i1YxeG9x0rGwMBg X-Yahoo-Profile: lojban_out X-Yahoo-Message-Num: 26636 --- Maxim Katcharov wrote: > 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? An expression that stands in the place of a name but may have a different referent on each occasion (hence the name of it). The useful ones are bound by quantifiers. (Lojban variables are, for example, {da, de, di}) > > Names: > > What's a name? An expression with a fixed referent. > > Predicates: > > Relation: Y > > What's the difference between a predicate and a relation? Predicates are one-placed *take one argument to make a formula), relations are more (in this case, two). > > 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]". We are modeling Lojban, whose quantifiers are first of all over variables, in just this position. I have not incorporated into this simplified version any of the derivative uses of quantifiers (including enumeration), because they have no special properties (that I know of yet) connected with the issue of singular versus plural. What do you have in mind? > > Descriptor: t > > What's a descriptor? Converts a formula into a name (cf. {le, lo} and the like). > > > > 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? One not in the scope of a quantitifier on it. > > 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? Well, ""abstraction" isn't quite right, though it is incoplete without its subject. "runs(alice)" is a sentence. A relation is like a predicate but has more arguments. > > 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. x is free in Fx but not in ExFx. > > > > A sentence is a formula which contains no free variables. > > > > A singularist model: > > > > Domain D: a non-empty set > > What is a set? Well, I suppose I had Cantorean (usual set theoretical) sets in mind, but nothing hangs on that. L-sets would do as well or we could just have a definite bunch (in the none-technical sense) of things. > > 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. This is the set of masses, each mass is a non-empty set of things in D. What does "type of identity" mean? > > 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? An object is, in this case, just something in D. A singleton is a set with exactly one member. > > Each name a concept > > Each name is (probably) not a concept. A name refers to an identity. Note, this sentence is part of what an interpretation does: assigns to each name a concept. > 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). I don't see what this is all about. A concept here is just another abstract entity in the metalanguage of the given language. I suppose its name may have some useful associations but none that need interfere here. For example it has nothing to do with the differences between things (in D) and properties -- what predicates mean. I don't understand where clones come in. > > Each predicate a function from concepts into {0, 1} > > Relation, predicate, function, formula. How are these different? Do you know any of the language of set theory or mathematics? These are pretty rudimentry. But if need be I can back up a bit more. A predicate is an expression which needs one term to make a formula, a relation is an expression which needs two terms to make a formula, a function is a mapping from one set of things into another set, a formula a predicate or relation filled out with appropriate number of terms or some compound of one or more such by connectives and quantifiers. > > 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? A function which gives each variable a meaning for the nonce. > What is A (regardless of being an assignment or not)? I don't understand this question. > So variables are identities, and concepts are abstractions? What else, > if not a concept, would a certain variable be 'functioned' to? I don't understand your terminology here. Variables are expression in the language; I gather that identities are not. I am not sure whether concepts are abstraction -- I am probably inclined to think of them as thoughts, but nothing hans on what they are, only on the role they play. xorxes has suggested another approach -- which I found harder to adapt to what I understood to be your position -- in which variables were "functioned" to things (in D). > > A(c/x) is an assignment just like A except that it assigns the concept c to variable x instead > > of A(x). > > Example? A simple assignment Q assigns Charlie to every variable; now for some reason we change and for the particular variable y17, we assign George. This new function is Q(George/y17). > > > > 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? It is a function from terms to their referents. > > > > 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. Again, I don't underand your use of "identity". The last sentence is just a definition saying that we are going to use the word "individual" to refer to sets (Masses) that have only one member. > > > 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. Distributively > > 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" Collectively (i.e., non-distributively) > > 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.