From @uga.cc.uga.edu:lojban@cuvmb.bitnet Sun Jun 18 00:05:34 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3454 ; Sun, 18 Jun 95 00:05:32 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Sun, 18 Jun 95 09:36:47 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa17906; 18 Jun 95 10:36 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 5991; Sun, 18 Jun 95 05:34:10 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 8245; Sun, 18 Jun 1995 05:33:08 -0400 Date: Sat, 17 Jun 1995 14:24:36 -0700 Reply-To: Gerald Koenig Sender: Lojban list From: Gerald Koenig Subject: Re: pc answers X-To: lojban@cuvmb.cc.columbia.edu To: Iain Alexander Message-ID: <9506181036.aa17906@punt2.demon.co.uk> Status: R pc replied to jorge: > > Ok, what do you want to say? Let's take "Three men touched three dogs" >into logic without thinking too much about it. That gives > there are x,y,z,w,v,u, mutually distinct [actually a conjunction >of 15 non-identities] and for all x1, x1 is a relevant man just in case >x1 is x, y, or z and for all y1, y1 is a relevant dog just in case y1 is >w, v, or u [so far we have that there are three men and three dogs of >interest; now for the serious content, we have a choice among] It seems to me that it is sufficient to say that the men are distinct one from another and that the dogs are distinct one from another. It seems that the men can be taken as distinct from the dogs without explicitly so stating. This gives: x\=y, x\=z, y\=z; and w\=v, w\=u, v\=u; for a total of 6 non-identies; not 15 as stated above. pc also said: > 1. for every relevant man z1 and every relevant dog w1, z1 touched w1 > 2. for some relevant man z1 and every relevant dog w1, z1 touched w1 > 3. for some relevant dog w1 and every releant man z1, z1 touched w1 > 4. for every relevant man z1 and some relevant dog w1, z1 touched w1 > 5. for every relevant dog w1 and some relevant man z1, z1 touched w1 > 6. for some relevant man z1 and relevant dog w1, z1 touched w1. I symbolize these as: 1. (z1)(w1) t(z1,w1). For each z1, For each w1, touches( z1,w1). 2. E(z1)(w1) t(z1,w1). For some z1, For each w1, touches(z1, w1). 3. E(w1)(z1) t(z1,w1). etc. 4. (z1)E(w1) t(z1,w1). 5. (w1)E(z1) t(z1,w1). 6. E(z1)E(w1)t(z1,w1). 2. and 5. differ only in the order of the quantifiers in the prenex: 2. E(z1)(w1) t(z1,w1). 5. (w1)E(z1) t(z1,w1). the same is true of 3. and 4. As I understand it the order here in the prenex does not matter; so 2. is equivalent to 5; and 3. is equivalent to 4. This yields only 4 distinct forms. This is reasonable because the form p[Q{w1}, Q{z1}] where p is a predicate and Q a quantifier (either the universal or the existential), has exactly 4 permutations. In spite of this disagreement in petty detail with pc's answer I do not disagree with one, no matter which, of his more than two other conclusions. I think that he has done precisely what is needed to clarify the quantifiers in lojban; that is, to put them back into correspondence with the established body of knowledge in symbolic logic. Attempts to solve quantifier problems by working only in English or only in lojban are less productive, in my opinion. Our roots in predicate calculus are still relevant. Thanks again to pc, jorge, and others for tackling the massive problem of the precise meanings of quantifiers. Rome was not built in a day. Stumbling down off the podium I remain, djer