From @uga.cc.uga.edu:lojban@cuvmb.bitnet Sun Jul 02 19:11:17 1995 Received: from punt3.demon.co.uk by stryx.demon.co.uk with SMTP id AA3713 ; Sun, 02 Jul 95 19:11:14 BST Received: from punt3.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Sat, 01 Jul 95 01:48:48 GMT Received: from uga.cc.uga.edu by punt3.demon.co.uk id aa16576; 1 Jul 95 2:48 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 3401; Fri, 30 Jun 95 21:46:21 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 2096; Fri, 30 Jun 1995 21:45:50 -0400 Date: Fri, 30 Jun 1995 21:48:34 EDT Reply-To: jorge@phyast.pitt.edu Sender: Lojban list From: jorge@phyast.pitt.edu Subject: Re: pc answers X-To: lojban@cuvmb.cc.columbia.edu To: Iain Alexander Message-ID: <9507010248.aa16576@punt3.demon.co.uk> Status: R djer's formula (plus an "&"): > > > E^!3(x) ( remna(x) & E^!9(y)(gerku(y) & pencu(x,y))) my comment: > > In any case, the E^!9(y) is within the scope of the other, so it > > doesn't in any way say that the nine y's are the same for every x, > > only that for each x there are nine y's that fit that relationship. > > So your formula admits that up to 27 dogs are being touched in all. pc: > No. Although the dogs are in the scope of the men, they are not > interdependent; this form is equivalent (with the & as you note) to the > form with the dog and man quantifiers reversed, 9x(dog x & 3y (man y & > touch y x)) Think of the And form, "there is a cimei and there is a > somei..." Wouldn't that be: E^!3(x) E^!9(y) (remna(x) & gerku(y) & pencu(x,y)) Otherwise, how do you write the subordinate case in that notation? Say a, b and c are the three men in question. I want to claim: ( remna(a) & E^!9(y)(gerku(y) & pencu(a,y)) ) & ( remna(b) & E^!9(y)(gerku(y) & pencu(b,y)) ) & ( remna(c) & E^!9(y)(gerku(y) & pencu(c,y)) ) and furthemore, that a, b, and c are the only things that satisfy this. Wouldn't the first formula say just that? Otherwise, why put the E^!9(y) inside of the claim for x, it seems like a misleading notation. Jorge