From edward.cherlin.sy.67@aya.yale.edu Wed Feb 20 04:06:00 2002 Return-Path: X-Sender: cherlin@pacbell.net X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_2); 20 Feb 2002 12:05:59 -0000 Received: (qmail 65630 invoked from network); 20 Feb 2002 12:05:59 -0000 Received: from unknown (216.115.97.172) by m3.grp.snv.yahoo.com with QMQP; 20 Feb 2002 12:05:59 -0000 Received: from unknown (HELO mta7.pltn13.pbi.net) (64.164.98.8) by mta2.grp.snv.yahoo.com with SMTP; 20 Feb 2002 12:05:59 -0000 Received: from there ([216.102.199.245]) by mta7.pltn13.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with SMTP id <0GRT00BWBYXYSO@mta7.pltn13.pbi.net> for lojban@yahoogroups.com; Wed, 20 Feb 2002 04:05:59 -0800 (PST) Date: Wed, 20 Feb 2002 04:05:58 -0800 Subject: Re: [lojban] Re: [jboske] RE: Anything but tautologies In-reply-to: <3b.2236fac5.29a30534@aol.com> To: lojban@yahoogroups.com Message-id: <0GRT00BWCYXZSO@mta7.pltn13.pbi.net> Organization: Web for Humans MIME-version: 1.0 X-Mailer: KMail [version 1.3.1] Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: quoted-printable References: <3b.2236fac5.29a30534@aol.com> X-eGroups-From: Edward Cherlin From: Edward Cherlin Reply-To: edward@webforhumans.com X-Yahoo-Group-Post: member; u=31895329 X-Yahoo-Profile: echerlin On Monday 18 February 2002 17:32, pycyn@aol.com wrote: > In a message dated 2/18/2002 5:29:05 PM Central Standard Time, > > jjllambias@hotmail.com writes: > > We seem to have at least four different interpretations of > > x1 and x4 of fancu: The refgrammar gives the impression that all of this must have been=20 worked out at least once, and the current discussion gives the=20 impression that nobody can remember what was decided. *<%-b > > xod: x1 is a name and x4 is the function > > cowan: x1 is the function and x4 is an expression (a text) > > lojbab: x1 is the function and x4 is something like li f(x)=3Dx*2, > > which is not very clear what it is because equations > > are not numbers. > > pc: x1=3Dx4 both are the function, with the proviso that good style > > requires to use a more helpful description in x4. Lewis Carroll: We have to specify the function, the name of the=20 function, what the function is called, what the _name_ of the=20 function is called, and what the function _is_, and similarly for the=20 domain and range, so we're short a dozen places. ed: x1 is a function, and x4 is an expression for evaluating it,=20 marked with ma'o to turn it into an operator (i.e., a function, but=20 in this case without the domain and range specified).=20 le fancu zo'e zo'e ma'o vei li xy te'a li re ve'hu so everybody is partly right and partly wrong. Both x1 and x4 are=20 functions, but of different kinds, and it is frequently appropriate=20 to have a named function for x1 and a transformed expression in x4. Part of the problem is that there is no generally-accepted method for=20 defining functions accurately in mathematics, in part because there=20 are numerous kinds of functions that behave differently. Lambda=20 calculus omits mention of domain and range, which are taken as the=20 set of natural numbers in the original theory, while Lojban omits=20 mention of arguments, which is fine if they are always drawn from x,=20 y, and z in that order, or if all of the argument variables appear in=20 the function expression. Another part of the problem is that we are all quite vague on the use=20 vs. mention distinctions, and none of us understands the Foundations=20 of Mathematics well enough to give useful definitions. Actually,=20 nobody understands FM that well, so it's OK if we improvise some. FM=20 is a Work in Progress with its own set of rwars, which we would do=20 well *not* to emulate. I can get My Brother the Math Professor to=20 recite chapter and verse if anybody doubts this. =20 > > I much prefer pc's version over any of the others, although even > > better for me would be to drop x4 altoghether. > > Why, thanks; I needed a pleasant surprise. > So, leave off fancu4 and put it in, when needed (as often) in > subordinate clauses. I don't think that will be necessary. --=20 Edward Cherlin "You can call me by name, pronouncing it "Veert", or by value,=20 pronouncing it "Worth"--Niklaus Wirth