From lojbanlists@wonderclown.com Tue Jan 01 08:34:08 2002 Return-Path: X-Sender: randy@wonderclown.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_1_3); 1 Jan 2002 16:34:08 -0000 Received: (qmail 23475 invoked from network); 1 Jan 2002 16:34:08 -0000 Received: from unknown (216.115.97.172) by m6.grp.snv.yahoo.com with QMQP; 1 Jan 2002 16:34:08 -0000 Received: from unknown (HELO mail8.nc.rr.com) (24.93.67.55) by mta2.grp.snv.yahoo.com with SMTP; 1 Jan 2002 16:34:08 -0000 Received: from aerosol ([66.26.254.133]) by mail8.nc.rr.com with Microsoft SMTPSVC(5.5.1877.687.68); Tue, 1 Jan 2002 11:34:04 -0500 Received: from rnortman by aerosol with local (Exim 3.33 #1 (Debian)) id 16LRrX-0000Gi-00; Tue, 01 Jan 2002 11:34:03 -0500 Date: Tue, 1 Jan 2002 11:34:03 -0500 To: lojban@yahoogroups.com Cc: thinkit41 Subject: Re: [lojban] Logical connective question. Message-ID: <20020101163403.GA568@aerosol> References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.3.24i Sender: Randall Nortman Return-Path: randy@wonderclown.com From: "randl. nortmn." X-Yahoo-Group-Post: member; u=91794573 X-Yahoo-Profile: uyndrklaun On Tue, Jan 01, 2002 at 10:13:44AM -0000, thinkit41 wrote: > I have a question about logical connectives that relates to my own > binary language. When you say something like AND (je), are you > asserting the falsehood of combinations that you list as 0? AND is > TFFF. You are asserting that X and Y being true is acceptable. But > are you also asserting that X and Y can't both be false (and > likewise the other two combinations)? Or are you just limiting your > assertion to the true entries? Having just read chapter 14 for the first time a couple of weeks ago, I am by no means an expert. However, I stuggled through the same uncertainty you're experiencing, and I eventually came up with my own explanation of how to interpret the truth tables presented in that chapter. I believe that what they mean is that any of the cases marked true is possible, and all those marked false are not possible. The "and" (.e) operator is not the best one to illustrate this point; rather look at IFF (.o), which has truth table TFFT. Since there are two true cases, this operator is asserting that: either A is true and B is true, or A is false and B is false, and, A being true and B being false is NOT possible, and A being false and B being true is NOT possible. In other words, A is fully dependent on B and vice versa. So of the four possible combinations of the truth of A and B, two are possible and two are not. The operator does not make any assertion as to which of the two possible combinations are actually true; merely that one or the other is true, and the others are not. (In particular, I would think that use of this operator leaves open the possibility that over time, A and B may oscillate between the two allowable states but never enter the disallowed states, at least within the time and space intervals supplied in the tense of the selbri, if any.) Returning to the "and" operator (.e), we see that its truth table (TFFF) has only one possible true combination, namely that A and B are both true, and asserts that all other combinations (in which one or both of A and B are false) are not possible. It is therefore asserting that A and B are most certainly both true. One should also note that under standard rules of logic, the four states (TT, TF, FT, FF) are mutually exclusive. That is, a system (A and B) cannot be in more than one of those states at any point in time and space. Therefore saying that something is in one of the states implies that it is not in the other three. That is, of course, until you consider quantum physics, but I don't think Lojban's logical connectives are equipped to deal with that, nor should they be. (The reader should have been tipped off that I'm more physicist than logician back when "oscillation" between "states" was first mentioned.) co'omi'e randl.