From pycyn@aol.com Tue Jan 01 18:16:52 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_1_3); 2 Jan 2002 02:16:52 -0000 Received: (qmail 27200 invoked from network); 2 Jan 2002 02:16:52 -0000 Received: from unknown (216.115.97.171) by m3.grp.snv.yahoo.com with QMQP; 2 Jan 2002 02:16:52 -0000 Received: from unknown (HELO imo-r08.mx.aol.com) (152.163.225.104) by mta3.grp.snv.yahoo.com with SMTP; 2 Jan 2002 02:16:51 -0000 Received: from Pycyn@aol.com by imo-r08.mx.aol.com (mail_out_v31_r1.9.) id r.168.685e9ba (4509) for ; Tue, 1 Jan 2002 21:16:45 -0500 (EST) Message-ID: <168.685e9ba.2963c78c@aol.com> Date: Tue, 1 Jan 2002 21:16:44 EST Subject: Re: [lojban] Logical connective question. To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_168.685e9ba.2963c78c_boundary" X-Mailer: AOL 7.0 for Windows US sub 118 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_168.685e9ba.2963c78c_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 1/1/2002 10:35:13 AM Central Standard Time, lojbanlists@wonderclown.com writes: > . 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.) > Physics aside, this is not bad. But, the notions of conditioning, osillation, and possibility don't apply really. P ije Q claims that both P and Q are true and that claim is false if one or both of them is false and true otherwise (i.e., if both are in fact true). P ijo Q claims that P and Q are either both true or both false -- right now; it says nothing about what conditions what, indeed about whether there is any relation between them at all except the happenstantial one that right now they are both in the same mode. Ten minutes from now P ijonai Q may be true. As for possibilities, with P ijo Q Pand Q true and P andQ false are both possible (and the other combinations impossible) IF P ijo Q is true, but, since it may be false, the other combinations are equally possible absolutely. You can get some more interesting things, more like conditioning and possibility, with additional tense markers that take the connectives in their scope. --part1_168.685e9ba.2963c78c_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 1/1/2002 10:35:13 AM Central Standard Time, lojbanlists@wonderclown.com writes:


.  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.)


Physics aside, this is not bad.  But, the notions of conditioning, osillation, and possibility don't apply really.  P ije Q claims that both P and Q are true and that claim is false if one or both of them is false and true otherwise (i.e., if both are in fact true).  P ijo Q claims that P and Q are either both true or both false -- right now; it says nothing about what conditions what, indeed about whether there is any relation between them at all except the happenstantial one that right now they are both in the same mode.  Ten minutes from now P ijonai Q may be true. 
As for possibilities, with P ijo Q Pand Q true and P andQ false are both possible (and the other combinations impossible) IF P ijo Q is true, but, since it may be false, the other combinations are equally possible absolutely.
You can get some more interesting things, more like conditioning and possibility, with additional tense markers that take the connectives in their scope. --part1_168.685e9ba.2963c78c_boundary--