Re: [lojban] Logical connective question.

["randl. nortmn." <lojbanlists@wonderclown.com>]

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.