From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Multiple Truth Values
Organization: Computer Science Department,  Stanford University.
Date: Sat, 9 Jan 1993 18:53:47 GMT

In article <1993Jan8.223915.17370@cs.sfu.ca> jamie@cs.sfu.ca (Jamie Andrews) writes:
>(Note cross-posting; also posted to soc.religion.eastern
> and soc.religion.bahai, which are moderated.)
>
>     There has been some talk lately on sci.logic about cultures
>and religions which have multiple truth values.  In particular,
>it has been asserted that the Jains have (or had at some time)
>seven truth values.
>
>     In traditional Western thought, in contrast, there are just
>two truth values (true and false).

Ouch.  This is an extreme misrepresentation of "Western thought."  Few
if any Western logicians or philosophers limited themselves to two
truth values prior to Peirce (c. 1870) in *any* context.  Before Boole,
people thought in terms of whether sentences were true or false, not in
terms of whether they had values like arithmetic expressions do.  And
no philosopher in his right mind, Western or otherwise, and before or
after Boole, would make the bald statement that sentences were either
true or false.  The diversity of the logical taxonomy of sentences has
long been a staple of the philosophical diet.

Boole was the first to provide an algebraically tractable truth value
semantics.  However he did not provide a two-truth-value semantics for
his logic, this was left to Peirce to supply, more than two decades
latter.  Boole interpreted his formulas as classes, i.e. as
predicates.  For Boole a proposition was not a Boolean formula in the
sense we understand it today but an equation between classes.  Boole
did not propose a truth-valued interpretation of equations, two-valued
or otherwise. And even if he had, he would presumably have acknowledged
the distinction between those equations that were tautologically true,
those that were true by definition of their terms, those that were
empirically true universally, those that were true here and now, those
that were satisfiable, etc.

Peirce invented the truth-table decision method for recognizing
tautologies.  But not even Peirce insisted that the two truth values of
his method constituted the scope of possible truth values.  This was a
particular mathematical abstraction for Peirce, not a hypothesis about
the possible truth values of real propositions.

The impression that "Western thought limits itself to two truth values"
appears to have obtained its real impetus from the binary nature of
digital computing and its connections with logic, and only then when
that became a commonplace within the past two or three decades.  People
have discovered that identifying truth values with bits makes logic
much easier to understand.  This is true, and two-valued logic is the
best place to start learning *mathematical* logic.  But it is no more
representative of "Western thought"'s taxonomy of truth values than the
natural numbers are representative of mathematics' diversity of
datatypes.

This is yet another example of how little time it takes for a
perspective to be perceived as a tradition.

Any culture with a weak work ethic is vulnerable to the
oversimplification that there are just two truth values.  So if the
Japanese are right about the Western work ethic then you may indeed be
right about traditional Western thought, provided "traditional" is
taken to mean something on the order of "dating back to the 1950's".

>Lately, logic researchers
>have been playing around with the "undefined" truth value and
>with a "both true and false" truth value.

True enough, provided you will also allow that lately mathematicians
have been playing around with negative numbers.  The algebra of truth
values is a rich subject that is not adequately represented by the
passage from {0,1} to its power set, to say the least!

>I think we sci.logic
>people would be interested in hearing about philosophically- or
>religiously-motivated theories of truth.

I think so too, although the context of your preceding sentence makes
this rather a non-sequitur.  Can we start over with just this sentence,
stripped of its misleading introduction?
-- 
Vaughan Pratt				There's safety in certain numbers.