On Fri, 21 Mar 1997, Jan de Koning wrote:
> In the first place, the "law of non-contradictions" is not generally valid.
> Some statement may be somewhere in between true and false. My math. prof.
> in a lecture in 1928 said: If you come out of the cold in a room, you may
> say: it is warm here, while someone who is there for over an hour will
> saay: no, it is cold.
This is not a refutation of the law of non-contradiction. That law sates
that a thing cannot both be and not be in the same time and in the same
respect. Clearly the perception of temperature does not violate this.
Nor does anything else, I venture.
> For many statements there is not an easy division
> between true and false. So, in Poland, Sienckewicz (spelling?) wrote a
> book on Many-valued Logic. In the U.S. Kleene defended that, but I have
> not followed recent literature. The law is also not accepted in the
> Intuitionist school of (math)logic.
The Polish mathematical logician J. Lukasiewicz did develop a multi-valent
logic, but his is only one of many multi-valent logics "out there."
(Is this who you were referring to? I am unfamiliar with Sienckewicz, but
that may be a lacuna in my education.) Such logics do not violate the law
of non-contradiction, but deny the principle of bivalence (or the law of
the excluded middle) which states that a proposition is either true or
false. Even Aristotle ( _De interpretatione_ 9) challenged bivalence,
claiming that propositions concerning future contingent states
of affairs were indeterminant--a third truth-value. All multi-valent
logics with which I am familiar have rather specialized applications, and
I doubt they would undermine the ordinary language use of "true" and
"false" as we have been using those words in the context of this
> Secondly, talking about "objective" truth is impossible. There is always
> some subject, that decides about the truth of a statement. What is the
> foundation of certain statements? I do not want to sound too negative, but
> the so-called scientific method tests suppositions. If no contradiction
> can be constructed, we assume it is (should be: may be) true.
It is common to confuse the question of truth with the question of method.
Although not universally accepted (what in philosophy--or any serious
discipline--is?), truth is best regarded first as a property of
propositions indicating correspondence to reality. So a proposition has a
truth-value in virtue of this correspondence. Now it may not be
empirically possible to determine that truth-value, and so we may never
know whether or not the proposition is true or not. But this latter issue
is one of method, not of truth. The "objectivity" of the truth of a
proposition rests in its correspondence to reality, not in my ability to
know whether or not that correspondence holds (which is why in philosophy
of science the term "verisimilitude" is much better when discussing a
theory than is "truth").
Consider two examples. P1: "The total number of protons in the universe
is n," where n is a finite integer, and we assume protons don't decay.
Now clearly we don't know the truth-value of P1, but we can imagine in
principle how it could be empirically determined. But note: the method of
determining the truth-value of P1 is independent of its truth-value.
Bivalence holds--P1 is either true or false.
Now, P2: "The total number of angels created by God is n," n is a
positive integer and we assume angels are not being created and
annihilated routinely. Now it is impossible to determine the truth-value
of P2 empirically, and it is also (pace some over-zealous medievals)
impossible to determine a priori. Nevertheless, P2 has a truth-value.
Bivalence holds. And someday, in God's presence, if it seems at all
important then, we can ask him and find the answer.
Finally, to summarize, I would maintain that ALL rational discourse (and
if scientific discussion is not rational discourse, we're all in trouble
here) presupposes the law of non-contradiction and cannot be done without
it. (Doubters, try to refute non-contradiction without using that very
law to do so!) Bivalence might not hold in all cases, and indeed in some
applications multi-valence might be the best logical model.