Friday, March 25, 2011

A New Defense of The Law of Noncontradiction

Fairly recently it has come about that some people are not accepting the law of noncontradiction as valid. This logical law states no propositional statement is both “a” and “not-a” at the same time and in the same sense. People intuitively believe this to be true; this is evidenced whenever a person makes any assertion. It is her basis for saying “X is true”; she believes she is correct and a contradictory view is incorrect.

All apologists and many laypersons know how to defend the law generically. That is, to anyone who claims the law of noncontradiction is false, the Christian can respond: “That statement is self-defeating. In order to deny the law is true, you must assume the law. You are saying the law is not in fact true but that it is only false.” This is typically enough for the objector.

However, some people dig further than this. They ask, “why can’t it be true that only some statements are necessarily true or false, and others are both true and false?” In order to invalidate a universally-quantified statement only one counterexample is needed. The idea is that simply because a statement like “the law of noncontradiction is false” assumes that it is only true or false and not both, it does not follow that all such statements are true or false. They bolster the argument further by clarifying this isn’t saying all statements are both true and false, but simply at least one is. How does one respond to this?

First, one must point out the inherent epistemic difficulty in affirming this. How is one to know which statements are both true and false and which are not? Someone may respond that whichever statements are both true and false are thus (and that we should not expect to see many of them). However, this is reasoning in a circle. Second, there is the ontological problem. For any statement, there remains no recourse for why that proposition should be viewed as only true or false, rather than both true and false. Any such rule proposed will be some variant on the law of noncontradiction. Since what’s good for the goose is good for the gander, if the law can be invoked in the sense of one proposition it can be in another.[1]

Since there is no non-arbitrary limit it seems either every proposition is both true and false or no proposition is both true and false. If the proposition “some statements are both true and false” is both true and false, then no propositions are true and false, all propositions are true and false, and some propositions are true and false. The sheer incoherence of this is enough to say that the statement itself must be either true or false. Advocates who say this statement is only true can only do so on a contradictory basis; a rule which says contradictory statements are not true. Without this, it is sheer arbitrariness to designate this statement as true. The law is inescapable, even if a counterexample is intended to function only rarely.


[1] After all, the only way to know a proposition is in fact both true and false is to assume it is both true and false. Nothing can be shown to be false whatsoever, since the basis of falsehood is contradiction to truth. Since life cannot be lived that way, truth then comes down to intuitive feeling. If we think it is either true or false, and not both true and false, then that statement is. The subjective nature of the problem then is revealed to be contradictory, since no one would hold that the statement “some statements are both true and false” is both true and false!

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