Two-Value Principle

a principle in classical (two-valued) logic according to which in all conceivable cases the question of the truth-value of any proposition permits only two answers: “true” or “false” (any other answer, including “both true and false,” is excluded). According to the two-value principle, any proposition is true or false independent of the existence of a means by which it would be possible (at least potentially) to indicate which of these two possibilities actually occurs. In other words, the two-value principle in essence postulates an a priori (and positive) solution to the problem of recognizing in an absolute sense the truth or falsehood of any proposition, independently of our cognitive ability. It is precisely in this sense that the two-value principle is a philosophical postulate about the onto-logical nature of formal logic, equivalent to the law of excluded middle. The two-value principle forms the basis of the so-called criteria of Philo (second century B.C.) for implication: the proposition “if A, then B” is true when A is false and B is anything or when B is true and A is anything; it is false only when A is true and B is false.