1. An efficient way to prove this is to take advantage of bivalence . 2. This contradicts the Principle of bivalence : every sentence must be either true or false. 3. Considering this thesis led Aristotle to reject the principle of bivalence for assertions concerning the future. 4. These are fundamentally consequences of the law of bivalence , which makes all such connectives merely Boolean functions. 5. The law of bivalence does not hold in intuitionistic logic, only the law of non-contradiction. 6. In formal logic, the principle of bivalence becomes a property that a semantics may or may not possess. 7. The argument relies heavily on the principle of bivalence : the idea that any proposition is either true or false. 8. Under this system, any theorem necessarily dependent on classical logic's principle of bivalence would fail to be valid. 9. In other words, P and not-P . This violates the law of noncontradiction and, by extension, bivalence . 10. Aristotle to embrace bivalence for such future contingents; Chrysippus, the Stoic logician, did embrace bivalence for this and all other propositions.
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