In philosophy of logic and language, the law of non-triviality is a proposed law, stating that it is not the case that all sentences (or propositions), including their negations, are true.
The Law is introduced formally in Graham Priest's book, Doubt Truth to be a Liar. However, the stance against trivialism has been established since, at least, Aristotle. In his Metaphysics, Aristotle attributes the view of trivialism, that all things are true, to the Pythagoreans. This, however, is thought by many to be a misinterpretation of Pythagorean thought on Aristotle's part.
However, the Law of Non-Triviality only becomes relevant in non-classical logics where the Law of Non-Contradiction does not apply. The Law of Non-Contradiction states that for no sentence is it the case that both the sentence and its negation is true; hence, the Law of Non-Triviality follows from the Law of Non-Contradiction. If the Law of Non-Contradiction is rejected, however, the Law of Non-Triviality must be established if trivialism is to be prevented.