  The law of excluded middle, LEM, is another of Aristotle's first principles, if perhaps not as first a principle as LNC. Just as Heraclitus's anti-LNC position, “that everything is and is not, seems to make everything true”, so too Anaxagoras's anti-LEM stance, “that an intermediate exists between two contradictories, makes everything false” (Metaphysics 1012a25–29). Of any two contradictories p and ¬p, LNC entails that at most one be true while LEM entails that at least one be true. A logic validates LEM if p v ¬p is a theorem in that logic. LEM thus imposes a constraint on logical syntax and is distinct from the Principle of Bivalence, the purely semantic property dictating that any given proposition is either true or false. The latter principle is rejected in some multivalued and supervaluationist logics that validate LEM, a point to which we return in §6 (see also   many-valued logics,  Sorites Paradox,  truth values). Despite the logical distinction between these two principles, in practice they are often conflated.