  In accounting for the incompatibility of truth and falsity, LNC lies at the heart of Aristotle's theory of opposition, governing both contradictories and contraries.  (See traditional square of opposition.)  Contradictory opposites (“She is sitting”/“She is not sitting”) are mutually exhaustive as well as mutually inconsistent; one member of the pair must be true and the other false, assuming with Aristotle that singular statements with  vacuous subjects are always false. As it was put by the medievals, contradictory opposites divide the true and the false between them; for Aristotle, this is the primary form of  opposition.[2]  Contrary opposites (“He is happy”/“He is sad”) are mutually inconsistent but not necessarily exhaustive; they may be simultaneously false, though not simultaneously true. LNC applies to both forms of opposition in that neither contradictories nor contraries may belong to the same object at the same time and in the same respect (Metaphysics 1011b17–19). What distinguishes the two forms of opposition is a second indemonstrable principle, the law of excluded middle (LEM): “Of any one subject, one thing must be either asserted or denied” (Metaphysics 1011b24). Both laws pertain to contradictories, as in a paired affirmation (“S is P”) and denial (“S isn't P”): the negation is true whenever the affirmation is false, and the affirmation is true when the negation is false. Thus, a corresponding affirmation and negation cannot both be true, by LNC, but neither can they both be false, by LEM. But while LNC applies both to contradictory and contrary oppositions, LEM holds only for contradictories: “Nothing can exist between two contradictories, but something may exist between contraries” (Metaphysics 1055b2): a dog cannot be both black and white, but it may be neither.