 The concept of negation is often semantically restricted to contradictory opposition between propositions, in which \(\neg A\) can be paraphrased (if not necessarily syntactically represented) as “it is not the case that \(A\)”. As introduced in Aristotle’s Categories (11b17), the genus of opposition (apophasis) is divided into species that include contrariety and contradiction. Contradictory opposites, whether affirmative and negative counterparts of a singular predication (Socrates is wise/Socrates isn’t wise) or quantified expressions (All pleasure is good/Some pleasure is not good), are mutually exhaustive as well as mutually exclusive, while contrary opposites (Socrates is wise/Socrates is unwise; All pleasure is good/No pleasure is good) do not mutually exhaust their domain. Contraries cannot be simultaneously true, though they may be simultaneously false. Members of a contradictory pair cannot be true or false simultaneously; contradictories “divide the true and the false between them” (see the entries on  contradiction  and the  traditional square of opposition).