  Stoic negations and conjunctions are truth-functional. Stoic (or at least Chrysippean) conditionals are true when the contradictory of the consequent is incompatible with its antecedent (D. L. 7.73). Two assertibles are contradictories of each other if one is the negation of the other (D. L. 7.73); that is, when one exceeds the other by a—pre-fixed—negation particle (S. E. M 8.89). The truth-functional Philonian conditional was expressed as a negation of a conjunction: that is, not as ‘if p, q’ but as ‘not both p and not q’. Stoic disjunction is exclusive and non-truth-functional. It is true when necessarily precisely one of its disjuncts is true. Later Stoics introduced a non-truth-functional inclusive disjunction (Aulus Gellius, N. A. 16.8.13–14).