  A conditional (sunêmmenon) was considered a non-simple proposition composed of two propositions and the connecting particle ‘if’. Philo, who may be credited with introducing truth-functionality into logic, provided the following criterion for their truth: A conditional is false when and only when its antecedent is true and its consequent is false, and it is true in the three remaining truth-value combinations. The Philonian conditional resembles material implication, except that—since propositions were conceived of as functions of time that can have different truth-values at different times—it may change its truth-value over time. For Diodorus, a conditional proposition is true if it neither was nor is possible that its antecedent is true and its consequent false. The temporal elements in this account suggest that the possibility of a truth-value change in Philo’s conditionals was meant to be improved on. With his own modal notions (see below) applied, a conditional is Diodorean-true now if and only if it is Philonian-true at all times. Diodorus’ conditional is thus reminiscent of strict implication. Philo’s and Diodorus’ conceptions of conditionals lead to variants of the ‘paradoxes’ of material and strict implication—a fact the ancients were aware of (Sextus Empiricus [S. E.] M. 8.109–117).