Editing Chrysippus (section)

===Conditional propositions===
The first logicians to debate conditional statements were [[Diodorus Cronus]] and his pupil [[Philo the Dialectician|Philo]]. Writing five-hundred years later, [[Sextus Empiricus]] refers to a debate between Diodorus and Philo.<ref name="sextus1">[[Sextus Empiricus]], ''Pyr. Hyp.'' ii. 110–112; ''Adv. Math.'' viii. 112–117</ref> Philo regarded all conditionals as true except those which with a correct [[antecedent (logic)|antecedent]] had an incorrect [[consequent]], and this meant a proposition such as "if it is day, then I am talking," is true unless it is day and I fall silent.<ref name="sextus2">Sextus Empiricus, ''Pyr. Hyp.'', ii. 110–112</ref> But Diodorus argued that a true conditional is one in which the antecedent clause could never lead to an untrue conclusion{{snd}}thus, because the proposition "if it is day, then I am talking" can be false, it is invalid.<ref name="sextus1"/> However, [[Paradoxes of material implication|paradoxical propositions]] were still possible such as "if atomic elements of things do not exist, atomic elements exists."<ref name="sextus2"/> Chrysippus adopted a much stricter view regarding conditional propositions, which made such paradoxes impossible:{{efn|When Sextus Empiricus reports the different criteria offered by ancient philosophers for the truth of conditional propositions, he does not mention Chrysippus by name, but modern scholars believe that Chrysippus authored, or, at least, held this view.<ref>See {{Harvnb|Gould|1970|pp=72–82}}</ref>}} to him, a conditional is true if denial of the consequent is logically incompatible with the antecedent.<ref name="johansen468">{{Harvnb|Johansen|Rosenmeier|1998|p=468}}</ref> This corresponds to the modern-day [[strict conditional]].<ref name="johansen468"/>