History of Contraposition in Ancient Logic

The rule of contraposition was used by Aristotle and later popularized during the medieval period in both Arabic and Latin logics. In this paper, we investigate the role of Aristotle and ancient commentators on developing the subject. We show that although Aristotle had used contraposition (on conditionals and indefinite affirmative categorical propositions), Proclus was the first to apply it to universal affirmatives and Philoponus was the first to name the rule. The latter used the rule on possible propositions too, which yielded to Simplicius’ thorough objections. We have found no ancient logician who could apply the rule to quantified categorical propositions except universal affirmatives, nor have we encountered any ancient logician who thoroughly investigated the rule with regard to all kinds of modal propositions. It seems that these developments occurred in later stages of the history of logic.