Athir al-Dīn al-Abharī and some contemporaries on Conditional Logic

Athir al-Dīn al-Abharī was the only Avicennan logician who denied the validity of conditional syllogism. He was also the first who doubted in the validity of conversion and contraposition of conditionals and dispensed with them. In the contemporary era, after 1968, some logical consequence systems have evolved under the title ‘Conditional Logic’, which rejected the validity of the same rules. A similarity between al-Abharī’s system and these contemporary’s is in their commitment to Modus Ponens and Modus Tollens. Analyzing the reasons that the two groups provided for denying conditional syllogism reveals that their rejections were rooted in their novel interpretations of ‘strict conditional’. On al-Abjarī’s view, the strict conditional ‘whenever A then B’ means that ‘A implies B in all assumptions in which the implication between A and B is possible’. On the contemporary conditional logicians’ view, the conditional proposition ‘if A then B’ in natural languages means that ‘other things being equal, A implies B’. The two interpretations are common in the fact that in addition to the assumption of antecedent, they both assume matters which are somehow related to the antecedent, and this is the common root for both groups to deny the validity of conditional syllogism.