Athir al-Din al-Abhari and some contemporaries on Conditional Logic

Athir al-Din al-Abhari is the only Avicennan logician who denies conditional syllogism. He also the first who doubted in conversion and contraposition of conditionals and dispensed with them. After 1968, some consequence systems under the title ‘Conditional Logic’ have evolved that reject the same rules. A similarity between Abhari and these contemporary systems is their commitment to Modus Ponens and Modus Tollens. Analyzing the reasons that the two groups provide for denying conditional syllogism reveals that their rejections is rooted in their novel interpretations of strict conditional. On Abjari’s view, the strict conditional ‘whenever A then B’ means ‘in all assumptions that the implication between A and B is possible, A implies B.’ 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 that in addition to the assumption of the premise, they both assume things that are somehow related to the premise, and this is the common root in the denial of conditional syllogism for both groups.