The principle that a necessarily false proposition implies any proposition, and that a necessarily true proposition is implied by any proposition, was apparently first propounded in twelfth century Latin logic, and came to be widely, though not universally, accepted in the fourteenth century. These principles seem never to have been accepted, or even seriously entertained, by Arabic logicians. In the present paper I explore some thirteenth century Arabic discussions of conditionals with impossible antecedents. The Persian-born scholar Afdal al-Dīn al-Khūnajī (d.1248) suggested the novel idea that two contradictory propositions may follow from the same impossible antecedent, and closely related to this point, he suggested that if an antecedent implied a consequent, then it would do so no matter how it was strengthened. These ideas led him, and those who followed him, to reject what has come to be known as ‘Aristotle’s thesis’ that nothing is implied by its own negation. Even these suggestions were widely resisted. Particularly influential were the counter-arguments of Naṣīr al-Dīn al-Tūṣī (d.1274).
