In this article, the author studies some central concepts in Avicenna's and sī's modal logics as presented in Avicenna's Al-Ish r t wa'l Tan īh t ( Pointers and Reminders ) and in sī's commentary. In this work, Avicenna introduces some remarkable distinctions in order to interpret Aristotle's modal syllogistic in the Prior Analytics . The author outlines a new interpretation of absolute sentences as temporally indefinite sentences and argues on the basis of this that Avicenna seems to subscribe to (...) the Principle of Plenitude. He also shows that he has no valid proof of the modal conversion rules and that he uses some rather ad hoc distinctions to show that Aristotle's modal syllogistic is correct. The author also notes some interesting differences between Avicenna's and sī's approaches to modal logic. (shrink)

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books, from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. (...) He ascribes a special status to the categories Quantity and Quality, whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. (shrink)

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 study, I explore some thirteenth century Arabic discussions of conditionals with impossible antecedents. The Persian-born scholar Afdal al-Dīn al-Kh najī (...) (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 implies a consequent, then it will do so no matter how it is strengthened. These ideas led him, and those who followed him, to reject what has come to be known as 'Aristotle's thesis' that no proposition is implied by its own negation. Even these suggestions were widely resisted. Particularly influential were the counter-arguments of Na īr al-Dīn al-T ī (d.1274). (shrink)