Ibn Sı̄nā on patterns of proofs

This section 9.3 of Ibn Sı̄nā’s Qiyās is a commentary on sections 25 and 26 of Aristotle’s Prior Analytics i, pages 41b36–43a19. NB the parallel passage in Ibn Sı̄nā’s Burhān iii.2, p. 136ff (Badawi). The paper below is what Wikipedia would call a stub. I will add and correct as time allows. I make the paper available now because it contains a complete translation of Qiyās section 9.3, which is a prerequisite for Ibn Sı̄nā’s section 9.6 on proof search, whose translation is already on this website. The relevant material is about the relationships between two kinds of compound syllogism, which Ibn Sı̄nā refers to as ‘connected’ and ‘separated’ compound syllogisms. The section contains historically interesting material on inductively defined classes and methods for proving their properties. The paper will discuss this material when I can get a better hold on what ideas in this area were already available in Ibn Sı̄nā’s time. I would be grateful for any leads on this. (An obvious place to look is the linguistic tradition starting with the Kitāb al-cayn.) The section also contains an unusually large amount of low-grade material; some of it looks like preliminary notes by students. Sifting out this material will be a major editorial chore. For this reason among others, the translation below is highly provisional. But I am hugely grateful to Amirouche Moktefi who went through the translation with me and made many improvements; we did this sitting in a cafe some forty miles from Aristotle’s birthplace.