Proof by Assumption of the Possible in Prior Analytics, 1.15; How Not to Blend Modal Frameworks

Abstract

The present paper aims to show that the reconstruction of the formal framework of the proofs in Pr. An. 1.15, as proposed by Malink and Rosen 2013 ('Proof by Assumption of the Possible in Prior Analytics 1.15 ', Mind, 122, is due to affront a double impasse. Malink and Rosen argue convincingly that Aristotle operates with two different modal frameworks, one as found in the system of modal logic presented in Prior Analytics 1.3 and 8-22, and one occurring in many of Aristotle's works, such as the Physics, De Caelo and the Metaphysics. However, they misconstrue the latter framework. More precisely, they misconstrue the domain of significance of what they call the 'Principle of Necessitation'. As a consequence, bringing the two frameworks into one results into a contradictory modal logic. On the other hand, if the Principle of Necessitation is rectified, the proofs put forward by Malink and Rosen in the same paper are no longer available. 1 The first is that, exactly because the project is so maximalistic both with respect to its formal and exegetical requirements, some counterintuitive semantical consequences unavoidably creep in, e.g. 'some numbers divisible by three are possibly healthy' turns out to be true (Malink 2013, 240-41, 259-60). The second is that some of Malink's definitions look unnecessarily complicated and ad hoc, e.g. K-incompatibility (Malink 2013, 267, 287). The third is that some of the formal proofs do not reflect the line of argument of Aristotle's own proofs, such as the proofs of Barbara XQM and Celarent XQM in the Prior Analytics 1.15 (Malink 2013, 297-98, fact 40.1-2). These proofs are the subject of Malink and Rosen 2013 and the ones we also discuss here. This article has been republished with minor changes. These changes do not impact the academic content of the article.