Demonstration By Reductio Ad Impossibile In Posterior Analytics 1. 26

Abstract

In Posterior Analytics 1. 26, Aristotle states that direct demonstrations are better than demonstrations by reductio ad impossibile. The former, he argues, proceed from premisses that are prior in nature to the conclusion, whereas the latter proceed from premisses that are posterior in nature to the conclusion. While Aristotle’s thesis in Posterior Analytics 1. 26 has been widely influential, his argument for it has proved difficult to understand and is often taken to be incoherent. I argue that Aristotle’s thesis relies on a deductive framework in which the only direct demonstrations are those that derive a universal conclusion. The relevant relation of priority in nature is determined by the order of terms in acyclic chains of immediate universal affirmations. Given this characterization of priority in nature, Aristotle’s argument in Posterior Analytics 1. 26 can be shown to be coherent and successful.