Abstract

In the Prior Analytics Aristotle famously endorses the validity of the mixed modal syllogism Barbara lxl, but in the Posterior Analytics we appear to find Aristotle arguing that since demonstrations are only of what cannot be otherwise, both premises need to be necessary. One would almost think that Aristotle had forgotten what he said about mixed modal syllogisms were it not for the fact that he also appears to refer to it directly in Posterior Analytics i.6. This is puzzling. In this paper I will consider evidence for and against taking both premises to be necessary and conclude that, in accordance with Barbara lxl, the major premise of a demonstration needs to be necessary but the minor premise need not be, and this because the minor term – which denotes the object of inquiry and that to which the demonstrator is trying to demonstrate that something belongs necessarily – may be an accidental term. In particular, I will be offering an original interpretation of Aristotle’s arguments against circular demonstration in Posterior Analytics i.3, which only makes sense if the minor premise is not necessary.