 It was elegant of Abelard to lay out these rules that entail the valid moods, but then again, the theory of the syllogism is an elegant and simple system. The simplicity of his nine rules reflects the simplicity of Aristotelian syllogistic, since on Aristotle’s view only the first two syllogisms and the rules of conversion plus the method of proof by impossibility and a couple of other consequences are needed to demonstrate all 24 valid moods.