 Now, while proto-traces of the substitutional conception of validity could be perceived in Aristotle as well as in some of the ancient commentators, with Abelard it is (arguably) for the first time presented as providing the grounds for a certain class of consequences. And yet, Abelard’s conception of consequence is not reduced to (ST), given that imperfect inferences are just as legitimate/valid as the perfect ones: imperfect inferences are those that fail the substitution criterion but satisfy the ‘necessity of consecution’ criterion. Thus, for Abelard, (ST) defines a special subclass among valid inferences, but a combination of (TP) and (Co) remains the true core of his notion of inference/consequence (see Dial. 283–4 for two senses of necessity of consecution). Indeed, in his subsequent discussion he deals with imperfect inferences much more extensively than with the perfect ones.