 When they interpreted Aristotle’s modal syllogistic, most medievals saw the need to introduce a distinction between different kinds of assertoric sentences. In the mixed syllogism L–L (L represents a necessity sentence), the assertoric minor premise cannot be any kind of assertoric sentence because then the terms could merely be accidentally connected. Kilwardby therefore introduced a distinction between absolutely (simpliciter) and as-of-now (ut nunc) assertoric sentences. The origins of this distinction can be found in Aristotle (An. Pr. I.15, 34b7–18), but Kilwardby of course uses his own per se/per accidens terminology to spell out the difference. An absolutely assertoric sentence involves a per se predication whereas an as-of-now assertoric sentence involves a per accidens predication. In this way, he can guarantee that an essential connection between the terms in a valid L–L syllogisms is preserved through to the conclusion. This is not unproblematic (see Lagerlund 2000, 39–42), though the distinction between different assertoric sentences needed somehow to be made and remained a problem throughout the later Middle Ages.