 Since a necessary premise entails an assertoric premise, every \(AN\) or \(NA\) combination of premises will entail the corresponding \(AA\) pair, and thus the corresponding \(A\) conclusion. Thus, \(ANA\) and \(NAA\) syllogisms are always valid. However, Aristotle holds that some, but not all, \(ANN\) and \(NAN\) combinations are valid. Specifically, he accepts Barbara \(NAN\) but rejects Barbara \(ANN\). Almost from Aristotle’s own time, interpreters have found his reasons for this distinction obscure, or unpersuasive, or both, and often have not followed his view. His close associated Theophrastus, for instance, adopted the simpler rule that the modality of the conclusion of a syllogism was always the “weakest” modality found in either premise, where \(N\) is stronger than \(A\) and \(A\) is stronger than \(P\) (and where \(P\) probably has to be defined as “not necessarily not”).