 In logic, Boethius’s translations of Aristotle and Porphyry (except for that of the Posterior Analytics, which was lost) remained standard throughout the Middle Ages. His commentaries—especially that on the Categories, the second commentary on the Isagoge and the second, more advanced commentary on On Interpretation—were the main instruments by which logicians from the ninth to the twelfth centuries came to understand the Aristotelian texts he had translated, and to grapple with their problems and the wider range of related philosophical issues raised by the late ancient tradition. Even twelfth-century philosophers as independently-minded as Abelard and Gilbert of Poitiers were deeply indebted to these commentaries. The logical text-books were equally important. Before the Prior Analytics became generally available in the later twelfth century, students learned syllogistic from Boethius’s monographs on it. The theory of topical argument, acquired especially from On Topical Differentiae, provided a framework for twelfth-century philosophers in propounding and analysing arguments, and from the combination of studying topical argument and the theory of hypothetical syllogisms as Boethius presented it, Abelard was led towards his rediscovery of propositional logic (cf. Martin (1987)). From the thirteenth century, onwards, however, both Boethius’s commentaries and his treatises became less influential. On Topical Differentiae, and On Division, continued to be studied, but not the treatises on categorical and hypothetical syllogisms. Users of the commentaries were infrequent, but they include Thomas Aquinas.