In 910 the abbey of Cluny was founded; and the monasteries of the Cluniac reform, which was introduced into England by St. Dunstan, contributed to
the emergence of Scholasticism. The university would be the result of merging such monasteries - or at least their intellectual powers - with the cathedral schools in the larger cities and the occasional law school.
For example, the monk Abbon, who died in 1004, directed a monastic school on the Loire, where, in addition to the study of the Scriptures and the Fathers, attention was given to grammar, logic, and mathematics.
Logic at that time was built around Aristotle (whose logical works were not lost, but rather had been translated into Latin by Boethius around 520 A.D.), commentary on Aritstotle by Boethius, and Porphyry.
A more prominent figure, however, is Gerbert of Aurillac. Born about 938, Gerbert became a monk of the Clunaic reform and studied
what could still be rescued from Spain after the Islamic invasions of 711. Spain would be slow to develop universities until freed from Muslim oppression. Gerbert managed to gain some understanding of the Arabic philosophy. The Scholastics generally were able to absorb and preserve elements of Arabic philosophy after Islam turned on Arab scholars and purged their work from itself. By the end of the Middle Ages, Europe had more of Arabic philosophy than Arabia. In any case, Gerbert
seems to have acquired some knowledge of Arabic science. Later he became direct of the school at Rheims.
The school at Rheims, founded in the late tenth century, belonged to a group of schools centered on the emerging curriculum of the “liberal arts” and a step closer to the concept of the university.
In his period of teaching at Rheims he lectured on logic; but he is more remarkable for his study both of the classical Latin literature then available and of mathematics.
The early roots would bring forth results when both Scholasticism and the concept of the university were more developed. Alfred Freddoso writes
that the most profound thinkers of the late medieval era (e.g., Bonaventure, Aquinas, Scotus, Ockham) viewed logic primarily as a tool, albeit an indispensable one, for dealing with the “big” questions in metaphysics and theology. To illustrate, Aquinas's perceptive discussions of the logic of reduplicative propositions occurs within his treatment of the doctrine of the Incarnation. Again, by the time that Ockham wrote his groundbreaking Summa Logicae, he had already employed almost all his distinctive logical insights in one or another metaphysical or theological context.
The sophisticated and nuanced approach to logic found among the late Scholastics continues to challenge philosophers in the twenty-first century:
the medievals managed to raise some deep questions in philosophical logic which have not been faced squarely by contemporary philosophers. For instance, as a recent work by Fred Sommers suggests, the two-name theory of predication may have been done in more by Fregean fiat than by decisive arguments. Again, one suspects that we could learn something from medieval logicians about the ontological issues surrounding the semantics of past- and future-tense sentences or the use of fictive terms (e.g., 'chimera').From early Scholasticism to later Scholasticism to contemporary twenty-first century philosophical questions about metaphysics, logic has played a continuously central role.