Most widely known for his love affair with Héloïse, about which we learn a good deal from his letters to her as well as from his Historia Calamitatum. He was also one of the great controversialists of his era. After studying under Roscelin (c.1095) and William of Champeaux (c.1100), he established himself as a master in his own right, and one to whom students flocked throughout his career. In the dispute about the nature of universals he was in the nominalist camp, holding that universals are utterances (voces) or mental terms, not things in the real world. The universality of a universal derives from the fact that it is predicable of many things. Nevertheless, unless a number of things are in the same state, the one universal term cannot be predicated of them. Hence although universals are not themselves real things, it is a common feature of real things that justifies the predication of a universal of them.
In his Dialectica Abelard takes up, among numerous other topics, the question, widely discussed in the Middle Ages, of the relation between human freedom and divine providence. If God, who is omniscient, knows that we are going to perform a given act, is it not necessary that we perform it, and in that case how can the act be free? Abelard's answer is that we do indeed act freely and that it is not merely our acts but our free acts that come under divine providence. God's foreknowing them carries no implication that we are not free to avoid performing them.