Logic

The study of logic was revived in the Latin West at the court of Charlemagne; his adviser, Alcuin, wrote the first medieval logical textbook (On Dialectic) in about 790. Logic was central to the intellectual life of medieval Europe in a way that it had not been in antiquity, and has not been since the Renaissance. Yet, until the 1130s, medieval logicians made do with what became known as the logica vetus ("old logic"): just Porphyry's Eisagoge, Aristotle's Categories and On Interpretation, and Boethius's commentaries and textbooks. They had only the most limited access to the Stoic tradition, through mentions by Boethius and the On Interpretation of Apuleius (second century C.E.). Ninth-century authors, such as John Scotus Erigena, were interested especially in the Categories—its metaphysical aspects and the question, raised by Augustine and by Boethius, of whether any of the ten categories distinguished by Aristotle apply to God. Anselm of Canterbury (1033 or 1034–1109) was a gifted logician who explored and questioned the Aristotelian doctrine of the Categories and made imaginative use of the ideas on possibility and necessity in On Interpretation.

In the twelfth century, the logica vetus was the central concern of the flourishing Paris schools. Peter Abelard (1079–1142), the greatest logician of the time, developed a nominalist metaphysics on its basis and elaborated a semantics to explain how sentences that use universal words (such as "Socrates is a man") are meaningful although there are no universal things, only particulars. Abelard also excelled in more purely logical matters. Starting from the hints and misunderstandings he found in Boethius, he rediscovered propositional logic and, in his Dialectica (c. 1116), he explored in great depth the truth conditions for conditional ("if … then …") sentences. Abelard was thus able to pioneer the analysis of sentences that are of ambiguous interpretation in terms of propositional logic, an aspect of logic that became especially popular from the 1130s onward, when On Sophistical Refutations and then the rest of Aristotle's logic (the logica nova—"new logic") became available. And he is one of the few logicians ever to have examined the logic of impersonal sentences, such as "It is good that he came today."