Medieval Logics

In the field of logic the dialogue between the three medieval Mediterranean civilizations was reduced to a minimum. The Byzantines, that had the entire corpus of Aristotle’s logical works, did not create any relevant innovations; while the original contributions of Islamic authors such as Abu Bishr Matta and Yahya Ibn Adi (10th c.), Abu’l Barakat (12th c.), and Ibn Taymiyya (13th c.) were not known in the West. In the Latin world, the first century of the Middle Ages did not see any significant developments of dialectics, the art of language that ‘distinguishes the true from the false,’ following the definition given by Alcuin during the Carolingian period: dialectics uses the devices of the division of an argument and of a concatenation of equivalent propositions, adopted often by Anselm of Canterbury. Writers of the high Middle Ages knew—through Boethius and the late-antique encyiclopedias—the doctrines of the syllogism, both those of Aristotelian origin (the demonstrative syllogism, which is verified according to a reference to reality already included in the premises and according to the formal correctness of the relationship between premises and conclusion) and those of Stoic origin (the hypothetical syllogism, in which the conclusion or consequence can be verified on the sole basis of the formal relationship between premises). The Aristotelian logic, with its ontological and semantic implications (the doctrine of the universals), as well as the post-Aristotelian logic, partly coming from the Stoics and partly from the original speculations of the medieval masters of logic (logica modernorum), underwent a radical change inside the municipal schools during the 12th c. Logical knowledge was systematized in the 13th c. in the writings of Peter of Spain and of William of Shyreswood, while in the 14th c. further logical developments led to the new devices of formalization and mathematization in the Merton school of logic and in the writings of Thomas Bradwardine; in the 15th c., finally, the work of Paul of Venice produced an important system of articulation for all of medieval logic. The logica modernorum was not the only non-Aristotelian logic created in the Latin world. In the last decades of 13th c., Ramon Lull formulated an original logic based on non-Aristotelian devices: correlatives and the combinatory art, which formed the ground for his ‘demonstration through equiparation’, a demonstration he considered superior to the syllogistics ones. The Lullian art would be broadly diffused during the Renaissance, when it was used as an inventive logic (a logic capable of finding valid arguments) and as a mnemonic and encyclopedic device.