8 research outputs found
Three 13th-Century Views of Quantified Modal Logic
There are two reasons why medieval logic is of interest to modern logician: One is to see how similar it is to modern logic and the other is to see how different it is. We study three 13th-century works on modal logic and give two examples of how their views of modal logic differ from modern views of the same: the nature of modality and the truth conditions for modal sentences. Because of the different goals of the medieval logicians, modern logicians must take care in arguing for or against the correctness of the medieval logical theories
Literature, Logic and Mathematics in the Fourteenth Century
This thesis assesses the extent to which fourteenth-century Middle English poets were interested in, and influenced by, traditions of thinking about logic and mathematics. It attempts to demonstrate the imaginative appeal of the logical problems called sophismata, which postulate absurd situations while making use of a stable but evolving, and distinctly recognisable, pool of examples. Logic and mathematics were linked. The âpuzzle-basedâ approach of late-medieval logic stemmed in part from earlier arithmetical puzzle collections. The fourteenth-century application of the âsophismaticâ method to problems concerned with what might now be called âPhysicsâ or âMechanicsâ sustained the symbiotic relationship of the two disciplines. An awareness of the importance of this tradition is perhaps indicated by the prominence of logical and mathematical tropes and scenarios in the works of three authors in particular: Geoffrey Chaucer, John Gower and the Gawain-poet. It is argued that, in the poetry of all three, what may loosely be called âsophismatic tropesâ are used to present concerns that the poets share with the logical and mathematical thought of their time. Certain themes recur, including the following: problematic promises; problematic reference to non-existent things; problems associated with divisibility, limits and the idea of a continuum; and, most importantly, problems focused on the contingency, or otherwise, of the future. The debate over future contingency was one of the fiercest scholastic controversies of the fourteenth century, with profound implications for both logical and theological thought. It is suggested here that the scholastic debate about future contingency has a visible impact on Chauntecleerâs prophetic dream in the Nunâs Priestâs Tale, Troilusâs apparent determinism in Troilus and Criseyde, Gowerâs presentation of causation in the Confessio Amantis, and the Gawain-poetâs treatment of covenants. The conclusion reached is that fourteenth-century logical and mathematical texts had a significantly wider cultural effect than is generally recognised