‘Everything true will be false’: Paul of Venice’s two solutions to the insolubles

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected

Paradoxes of signification

Ian Rumfitt has recently drawn our attention to a couple of paradoxes of signification, claiming that although Thomas Bradwardine's "multiple-meanings'' account of truth and signification can solve the first of them, it cannot solve the second. Bradwardine's solution appears to turn on a distinction between the principal and the consequential signification of an utterance. The paradoxes of signification were in fact much discussed by Bradwardine's successors in the fourteenth century. It is shown that Bradwardine's account of signification turns not on a distinction between principal and consequential signification, but between partial and total signification, and that accordingly his solution, unlike those of his successors, does not fall prey to Rumfitt's paradoxes.PostprintPeer reviewe

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 ‘puzzle-based’ approach of late-medieval logic stemmed in part from earlier arithmetical puzzle collections. The fourteenth-century application of the ‘sophismatic’ method to problems concerned with what might now be called ‘Physics’ or ‘Mechanics’ 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 ‘sophismatic tropes’ 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 Chauntecleer’s prophetic dream in the Nun’s Priest’s Tale, Troilus’s apparent determinism in Troilus and Criseyde, Gower’s presentation of causation in the Confessio Amantis, and the Gawain-poet’s treatment of covenants. The conclusion reached is that fourteenth-century logical and mathematical texts had a significantly wider cultural effect than is generally recognised

Rebirth, reform, and resilience: universities in transition, 1300-1700

(print) 367 p., [1] p. of plates ; 24 cmUniversities in transition, 1300-1700JAMES M. KITTELSON : OHIO STATE UNIVERSITY Introduction : The Durability of the Universities of Old Europe 1 -- HEIKO A. OBERMAN : UNIVERSITY OF TUBINGEN University and Society on the Threshold of Modern Times : The German Connection 19 -- LEWIS W. SPITZ : STANFORD UNIVERSITY The Importance of the Reformation for Universities : Culture and Confession in the Critical Years 42 -- EDWARD GRANT : INDIANA UNIVERSITY Science and the Medieval University 68 -- WILLIAM J. COURTENAY : UNIVERSITY OF WISCONSIN The Role of English Thought in the Transformation of University Education in the Late Middle Ages 103 -- JOHN M. FLETCHER : UNIVERSITY OF ASTON IN BIRMINGHAM University Migrations in the Late Middle Ages with Particular Reference to the Stamford Secession 163 -- PAUL W. KNOLL : UNIVERSITY OF SOUTHERN CALIFORNIA The University of Cracow in the Conciliar Movement 190 -- GUY FITCH LYTLE : UNIVERSITY OF TEXAS The Careers of Oxford Students in the Later Middle Ages 213 -- JAMES H. OVERFIELD : UNIVERSITY OF VERMONT University Studies and the Clergy in Pre-Reformation Germany 254 -- M. A. SCREECH : UNIVERSITY COLLEGE, LONDON Two Attitudes toward Hebrew Studies : Erasmus and Rabelais 293 -- JOHN M. FLETCHER and JULIAN DEAHL : UNIVERSITY OF ASTON IN BIRMINGHAM European Universities, 1300-1700 : The Development of Research, 1969-1979, with a Summary Bibliography 324 -- Notes on Contributors 359 -- Index 36