Durham E-Theses Literature, Logic and Mathematics in the Fourteenth Century BAKER, DAVID,PHILIP How to cite: BAKER, DAVID,PHILIP (2013) Literature, Logic and Mathematics in the Fourteenth Century, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/7716/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk Literature, Logic and Mathematics in the Fourteenth Century David Philip Baker Thesis submitted for the Degree of Doctor of Philosophy Department of English Studies Durham University 2013 1 Abstract 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. 2 Table of Contents List of Illustrations ..................................................................................................................... 6 List of Abbreviations.................................................................................................................. 7 Declaration ................................................................................................................................. 8 Statement of Copyright .............................................................................................................. 9 Acknowledgements .................................................................................................................. 10 Dedication ................................................................................................................................ 11 Preface ...................................................................................................................................... 12 Introduction: Logical Ideas and Middle English Literature ............................................. 13 Logic and the Imagination ................................................................................................ 13 Logic in Literary Criticism ............................................................................................... 19 Building the World of Logic ............................................................................................ 25 The World of Logic and its Inhabitants ........................................................................... 32 From Logic to Literature .................................................................................................. 35 Logic and Mathematics .................................................................................................... 42 Fourteenth-Century Logicians ......................................................................................... 45 Robert Holcot .................................................................................................. 46 Thomas Bradwardine ...................................................................................... 48 William Heytesbury ........................................................................................ 50 John Buridan ................................................................................................... 52 John Wyclif ..................................................................................................... 54 Ralph Strode .................................................................................................... 57 The Development of the Controversy over Future Contingency in the Fourteenth Century ........................................................................... 59 Chapter 1: Mathematics and Contingency in The Canterbury Tales ................................ 73 Chaucer and the Logicians ................................................................................................ 73 The Summoner’s Tale ......................................................................................................... 77 The Summoner’s Tale and Ars-metrike ........................................................................... 77 The Summoner’s Tale and Insolubles .............................................................................. 85 3 Empty Utterances ............................................................................................................. 92 The Nun’s Priest’s Tale .................................................................................................... 100 The Bradwardine Connection ........................................................................................ 100 Holcot’s Fabulous Logic ................................................................................................ 111 Holcot’s Wisdom Commentary ...................................................................................... 116 A Holcotian Reading of the Nun’s Priest’s Tale ............................................................ 122 Chapter 2: Logic and Determinism in Troilus and Criseyde ........................................... 133 ‘Termes of Phisik’ ........................................................................................................... 133 The Frenzy to Measure .................................................................................................. 137 The Heat of Love ........................................................................................................... 139 The Indivisibilist ............................................................................................................ 147 Wyclif, Chaucer, Strode ................................................................................................. 150 Reprobation in the ‘Responsiones’ ................................................................................ 158 The Logic of Reprobation .............................................................................................. 164 Troilus: The Paradox in Practice .................................................................................... 169 Strange Beginnings ........................................................................................................ 174 The Departing ................................................................................................................. 180 The End of Troilus ......................................................................................................... 183 Chapter 3: Causation and the Future in the Confessio Amantis .................................... 186 Chaucer’s Dedicated Friends: Gower and Strode .......................................................... 186 The Philosopher’s Poem ................................................................................................ 188 Philosophical Gower ...................................................................................................... 195 Cause and Contingency in the Confessio ....................................................................... 198 Time for a Change: ‘Asymmetric’