Handbook of the History of Logic, Volume 2: Mediaeval and Renaissance Logic

Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-19th century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the 11th and 16th centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to inquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece. Mediaeval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. - Provides detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic Cover......Page 1 Mediaeval and Renaissance Logic......Page 4 Copyright......Page 5 Contents......Page 6 Preface......Page 8 List of Contributors......Page 10 1 INTRODUCTION......Page 12 2 THE ANCIENT LATIN TRADITION......Page 13 3 CAROLINGIAN BEGINNINGS......Page 33 4 THE DEVELOPMENT OF A BOETHIAN TRADITION......Page 49 5 THE ELEVENTH CENTURY: LOGIC AND THEOLOGY......Page 54 BIBLIOGRAPHY......Page 68 1 THE CURRICULUM......Page 76 2 THE FORM OF COMMENTARIES......Page 77 3 THE 'EARLY TWELFTH-CENTURY' COMMENTARIES......Page 79 4 THE TREATISES AND THEIR FORM......Page 81 5 LOGIC AND THE TRIVIUM......Page 83 6 TESTIMONIES AND KNOWN MASTERS......Page 84 7 PHILOSOPHICAL THEMES TO BE EXPLORED......Page 86 BIBLIOGRAPHY......Page 90 Peter Abelard and his Contemporaries......Page 94 PART 1: ABELARD ON WORDS, CATEGORICAL PROPOSITIONS AND CATEGORICAL SYLLOGISMS......Page 96 PART 2: ABELARD ON TOPICS, HYPOTHETICAL PROPOSITIONS AND HYPOTHETICAL SYLLOGISMS......Page 132 PART 3: ABELARD'S CONTEMPORARIES......Page 153 BIBLIOGRAPHY......Page 162 INTRODUCTION......Page 168 1 CORE ELEMENTS OF MEDIEVAL LOGIC......Page 169 2 EXTENDING CATEGORICAL PROPOSITIONS......Page 184 3 SIGNIFICATION AND SUPPOSITION......Page 197 4 TYPES OF SUPPOSITION......Page 203 5 AMPLIATION AND RESTRICTION......Page 213 6 NON-EXTENSIONAL CONTEXTS......Page 226 7 MODES OF SUPPOSITION: THE EARLY VIEW......Page 233 8 MODES OF SUPPOSITION: THE LATER VIEW......Page 252 9 ISSUES ABOUT MODES OF SUPPOSITION......Page 277 BIBLIOGRAPHY......Page 287 1 INTRODUCTION......Page 292 2 BACKGROUND......Page 293 3 ARABIC LOGIC IN LATIN......Page 295 4 THE COMMENTARIES ON ARISTOTLE'S ORGANON......Page 313 5 TREATISES ON LOGIC......Page 325 6 CONCLUSIONS......Page 353 BIBLIOGRAPHY......Page 354 INTRODUCTION......Page 358 PART II: THE LOGIC OF INTENTIONS......Page 381 BIBLIOGRAPHY......Page 396 SOME HISTORICAL-PHILOSOPHICAL PRELIMINARIES......Page 400 SOME METHODOLOGICAL PROVISOS......Page 401 VIA ANTIQUA SEMANTICS......Page 403 OCKHAM'S COMPLAINTS......Page 416 OCKHAM'S ALTERNATIVE......Page 418 BURIDAN'S SEMANTICS......Page 425 CONCLUSION: RECONSTRUCTING MEDIEVAL LOGIC......Page 438 APPENDIX......Page 441 Logic in the 14th Century after Ockham......Page 444 1 NAMES, DATES AND PLACES......Page 445 2 SEMANTICS......Page 459 3 CONSEQUENCES......Page 478 4 OBLIGATIONS......Page 495 BIBLIOGRAPHY......Page 509 Original Texts......Page 513 Medieval Modal Theories and Modal Logic......Page 516 1 GENERAL SEMANTIC PARADIGMS FROM BOETHIUS TO THOMAS AQUINAS......Page 518 2 MODAL SEMANTICS AND MODAL LOGIC IN TWELFTH AND THIRTEENTH CENTURIES......Page 542 3 LATER MEDIAEVAL DEVELOPMENTS......Page 560 4 APPLIED MODAL LOGIC......Page 570 CONCLUDING REMARKS......Page 578 BIBLIOGRAPHY......Page 580 Treatments of the Paradoxes of Self-reference......Page 590 INSOLUBILIA MONACENSIA......Page 591 'THE POSITUM IS FALSE' AS THE POSITUM......Page 594 THOMAS BRADWARDINE......Page 597 RICHARD KILVINGTON......Page 606 WILLIAM HEYTESBURY......Page 608 JOHN BURIDAN......Page 611 BIBLIOGRAPHY......Page 617 INTRODUCTION......Page 620 1 ARISTOTLE: TEXTS AND COMMENTARIES......Page 622 2 THE FATE OF THE MEDIEVAL CONTRIBUTIONS TO LOGIC......Page 629 3 THE NEW TEXTBOOKS......Page 635 Part Two" Claims about Humanist Logic......Page 641 1 LORENZO VALLA......Page 642 2 DIALECTIC AND PROBABILITY......Page 643 3 RHETORIC AND ITS RELATION TO DIALECTIC......Page 647 4 INFORMAL ARGUMENTATION......Page 649 CONCLUSION......Page 653 1 INTRODUCTION......Page 656 2 CARAMUEL'S LOGIC......Page 657 3 RELATIONAL LOGIC......Page 665 BIBLIOGRAPHY......Page 675 1 INTRODUCTION......Page 678 2 THE NATURE OF LOGIC......Page 679 3 IDEAS OR TERMS......Page 682 4 PROPOSITIONS......Page 685 5 COMPOUND PROPOSITIONS AND INCIDENTAL OR SUBORDINATE PROPOSITIONS......Page 694 6 CATEGORICAL SYLLOGISMS......Page 696 7 A GENERAL METHOD FOR EVALUATING SYLLOGISMS......Page 700 8 SYLLOGISMS OF PROPOSITIONAL LOGIC......Page 702 9 DILEMMAS AND FALLACIES......Page 703 10 METHOD......Page 706 11 PROBABILITY AND CONTINGENT REASONING......Page 708 BIBLIOGRAPHY......Page 709 Index......Page 712 Mediaeval and Renaissance Logic , (2008). 978-0-444-51625-1 Cover 1 Mediaeval and Renaissance Logic 4 Copyright 5 Contents 6 Preface 8 List of Contributors 10 The Latin Tradition Logic before 1100 12 1 INTRODUCTION 12 2 THE ANCIENT LATIN TRADITION 13 3 CAROLINGIAN BEGINNINGS 33 4 THE DEVELOPMENT OF A BOETHIAN TRADITION 49 5 THE ELEVENTH CENTURY: LOGIC AND THEOLOGY 54 ACKNOWLEDGEMENTS 68 BIBLIOGRAPHY 68 Logic at the Turn of the Twelfth Century 76 1 THE CURRICULUM 76 2 THE FORM OF COMMENTARIES 77 3 THE 'EARLY TWELFTH-CENTURY' COMMENTARIES 79 4 THE TREATISES AND THEIR FORM 81 5 LOGIC AND THE TRIVIUM 83 6 TESTIMONIES AND KNOWN MASTERS 84 7 PHILOSOPHICAL THEMES TO BE EXPLORED 86 BIBLIOGRAPHY 90 Peter Abelard and his Contemporaries 94 PART 1: ABELARD ON WORDS, CATEGORICAL PROPOSITIONS AND CATEGORICAL SYLLOGISMS 96 PART 2: ABELARD ON TOPICS, HYPOTHETICAL PROPOSITIONS AND HYPOTHETICAL SYLLOGISMS 132 PART 3: ABELARD'S CONTEMPORARIES 153 BIBLIOGRAPHY 162 The Development of Supposition Theory in the Later 12th through 14th Centuries 168 INTRODUCTION 168 1 CORE ELEMENTS OF MEDIEVAL LOGIC 169 2 EXTENDING CATEGORICAL PROPOSITIONS 184 3 SIGNIFICATION AND SUPPOSITION 197 4 TYPES OF SUPPOSITION 203 5 AMPLIATION AND RESTRICTION 213 6 NON-EXTENSIONAL CONTEXTS 226 7 MODES OF SUPPOSITION: THE EARLY VIEW 233 8 MODES OF SUPPOSITION: THE LATER VIEW 252 9 ISSUES ABOUT MODES OF SUPPOSITION 277 ACKNOWLEDGEMENTS 287 BIBLIOGRAPHY 287 The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 292 1 INTRODUCTION 292 2 BACKGROUND 293 3 ARABIC LOGIC IN LATIN 295 4 THE COMMENTARIES ON ARISTOTLE'S ORGANON 313 5 TREATISES ON LOGIC 325 6 CONCLUSIONS 353 BIBLIOGRAPHY 354 Logic and Theories of Meaning in the Late 13th and Early 14th Century including the Modistae 358 INTRODUCTION 358 PART II: THE LOGIC OF INTENTIONS 381 BIBLIOGRAPHY 396 The Nominalist Semantics of Ockham and Buridan: A ‘Rational Reconstruction’ 400 SOME HISTORICAL-PHILOSOPHICAL PRELIMINARIES 400 SOME METHODOLOGICAL PROVISOS 401 VIA ANTIQUA SEMANTICS 403 OCKHAM'S COMPLAINTS 416 OCKHAM'S ALTERNATIVE 418 BURIDAN'S SEMANTICS 425 CONCLUSION: RECONSTRUCTING MEDIEVAL LOGIC 438 APPENDIX 441 Logic in the 14th Century after Ockham 444 1 NAMES, DATES AND PLACES 445 2 SEMANTICS 459 3 CONSEQUENCES 478 4 OBLIGATIONS 495 ACKNOWLEDGEMENTS 509 BIBLIOGRAPHY 509 Original Texts 513 Medieval Modal Theories and Modal Logic 516 1 GENERAL SEMANTIC PARADIGMS FROM BOETHIUS TO THOMAS AQUINAS 518 2 MODAL SEMANTICS AND MODAL LOGIC IN TWELFTH AND THIRTEENTH CENTURIES 542 3 LATER MEDIAEVAL DEVELOPMENTS 560 4 APPLIED MODAL LOGIC 570 CONCLUDING REMARKS 578 BIBLIOGRAPHY 580 Treatments of the Paradoxes of Self-reference 590 INSOLUBILIA MONACENSIA 591 'THE POSITUM IS FALSE' AS THE POSITUM 594 THOMAS BRADWARDINE 597 RICHARD KILVINGTON 606 WILLIAM HEYTESBURY 608 JOHN BURIDAN 611 BIBLIOGRAPHY 617 Developments in the Fifteenth and Sixteenth Centuries 620 INTRODUCTION 620 Part One" Historical Overview 622 1 ARISTOTLE: TEXTS AND COMMENTARIES 622 2 THE FATE OF THE MEDIEVAL CONTRIBUTIONS TO LOGIC 629 3 THE NEW TEXTBOOKS 635 Part Two" Claims about Humanist Logic 641 1 LORENZO VALLA 642 2 DIALECTIC AND PROBABILITY 643 3 RHETORIC AND ITS RELATION TO DIALECTIC 647 4 INFORMAL ARGUMENTATION 649 CONCLUSION 653 Relational Logic of Juan Caramuel 656 1 INTRODUCTION 656 2 CARAMUEL'S LOGIC 657 3 RELATIONAL LOGIC 665 BIBLIOGRAPHY 675 Port Royal: The Stirrings of Modernity 678 1 INTRODUCTION 678 2 THE NATURE OF LOGIC 679 3 IDEAS OR TERMS 682 4 PROPOSITIONS 685 5 COMPOUND PROPOSITIONS AND INCIDENTAL OR SUBORDINATE PROPOSITIONS 694 6 CATEGORICAL SYLLOGISMS 696 7 A GENERAL METHOD FOR EVALUATING SYLLOGISMS 700 8 SYLLOGISMS OF PROPOSITIONAL LOGIC 702 9 DILEMMAS AND FALLACIES 703 10 METHOD 706 11 PROBABILITY AND CONTINGENT REASONING 708 BIBLIOGRAPHY 709 Index 712 1. "Logic before 1100: The Latin Tradition" by John Marenbon 2. "Beginning of Scholastic Logic before Abelard" by Yukio Iwakuma 3. "The Logic of Abelard and His Contemporaries" by Ian Wilks 4. "The Development of Supposition Theory in the Later 12th and Early 13th Centuries" by Terence Parsons 5. "Assimilation of Aristotelian and Arabic Logic up to the Later 13th Century" by Henrik Lagerlund 6. "Logic and Theories of Meaning in the Late 13th and Early 14th Century Including the Modistae" by Ria van der Lecq 7. "The Nominalist Semantics of William Ockham and John Buridan" by Gyula Klima 8. "Logic in the 14th Century after Ockham" by Catarina Dutilh-Novaes 9. "Treatments of Modal and Other 'Opaque' Contexts in Mediaeval Logic" by Simo Knuuttila 10. "Treatments of the Paradoxes of Self-reference" by Mikko Yrjonsuuri 11. "Developments in the 15th and 16th Centuries" by Jennifer Ashworth 12. "Relational Logic of Juan Caramuel" by Petr Dvorak 13. "Port Royal: The Stirrings of Modernity" by Russell Wahl. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality