Handbook of the history of logic. Volume 11, Logic : a history of its central concepts / monograph

The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. Covers in depth the notion of logical consequence Discusses the central concept in logic of modality Includes the use of diagrams in logical reasoning Front Cover......Page 1 Logic: A History of its Central Concepts......Page 4 Copyright......Page 5 Dedication......Page 6 Contents......Page 7 Preface......Page 8 List of Authors......Page 11 1 Introduction......Page 12 2 Aristotle [384 BCE-322 BCE]......Page 18 3 Stoics [300 BCE-200 CE]......Page 21 4 Medievals [476 CE-1453 CE]......Page 22 5 Leibniz [1646-1716]......Page 29 6 Kant [1724-1804]......Page 30 7 Blozano [1781-1848]......Page 32 9 Frege [1848-1925]......Page 34 10 Russell [1872-1970]......Page 36 11 Carnap [1891-1970]......Page 39 12 Gentzen [1909-1945]......Page 42 13 Tarski [1902-1983]......Page 43 14 Godel [1906-1978]......Page 46 15 Modal Logics......Page 48 16 Nonmonotonic Options......Page 50 17 The Substructural Landscape......Page 52 18 Monism or Pluralism......Page 54 Bibliography......Page 58 1 Aristotle's Quantification Theory......Page 64 2 Quantifiers in Medieval Logic......Page 74 3 The Textbook Theories of Quantification......Page 86 4 The Rise of Modern Logic......Page 97 5 Contemporary Quantification Theory......Page 109 Bibliography......Page 123 Introduction: Grice as a Catalyst......Page 128 Acknowledgments......Page 169 Bibliography......Page 170 1 Aristotelian Foundations......Page 176 2 Stoic Logic......Page 178 3 Hypothetical Syllogisms......Page 189 4 Early Medieval Theories......Page 193 5 Later Medieval Theories......Page 196 6 Leibniz's Logic......Page 202 7 Standard Modern-Era Logic......Page 206 8 Bolzano......Page 209 9 Boole......Page 215 10 Frege......Page 223 11 Peirce and Peano......Page 226 12 On to the Twentieth Century......Page 229 Bibliography......Page 231 1 An Emblematic Concept of Modern Logic......Page 236 2 From Tarski to Suszko......Page 240 3 The Initial Bouillon: Three Wise Men......Page 248 4 Developing Stage......Page 262 5 Many Truth-Values......Page 275 6 Structures, Models, Worlds......Page 284 7 Non Truth-Functional Truth-Values......Page 293 Bibliography......Page 299 1 Extensional Modal Conceptions in Ancient and Medieval Philosophy......Page 310 2 Modality as Alternativeness......Page 318 Primary Literature......Page 334 Secondary Literature......Page 336 2 Object Language Natural Deduction......Page 342 3 The Metatheory of Natural Deduction......Page 370 4 Problems and Projects......Page 393 Bibliography......Page 407 Elementary Logic Textbooks Described in Table 1......Page 414 1 Two Thousand Three Hundred Years of Connexive Implication......Page 416 2 Connexive Conditionals: An Empirical Approach......Page 422 3 Paradoxes of Implication......Page 425 4 The Avoidance of Paradox......Page 427 5 A Consistent System of Connexive Logic......Page 428 6 Connexive Logic in Subproof Form......Page 431 7 Connexive Logic and the Syllogism......Page 434 8 Connexive Class Logic......Page 435 9 First-Degree Connexive Formulae......Page 436 10 Causal Implication......Page 438 11 Contemporary Work on Connexive Implication: Meyer, Routley, Mortensen, Priest, Lowe, Pizzi, Wansing, Rahman and Ruckert......Page 444 Bibliography......Page 448 1 Introduction......Page 452 2 Prehistory of Types......Page 457 3 Type Theory in Principia Mathematica......Page 466 4 History of the Deramification......Page 497 5 The Simple Theory of Types......Page 502 6 Conclusion......Page 507 Bibliography......Page 509 1 Introductory Remarks......Page 514 2 Aristotle (384-322 BC)......Page 516 3 The Hellenistic and Mediaeval Periods......Page 539 4 Francis Bacon (1561-1626)......Page 548 5 Antoine Arnauld (1612-1694) and Pierre Nicole (1625-1695)......Page 553 6 Isaac Watts: An Interlude......Page 565 7 John Locke......Page 566 8 Richard Whately (1787-1863)......Page 577 9 John Stuart Mill (1806-1873)......Page 581 10 Augustus Demorgan (1806-1871)......Page 598 11 The Great Depression: (1848-1970)......Page 602 12 Now......Page 605 Bibliography......Page 606 1 Introduction......Page 612 2 The Golden Age of Logic Diagrams......Page 617 3 Representing Information with Diagrams......Page 624 4 Manipulating Information with Diagrams......Page 639 5 The Frege-Peirce Affair......Page 650 6 Revival in a New Age......Page 671 Bibliography......Page 678 Index......Page 684 Logic: A History of its Central Concepts, 11, (2012). 978-0-444-52937-4 Front Cover 1 Logic: A History of its Central Concepts 4 Copyright 5 Dedication 6 Contents 7 Preface 8 List of Authors 11 A History of the Consequence Relations 12 1 Introduction 12 2 Aristotle [384 BCE-322 BCE] 18 3 Stoics [300 BCE-200 CE] 21 4 Medievals [476 CE-1453 CE] 22 5 Leibniz [1646-1716] 29 6 Kant [1724-1804] 30 7 Blozano [1781-1848] 32 8 Boole [1815-1864] 34 9 Frege [1848-1925] 34 10 Russell [1872-1970] 36 11 Carnap [1891-1970] 39 12 Gentzen [1909-1945] 42 13 Tarski [1902-1983] 43 14 Godel [1906-1978] 46 15 Modal Logics 48 16 Nonmonotonic Options 50 17 The Substructural Landscape 52 18 Monism or Pluralism 54 Bibliography 58 A History of Quantification 64 1 Aristotle's Quantification Theory 64 2 Quantifiers in Medieval Logic 74 3 The Textbook Theories of Quantification 86 4 The Rise of Modern Logic 97 5 Contemporary Quantification Theory 109 Bibliography 123 History of Negation 128 Introduction: Grice as a Catalyst 128 Acknowledgments 169 Bibliography 170 A History of the Connectives 176 1 Aristotelian Foundations 176 2 Stoic Logic 178 3 Hypothetical Syllogisms 189 4 Early Medieval Theories 193 5 Later Medieval Theories 196 6 Leibniz's Logic 202 7 Standard Modern-Era Logic 206 8 Bolzano 209 9 Boole 215 10 Frege 223 11 Peirce and Peano 226 12 On to the Twentieth Century 229 Bibliography 231 A History of Truth-Values 236 1 An Emblematic Concept of Modern Logic 236 2 From Tarski to Suszko 240 3 The Initial Bouillon: Three Wise Men 248 4 Developing Stage 262 5 Many Truth-Values 275 6 Structures, Models, Worlds 284 7 Non Truth-Functional Truth-Values 293 Acknowledgments 299 Bibliography 299 A History of Modal Traditions 310 1 Extensional Modal Conceptions in Ancient and Medieval Philosophy 310 2 Modality as Alternativeness 318 Primary Literature 334 Secondary Literature 336 A History of Natural Deduction 342 1 Introduction 342 2 Object Language Natural Deduction 342 3 The Metatheory of Natural Deduction 370 4 Problems and Projects 393 Acknowledgments 407 Bibliography 407 Elementary Logic Textbooks Described in Table 1 414 A History of Connexivity 416 1 Two Thousand Three Hundred Years of Connexive Implication 416 2 Connexive Conditionals: An Empirical Approach 422 3 Paradoxes of Implication 425 4 The Avoidance of Paradox 427 5 A Consistent System of Connexive Logic 428 6 Connexive Logic in Subproof Form 431 7 Connexive Logic and the Syllogism 434 8 Connexive Class Logic 435 9 First-Degree Connexive Formulae 436 10 Causal Implication 438 11 Contemporary Work on Connexive Implication: Meyer, Routley, Mortensen, Priest, Lowe, Pizzi, Wansing, Rahman and Ruckert 444 Bibliography 448 A History of Types 452 1 Introduction 452 2 Prehistory of Types 457 3 Type Theory in Principia Mathematica 466 4 History of the Deramification 497 5 The Simple Theory of Types 502 6 Conclusion 507 Acknowledgements 509 Bibliography 509 A History of the Fallacies in Western Logic 514 1 Introductory Remarks 514 2 Aristotle (384-322 BC) 516 3 The Hellenistic and Mediaeval Periods 539 4 Francis Bacon (1561-1626) 548 5 Antoine Arnauld (1612-1694) and Pierre Nicole (1625-1695) 553 6 Isaac Watts: An Interlude 565 7 John Locke 566 8 Richard Whately (1787-1863) 577 9 John Stuart Mill (1806-1873) 581 10 Augustus Demorgan (1806-1871) 598 11 The Great Depression: (1848-1970) 602 12 Now 605 Bibliography 606 A History of Logic Diagrams 612 1 Introduction 612 2 The Golden Age of Logic Diagrams 617 3 Representing Information with Diagrams 624 4 Manipulating Information with Diagrams 639 5 The Frege-Peirce Affair 650 6 Revival in a New Age 671 Acknowledgments 678 Bibliography 678 Index 684

The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject.

Covers in depth the notion of logical consequence

Discusses the central concept in logic of modality

Includes the use of diagrams in logical reasoning

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