An introduction to the history of philosophical and formal logic : from Aristotle to Tarski

"The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages (Aristotle and The Stoics) The early modern period (Bolzano, Boole) High modern period (Frege, Peano & Russell and Hilbert) Early 20th century (Godel and Tarski) Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic."-- Provided by publisher Cover page 1 Halftitle page 2 Series page 3 Title page 4 Copyright page 5 Contents 6 Preface 8 Introduction 10 References 34 Part I The Origins of Formal Logic 36 1 Aristotle’s Logic 38 1 The syllogism 38 2 A lesson from Plato: Names and verbs 40 3 Affirmation and denial 42 4 Categorical propositions 44 5 Further syllogisms 47 6 Counterexamples: ‘There is no syllogism’ 52 7 Modal syllogistic 54 8 Appendix: The medieval mnemonics 56 Notes 57 References 58 Secondary 58 2 Stoic Logic 60 1 Stoic logic in context 60 2 The Stoic logical system 63 3 Conclusion 77 References 77 3 Medieval Logic 80 1 Introduction 80 2 The reception of Aristotle 80 3 Properties of terms 81 4 Theories of consequences 86 5 Insolubilia and sophismata 90 6 Obligational disputations 96 7 Conclusion 102 Notes 103 References 104 Part II The Early Modern Period 108 4 Leibniz 110 1 Introduction 110 2 Leibniz as a logician 110 3 Systematizing syllogistics 113 4 Combinatorics, the alphabet of human thoughts and the philosophical language 117 5 The logical calculi 121 6 Rational grammar 124 References 127 Works by Leibniz 127 Other works 127 5 Bolzano 130 1 Introduction 130 2 Life 131 3 Propositions and ideas 131 4 Variation 135 5 Bolzano’s theory of grounding 142 6 Conclusion 147 Notes 147 References 148 Solutions to exercises 149 6 Boole 152 1 Life and works 152 2 The laws of thought 154 3 Limitations of Boole’s theory 162 4 Boole’s algebra, and Boolean algebra 166 Notes 169 Part III Mathematical Logic 172 7 C.S. Peirce 174 1 The Alpha Graphs 175 2 The Beta Graphs 178 3 The need for more than Alpha and Beta Graphs 182 4 The Gamma Graphs 186 5 Tempo-modal predicate logic and existential graphs 188 References 189 8 Frege 192 Introduction 192 1 Locating the watershed 193 2 Frege’s philosophy of logic 197 3 Begriffsschrift 200 4 The rise and fall of Frege’s project 219 Notes 223 References 232 9 Peano and Russell 238 Introduction 238 1 Giuseppe Peano 238 2 From Peano to Russell 240 3 Bertrand Russell 243 Conclusion 249 Note 250 Further reading 250 References 251 10 Hilbert 252 1 A mathematician’s cast of mind 252 2 Model theory 253 3 Proof theory 257 4 Logical completeness 264 5 Conclusion 272 Problems 272 References 273 Part IV Twentieth-Century Logic 276 11 Gödel 278 1 Introduction 278 2 The Completeness Theorem 279 3 Incompleteness 285 4 The sequel 294 Further reading 299 References 299 12 Tarski 302 1 Introduction 302 2 The theory of truth 304 3 The Banach–Tarski paradox 311 4 Decidable and undecidable theories 314 Notes 320 References 320 Index 324 The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages (Aristotle and The Stoics); The early modern period (Bolzano, Boole); High modern period (Frege, Peano & Russell and Hilbert); Early 20th century (Godel and Tarski). Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions.0By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic IntroductionPart I: The Origins of Formal Logic 1. Aristotle's Logic, Adriane Rini2. Stoic Logic, Katerina Ierodiakonou 3. Medieval Logic, Sara L. Uckleman Part II: The Early Modern Period 4. Leibniz, Jaap Maat 5. Bolzano, Joenne Kriener6. Boole, Giulia Terzian Part III: Mathematical Logic 7. C. S. Peirce, Peter Ohrstrom 8. Frege, Walter B. Pedriali 9. Peano and Russell, Alexander Bird10. Hilbert, Curtis Franks Part IV: Twentieth Century Logic 10. Goedel, P. D. Welch12. Tarski, Benedict Eastaugh Index