In this book Juliette Kennedy presents an original perspective on foundations of mathematics. Departing from Goedel and Tarski's work, the treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with an entirely new twist.
In this book Juliette Kennedy presents an original perspective on foundations of mathematics. Departing from Goedel and Tarski's work, the treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with an entirely new twist.
Juliette Kennedy is Associate Professor of Mathematics and Statistics at the University of Helsinki. Her research focuses on set theory, history of logic and philosophy of mathematics, and she is Editor of Interpreting Gödel: Critical Essays (Cambridge, 2014).
Inhaltsangabe
1. Introduction 1.1 The Syntax/Semantics Distinction 1.2 Our Logical Pluralism 1.3 Formal vs Linguistic Semantics 2. Formalism Freeness and Entanglement: Definitions 2.1 Precedents 2.2 Entanglement and Formalism Freeness: Varieties 2.3 A Simple Preference for Semantic Methods? 3. Computability: the Primary Example 3.1 On Adequacy 3.2 Different Notions of Computability Emerge in the 1930s 3.3 The 'Scope Problem' 3.4 Turing's Analysis of Computability 3.5 Gödel's Reaction to Turing's Work at the Time 3.6 Coda: a Word About Deviant Encodings 4. Gödel and Formalism Independence 4.1 Gödel on Formalism 4.2 Episodes of Formalism Independence in Gödel's Writings 4.3 Gödel's Princeton Bicentennial Lecture 4.4 Implementation 4.5 Logical Autonomy? 5. Tarski and 'the Mathematical' 5.1 'The Mathematical', Definable Sets of Reals, and Naïve Set Theory 5.2 Tarski's Naturalism 5.3 Squeezing First Order Definability 5.4 Tarski and Logicality 5.5 In Sum: Parataxis 5.6 Coda: an Improvement of McGee's Theorem 6. Model Theoretic Aspects 6.1 Abstract Elementary Classes 6.2 Patchwork Foundations, On-Again-Off-Again-Sim and Implicit Syntax 6.3 Implicit Syntax, Implicit Logic 6.4 A Remark on Set Theory 6.5 Symbiosis 6.6 Coda: Symbiosis in Detail 7. On the Side of Natural Language.
1. Introduction 1.1 The Syntax/Semantics Distinction 1.2 Our Logical Pluralism 1.3 Formal vs Linguistic Semantics 2. Formalism Freeness and Entanglement: Definitions 2.1 Precedents 2.2 Entanglement and Formalism Freeness: Varieties 2.3 A Simple Preference for Semantic Methods? 3. Computability: the Primary Example 3.1 On Adequacy 3.2 Different Notions of Computability Emerge in the 1930s 3.3 The 'Scope Problem' 3.4 Turing's Analysis of Computability 3.5 Gödel's Reaction to Turing's Work at the Time 3.6 Coda: a Word About Deviant Encodings 4. Gödel and Formalism Independence 4.1 Gödel on Formalism 4.2 Episodes of Formalism Independence in Gödel's Writings 4.3 Gödel's Princeton Bicentennial Lecture 4.4 Implementation 4.5 Logical Autonomy? 5. Tarski and 'the Mathematical' 5.1 'The Mathematical', Definable Sets of Reals, and Naïve Set Theory 5.2 Tarski's Naturalism 5.3 Squeezing First Order Definability 5.4 Tarski and Logicality 5.5 In Sum: Parataxis 5.6 Coda: an Improvement of McGee's Theorem 6. Model Theoretic Aspects 6.1 Abstract Elementary Classes 6.2 Patchwork Foundations, On-Again-Off-Again-Sim and Implicit Syntax 6.3 Implicit Syntax, Implicit Logic 6.4 A Remark on Set Theory 6.5 Symbiosis 6.6 Coda: Symbiosis in Detail 7. On the Side of Natural Language.
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