'Kennedy creatively embeds Gödel's ideal of 'formalism freeness' into myriad results in contemporary logic and foundations of mathematics, offering novel historical reconstructions of Tarski and Turing. A cutting-edge work of philosophy that synthesizes, while going beyond, our current ideas about foundations.' Juliet Floyd, Boston University

Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Gödel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.
Les mer
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.
Les mer
Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.

Produktdetaljer

ISBN
9781108940573
Publisert
2022-08-11
Utgiver
Cambridge University Press
Vekt
300 gr
Høyde
228 mm
Bredde
152 mm
Dybde
10 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
199

Forfatter

Biografisk notat

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).