Goedel, Tarski and the Lure of Natural Language
Logical Entanglement, Formalism Freeness
Published on 11. August 2022
Book
Paperback/Softback
200 pages
978-1-108-94057-3 (ISBN)
Description
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 Goedel 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.
Reviews / Votes
'Kennedy creatively embeds Goedel'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 UniversityMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 226 mm
Width: 150 mm
Thickness: 11 mm
Weight
290 gr
ISBN-13
978-1-108-94057-3 (9781108940573)
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Schweitzer Classification
Other editions
Additional editions
Juliette Kennedy
Goedel, Tarski and the Lure of Natural Language
Logical Entanglement, Formalism Freeness
Book
12/2020
Cambridge University Press
€122.50
Shipment within 15-20 days
Person
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 Goedel: Critical Essays (Cambridge, 2014).
Content
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 Goedel's Reaction to Turing's Work at the Time; 3.6 Coda: a Word About Deviant Encodings; 4. Goedel and Formalism Independence; 4.1 Goedel on Formalism; 4.2 Episodes of Formalism Independence in Goedel's Writings; 4.3 Goedel'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 Naive 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.