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Godel, Tarski and the Lure of Natural Language Juliette Kennedy (University of Helsinki)

Godel, Tarski and the Lure of Natural Language By Juliette Kennedy (University of Helsinki)

Godel, Tarski and the Lure of Natural Language by Juliette Kennedy (University of Helsinki)

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Summary

In this book Juliette Kennedy presents an original perspective on foundations of mathematics. Departing from Godel 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.

Godel, Tarski and the Lure of Natural Language Summary

Godel, Tarski and the Lure of Natural Language: Logical Entanglement, Formalism Freeness by Juliette Kennedy (University of Helsinki)

Is mathematics 'entangled' with its various formalisations? Or arethe central conceptsof mathematics largely insensitivetoformalisation, 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 bywhat she calls the 'natural language moves' of Godeland Tarski, Juliette Kennedy considers what rolesthe concepts of 'entanglement' and 'formalism freeness' play in a range oflogical 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. Thetreatment is historically, logically and set-theoretically rich, andtopics such as naturalism and foundations receive their due, but now with a new twist.

Godel, Tarski and the Lure of Natural Language Reviews

'Kennedy creatively embeds Godel'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

About Juliette Kennedy (University of Helsinki)

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 Godel: Critical Essays (Cambridge, 2014).

Table of Contents

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 Godel's Reaction to Turing's Work at the Time; 3.6 Coda: a Word About Deviant Encodings; 4. Godel and Formalism Independence; 4.1 Godel on Formalism; 4.2 Episodes of Formalism Independence in Godel's Writings; 4.3 Godel'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.

Additional information

NPB9781107012578
9781107012578
1107012570
Godel, Tarski and the Lure of Natural Language: Logical Entanglement, Formalism Freeness by Juliette Kennedy (University of Helsinki)
Juliette Kennedy (University of Helsinki)
New
Hardback
Cambridge University Press
2020-12-17
220
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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