Gödel, Tarski and the lure of natural language : logical entanglement, formalism freeness

著者

• Kennedy, Juliette

書誌事項

Gödel, Tarski and the lure of natural language : logical entanglement, formalism freeness

Juliette Kennedy

Cambridge University Press, 2021

• : hbk

注記

Includes bibliographical references (p. 169-183) and index

内容説明・目次

内容説明

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.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BC06315217
• ISBN:
  • 9781107012578
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xii, 187 p.
• 大きさ: 24 cm