Coverart for item
The Resource Philosophy and model theory, Tim Button and Sean Walsh ; with a historical appendix by Wilfrid Hodges

Philosophy and model theory, Tim Button and Sean Walsh ; with a historical appendix by Wilfrid Hodges

Label
Philosophy and model theory
Title
Philosophy and model theory
Statement of responsibility
Tim Button and Sean Walsh ; with a historical appendix by Wilfrid Hodges
Creator
Contributor
Subject
Language
eng
Summary
Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike
http://library.link/vocab/creatorName
Button, Tim,
Dewey number
190
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Walsh, Sean,
http://library.link/vocab/subjectName
Philosophy, Modern
Label
Philosophy and model theory, Tim Button and Sean Walsh ; with a historical appendix by Wilfrid Hodges
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
  • Cover; Philosophy and Model Theory; Copyright; Preface; Topic selection; Structuring the book; Presuppositions and proofs; Acknowledgements; Contents; A: Reference and realism; Introduction to Part A; 1: Logics and languages; 1.1 Signatures and structures; 1.2 First-order logic: a first look; Syntax for first-order logic; Semantics: the trouble with quantifiers; Why it is worth considering different approaches; 1.3 The Tarskian approach to semantics; 1.4 Semantics for variables; 1.5 The Robinsonian approach to semantics; 1.6 Straining the notion of â#x80;#x98;languageâ#x80;#x99;
  • 1.7 The Hybrid approach to semantics1.8 Linguistic compositionality; 1.9 Second-order logic: syntax; 1.10 Full semantics; 1.11 Henkin semantics; 1.12 Consequence; 1.13 Definability; 1.A First- and second-order arithmetic; 1.B First- and second-order set theory; 1.C Deductive systems; 2: Permutations and referential indeterminacy; 2.1 Isomorphism and the Push-Through Construction; 2.2 Benacerraf â#x80;#x99;s use of Push-Through; 2.3 Putnamâ#x80;#x99;s use of Push-Through; The permutation argument; Preferable models; Referential indeterminacy for moderate objects-platonism
  • 2.4 Attempts to secure reference in mathematicsShapiroâ#x80;#x99;s ante rem structuralism; Putnamâ#x80;#x99;s internal realism (constructivist reading); Syntactic Priority; 2.5 Supervaluationism and indeterminacy; 2.6 Conclusion; 2.A Eligibility, definitions, and Completeness; 2.B Isomorphism and satisfaction; 3: Ramsey sentences and Newmanâ#x80;#x99;s objection; 3.1 The o/t dichotomy; 3.2 Ramsey sentences; 3.3 The promise of Ramsey sentences; 3.4 A caveat on the o/t dichotomy; 3.5 Newmanâ#x80;#x99;s criticism of Russell; 3.6 The Newman-conservation-objection; 3.7 Observation vocabulary versus observable objects
  • 3.8 The Newman-cardinality-objection3.9 Mixed-predicates again: the case of causation; 3.10 Natural properties and just more theory; 3.A Newman and elementary extensions; 3.B Conservation in first-order theories; 4: Compactness, infinitesimals, and the reals; 4.1 The Compactness Theorem; 4.2 Infinitesimals; 4.3 Notational conventions; 4.4 Differentials, derivatives, and the use of infinitesimals; 4.5 The orders of infinite smallness; 4.6 Non-standard analysis with a valuation; 4.7 Instrumentalism and conservation; 4.8 Historical fidelity; 4.9 Axiomatising non-standard analysis
  • Axiomatising elementary extensionsAxiomatising the reals; Axiomatising non-standardness; 4.10 Axiomatising the reals; 4.A Gödelâ#x80;#x99;s Completeness Theorem; 4.B A model-theoretic proof of Compactness; 4.C The valuation function of Â4.6; 5: Sameness of structure and theory; 5.1 Definitional equivalence; 5.2 Sameness of structure and ante rem structuralism; 5.3 Interpretability; 5.4 Biinterpretability; 5.5 From structures to theories; 5.6 Interpretability and the transfer of truth; Counterexamples to the Truth-Transfer Thesis; Bridge principles; Difficulties concerning bridge principles
Control code
on1027965733
Dimensions
unknown
Edition
First edition
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9780191863424
Level of compression
unknown
Note
Oxford University Press
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)1027965733
Label
Philosophy and model theory, Tim Button and Sean Walsh ; with a historical appendix by Wilfrid Hodges
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
  • Cover; Philosophy and Model Theory; Copyright; Preface; Topic selection; Structuring the book; Presuppositions and proofs; Acknowledgements; Contents; A: Reference and realism; Introduction to Part A; 1: Logics and languages; 1.1 Signatures and structures; 1.2 First-order logic: a first look; Syntax for first-order logic; Semantics: the trouble with quantifiers; Why it is worth considering different approaches; 1.3 The Tarskian approach to semantics; 1.4 Semantics for variables; 1.5 The Robinsonian approach to semantics; 1.6 Straining the notion of â#x80;#x98;languageâ#x80;#x99;
  • 1.7 The Hybrid approach to semantics1.8 Linguistic compositionality; 1.9 Second-order logic: syntax; 1.10 Full semantics; 1.11 Henkin semantics; 1.12 Consequence; 1.13 Definability; 1.A First- and second-order arithmetic; 1.B First- and second-order set theory; 1.C Deductive systems; 2: Permutations and referential indeterminacy; 2.1 Isomorphism and the Push-Through Construction; 2.2 Benacerraf â#x80;#x99;s use of Push-Through; 2.3 Putnamâ#x80;#x99;s use of Push-Through; The permutation argument; Preferable models; Referential indeterminacy for moderate objects-platonism
  • 2.4 Attempts to secure reference in mathematicsShapiroâ#x80;#x99;s ante rem structuralism; Putnamâ#x80;#x99;s internal realism (constructivist reading); Syntactic Priority; 2.5 Supervaluationism and indeterminacy; 2.6 Conclusion; 2.A Eligibility, definitions, and Completeness; 2.B Isomorphism and satisfaction; 3: Ramsey sentences and Newmanâ#x80;#x99;s objection; 3.1 The o/t dichotomy; 3.2 Ramsey sentences; 3.3 The promise of Ramsey sentences; 3.4 A caveat on the o/t dichotomy; 3.5 Newmanâ#x80;#x99;s criticism of Russell; 3.6 The Newman-conservation-objection; 3.7 Observation vocabulary versus observable objects
  • 3.8 The Newman-cardinality-objection3.9 Mixed-predicates again: the case of causation; 3.10 Natural properties and just more theory; 3.A Newman and elementary extensions; 3.B Conservation in first-order theories; 4: Compactness, infinitesimals, and the reals; 4.1 The Compactness Theorem; 4.2 Infinitesimals; 4.3 Notational conventions; 4.4 Differentials, derivatives, and the use of infinitesimals; 4.5 The orders of infinite smallness; 4.6 Non-standard analysis with a valuation; 4.7 Instrumentalism and conservation; 4.8 Historical fidelity; 4.9 Axiomatising non-standard analysis
  • Axiomatising elementary extensionsAxiomatising the reals; Axiomatising non-standardness; 4.10 Axiomatising the reals; 4.A Gödelâ#x80;#x99;s Completeness Theorem; 4.B A model-theoretic proof of Compactness; 4.C The valuation function of Â4.6; 5: Sameness of structure and theory; 5.1 Definitional equivalence; 5.2 Sameness of structure and ante rem structuralism; 5.3 Interpretability; 5.4 Biinterpretability; 5.5 From structures to theories; 5.6 Interpretability and the transfer of truth; Counterexamples to the Truth-Transfer Thesis; Bridge principles; Difficulties concerning bridge principles
Control code
on1027965733
Dimensions
unknown
Edition
First edition
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9780191863424
Level of compression
unknown
Note
Oxford University Press
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)1027965733

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