The limits of abstraction Kit Fine.
Idioma: Español Detalles de publicación: Oxford New York Oxford University Press 2002.Descripción: x, 203 p. 23 cmISBN:- 9780199533633
- 510/.1 21
- QA8.4 .F56 2002
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| Libro | CARIBET Biblioteca Arquitectura Colección General CARIBET | QA 8.4.F56 2002 (Navegar estantería(Abre debajo)) | Disponible | 91000000026567 |
Descripciones mejoradas de Syndetics:
What is abstraction? To what extent can it account for the existence and identity of abstract objects? And to what extent can it be used as a foundation for mathematics? Kit Fine provides rigorous and systematic answers to these questions along the lines proposed by Frege, in a book concerned both with the technical development of the subject and with its philosophical underpinnings.Fine proposes an account of what it is for a principle of abstraction to be acceptable, and these acceptable principles are exactly characterized. A formal theory of abstraction is developed and shown to be capable of providing a foundation for both arithmetic and analysis. Fine argues that the usual attempts to see principles of abstraction as forms of stipulative definition have been largely unsuccessful but there may be other, more promising, ways of vindicating the various forms of contextual definition. The Limits of Abstraction breaks new ground both technically and philosophically, and will be essential reading for all who work on the philosophy of mathematics.
Includes bibliographical references (p. [193]-196) and indexes.
Machine generated contents note: I. Philosophical Introduction 1 -- 1. Truth 3 -- 2. Definition 15 -- 3. Reconceptualization 35 -- 4. Foundations 41 -- 5. The Identity of Abstracts 46 -- II. The Context Principle 55 -- 1. What is the Context Principle? 56 -- 2. Completeness 60 -- 3. The Caesar Problem 68 -- 4. Referential Determinacy 77 -- 5. Predicativity 81 -- 6. The Possible Predicative Content of Hume's Law 90 -- III. The Analysis of Acceptability 101 -- 1. Language and Logic 101 -- 2. Models 105 -- 3. Preliminary Results 107 -- 4. Tenability 114 -- 5. Generation 118 -- 6. Categoricity 122 -- 7. Invariance 138 -- 8. Hyperinflation 156 -- 9. Internalized Proofs 161 -- IV. The General Theory of Abstraction 165 -- 1. The Systems 165 -- 2. Semantics 175 -- 3. Derivations 189 -- 4. Further Work 191.
Tabla de contenidos provista por Syndetics
- Introduction(p. ix)
- I Philosophical Introduction(p. 1)
- 1 Truth(p. 3)
- 2 Definition(p. 15)
- 3 Reconceptualization(p. 35)
- 4 Foundations(p. 41)
- 5 The Identity of Abstracts(p. 46)
- II The Context Principle(p. 55)
- 1 What is the Context Principle?(p. 56)
- 2 Completeness(p. 60)
- 3 The Caesar Problem(p. 68)
- 4 Referential Determinacy(p. 77)
- 5 Predicativity(p. 81)
- 6 The Possible Predicative Content of Hume's Law(p. 90)
- III The Analysis of Acceptability(p. 101)
- 1 Language and Logic(p. 101)
- 2 Models(p. 105)
- 3 Preliminary Results(p. 107)
- 4 Tenability(p. 114)
- 5 Generation(p. 118)
- 6 Categoricity(p. 122)
- 7 Invariance(p. 138)
- 8 Hyperinflation(p. 156)
- 9 Internalized Proofs(p. 161)
- IV The General Theory of Abstraction(p. 165)
- 1 The Systems(p. 165)
- 2 Semantics(p. 175)
- 3 Derivations(p. 189)
- 4 Further Work(p. 191)
- References(p. 193)
- Main Index(p. 197)
- Index of First Occurrence of Formal Symbols and Definitions(p. 200)