Kit Fine

The Limits of Abstraction

• Gebundenes Buch

Produktbeschreibung

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 that 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 is essential reading for all those working on the philosophy of mathematics.

---

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits of Abstraction breaks new ground both technically and philosophically.

Produktdetails

• Verlag: Oxford University Press, USA
• Seitenzahl: 216
• Erscheinungstermin: 12. Dezember 2002
• Englisch
• Abmessung: 215mm x 160mm x 17mm
• Gewicht: 358g
• ISBN-13: 9780199246182
• ISBN-10: 0199246181
• Artikelnr.: 22060243

Autorenporträt

Kit Fine is Professor of Philosophy at New York University.

Inhaltsangabe

Introduction
Philosophical Introduction
2: Definition
3: Reconceptualization
4: Foundations
5: The Identity of Abstracts
The Context Principle
2: Completeness
3: The Caesar Problem
4: Referential Determinacy
5: Predicativity
6: The Possible Predicative Content of Hume's Law
The Analysis of Acceptability
2: Models
3: Preliminary Results
4: Tenability
5: Generation
6: Categoricity
7: Invariance
8: Hyperinflation
9: Internalized Proofs
The General Theory of Abstraction
2: Semantics
3: Derivations
4: Further Work
References, Index