The Limits of Abstraction

The Limits of Abstraction

by Kit Fine
     
 

ISBN-10: 0199246181

ISBN-13: 9780199246182

Pub. Date: 12/12/2002

Publisher: Oxford University Press, USA

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.  See more details below

Overview

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.

Product Details

ISBN-13:
9780199246182
Publisher:
Oxford University Press, USA
Publication date:
12/12/2002
Pages:
213
Product dimensions:
8.60(w) x 5.50(h) x 0.80(d)

Table of Contents

Introduction
Philosophical Introduction
1. Truth
2. Definition
3. Reconceptualization
4. Foundations
5. The Identity of Abstracts
The Context Principle
1. What is the Context Principle?
3. The Caesar Problem
4. Referential Determinacy
5. Predicativity
6. The Possible Predicative Content of Hume's Law
The Analysis of Acceptability
1. Language and Logic
3. Preliminary Results
4. Tenability
5. Generation
6. Categoricity
7. Invariance
8. Hyperinflation
9. Internalized Proofs
The General Theory of Abstraction
1. The System
3. Derivations
4. Further Work
References, Index

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