The Limits of Abstraction

The Limits of Abstraction

by Kit Fine
     
 

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ISBN-10: 0199533636

ISBN-13: 9780199533633

Pub. Date: 07/15/2008

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.

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:
9780199533633
Publisher:
Oxford University Press, USA
Publication date:
07/15/2008
Pages:
216
Product dimensions:
5.30(w) x 8.40(h) x 0.50(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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