The Limits of Abstraction [Hardcover]

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 Abstractionbreaks new ground both technically and philosophically.

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

It is a great book. In demanding but always succinct prose, it presents a wealth of distinctions, insights, and arguments. --Oystein Linnebo,Australasian Journal of Philosophy

Kit Fineis Professor of Philosophy at New York University.