Pluralism in Mathematics: A New Position in Philosophy of Mathematics

• Main Author: Friend, Michèle (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2014.
• Series: Logic, Epistemology, and the Unity of Science, 32
• Subjects: Philosophy.; Logic.; Philosophy and science.; Mathematical logic.; Philosophy of Science.; Mathematical Logic and Foundations.

This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s St...

Table of Contents:

• Introduction
• Part I. Motivating the Pluralist Position from Familiar Positions
• Chapter 1. Introduction. The Journey from Realism to Pluralism
• Chapter 2. Motivating Pluralism. Starting from Maddy’s Naturalism
• Chapter 3. From Structuralism to Pluralism
• Chapter 4. Formalism and Pluralism Co-written with Andrea Pedeferri
• Part II. Initial Presentation of Pluralism.- Chapter 5. Philosophical Presentation of Pluralism
• Chapter 6. Using a Formal Theory of Logic Metaphorically
• Chapter 7. Rigour in Proof Co-written with Andrea Pedeferri
• Chapter 8. Mathematical Fixtures
• Part III. Transcendental Presentation of Pluralism
• Chapter 9. The Paradoxes of Tolerance and the Transcendental Paradoxes
• Chapter 10. Pluralism Towards Pluralism
• Part IV. Putting Pluralism to Work. Applications
• Chapter 11. A Pluralist Approach to Proof in Mathematics
• Chapter 12. Pluralism and Together-Inconsistent Philosophies of Mathematics
• Chapter 13. Suggestions for Further Pluralist Enquiry
• Conclusion.