Pluralism in Mathematics: A New Position in Philosophy of Mathematics

This book draws on philosophy, mathematics and logic to give an account of Pluralism, which is a family of positions in the philosophy of mathematics. Discussion ranges from motivation, to rigor and proof for the Pluralist, to applications in mathematics.

Offers a radical approach, developing a position on Pluralism Provides a cross disciplinary approach, drawing upon mathematical positions whilst presenting a philosophical account Scrutinizes the transcendental presentation of Pluralism

Inhalt
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.