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.

Klappentext

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 Structuralism and Formalism.

In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry.

In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word 'pluralism' with care.

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.