Details
Pluralism in Mathematics: A New Position in Philosophy of Mathematics
Logic, Epistemology, and the Unity of Science, Band 32
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96,29 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 20.11.2013 |
| ISBN/EAN: | 9789400770584 |
| Sprache: | englisch |
| Anzahl Seiten: | 291 |
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Beschreibungen
<p>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. </p><p>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.</p><p>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. </p>
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.
<p>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. </p><p>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.</p><p>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. </p>
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
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.
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