Pluralism In Mathematics: A New Position In Philosophy Of Mathematics by Mich FriendPluralism In Mathematics: A New Position In Philosophy Of Mathematics by Mich Friend

Pluralism In Mathematics: A New Position In Philosophy Of Mathematics

byMich Friend

Hardcover | December 4, 2013

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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.

Title:Pluralism In Mathematics: A New Position In Philosophy Of MathematicsFormat:HardcoverDimensions:291 pages, 23.5 × 15.5 × 0.07 inPublished:December 4, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:940077057X

ISBN - 13:9789400770577

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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.