Pluralism In Mathematics A New Position In Philosophy Of Mathematics [EPUB]
E-Book Overview
"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."--Page 4 de la couverture.
E-Book Information
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Series: Logic epistemology and the unity of science (Print) 32
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Year: 2,014
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City: Dordrecht
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Pages: 1 vol. (XVII-291 p.) ; 25 cm
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Language: English
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Identifier: 9789400770577,9789400770584,940077057X
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Org File Size: 1,297,339
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Extension: epub
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Tags:
Logique
Logique mathématique
Mathematics--Philosophy
Mathématiques--Philosophie
Philosophie des sciences
Pluralism
Pluralisme (Philosophie)
Logique mathématique
Mathematics -- Philosophy
Mathématiques -- Philosophie
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Toc: 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.