ISBN:
9789400770584
Language:
English
Pages:
Online-Ressource (XVII, 291 p. 16 illus, online resource)
Series Statement:
Logic, Epistemology, and the Unity of Science 32
Series Statement:
SpringerLink
Series Statement:
Bücher
Parallel Title:
Druckausg. Friend, Michèle Pluralism in mathematics
Keywords:
Philosophy (General)
;
Logic
;
Science Philosophy
;
Logic, Symbolic and mathematical
;
Philosophy
;
Philosophy (General)
;
Logic
;
Science Philosophy
;
Logic, Symbolic and mathematical
;
Logic
;
Logic, Symbolic and mathematical
;
Philosophy
;
Philosophy (General)
;
Science Philosophy
;
Pluralismus
;
Mathematik
Abstract:
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.
Description / Table of Contents:
IntroductionPart 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.
Note:
Description based upon print version of record
DOI:
10.1007/978-94-007-7058-4
URL:
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