Mathematical Knowledge and the Interplay of Practices
eBook - ePub

Mathematical Knowledge and the Interplay of Practices

José Ferreirós

  1. 360 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Mathematical Knowledge and the Interplay of Practices

José Ferreirós

Book details
Table of contents
Citations

About This Book

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results.Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty.Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

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Information

Publisher
Princeton University Press
Year
2015
ISBN
9781400874002
Topic
Filosofía
Subtopic
Filosofía y ética en la ciencia

Table of contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. List of Illustrations
  6. Foreword
  7. 1 On Knowledge and Practices: A Manifesto
  8. 2 The Web of Practices
  9. 3 Agents and Frameworks
  10. 4 Complementarity in Mathematics
  11. 5 Ancient Greek Mathematics: A Role for Diagrams
  12. 6 Advanced Math: The Hypothetical Conception
  13. 7 Arithmetic Certainty
  14. 8 Mathematics Developed: The Case of the Reals
  15. 9 Objectivity in Mathematical Knowledge
  16. 10 The Problem of Conceptual Understanding
  17. References
  18. Index
Citation styles for Mathematical Knowledge and the Interplay of Practices

APA 6 Citation

Ferreirós, J. (2015). Mathematical Knowledge and the Interplay of Practices ([edition unavailable]). Princeton University Press. Retrieved from https://www.perlego.com/book/738797/mathematical-knowledge-and-the-interplay-of-practices-pdf (Original work published 2015)

Chicago Citation

Ferreirós, José. (2015) 2015. Mathematical Knowledge and the Interplay of Practices. [Edition unavailable]. Princeton University Press. https://www.perlego.com/book/738797/mathematical-knowledge-and-the-interplay-of-practices-pdf.

Harvard Citation

Ferreirós, J. (2015) Mathematical Knowledge and the Interplay of Practices. [edition unavailable]. Princeton University Press. Available at: https://www.perlego.com/book/738797/mathematical-knowledge-and-the-interplay-of-practices-pdf (Accessed: 14 October 2022).

MLA 7 Citation

Ferreirós, José. Mathematical Knowledge and the Interplay of Practices. [edition unavailable]. Princeton University Press, 2015. Web. 14 Oct. 2022.