Mathematical knowledge and the interplay of practices / José Ferreirós.

Format:

Book

Author/Creator:

Ferreirós, José, author.

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Physical Description:

1 online resource (358 p.)

Edition:

Pilot project. eBook available to selected US libraries only

Place of Publication:

Princeton, NJ : Princeton University Press, [2015]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

List of Illustrations

Foreword

1. On Knowledge and Practices

2. The Web of Practices

3. Agents and Frameworks

5. Ancient Greek Mathematics

6. Advanced Math

7. Arithmetic Certainty

8. Mathematics Developed

9. Objectivity in Mathematical Knowledge

10. The Problem of Conceptual Understanding

References

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

ISBN:

9781400874002

1400874009

OCLC:

984662405