History of Science & Knowledge

# Mathematical Knowledge and the Interplay of Practices

### Hardcover

- Price:
- $45.00 / £38.00
- ISBN:
- Published:
- 12/22/2015
- Copyright:
- 2016
- Pages:
- 360
- Size:
- 6 x 9.25 in.
- 6 line illus.

### ebook

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.