TY  - BOOK
AU  - Ferreirós,José
TI  - Mathematical Knowledge and the Interplay of Practices
SN  - 9780691167510
AV  - QA8.4 
U1  - 510.1 23
PY  - 2015///]
CY  - Princeton, NJ : 
PB  - Princeton University Press, 
KW  - Knowledge, Theory of
KW  - Mathematics
KW  - Philosophy
KW  - SCIENCE / Philosophy & Social Aspects
KW  - bisacsh
KW  - Axiom of Choice
KW  - Axiom of Completeness
KW  - Continuum Hypothesis
KW  - Elements
KW  - Euclidean geometry
KW  - FrameworkЁgent couples
KW  - Georg Cantor
KW  - Greek geometry
KW  - J. H. Lambert
KW  - Kenneth Manders
KW  - Peano Arithmetic
KW  - Philip S. Kitcher
KW  - Riemann Hypothesis
KW  - Sir Isaac Newton
KW  - ZermeloІraenkel axiom system
KW  - advanced mathematics
KW  - agents
KW  - arbitrary infinity
KW  - arbitrary set
KW  - arithmetical knowledge
KW  - axioms
KW  - basic arithmetic
KW  - certainty
KW  - classical arithmetic
KW  - cognition
KW  - complementarity
KW  - complex numbers
KW  - conceptual understanding
KW  - continuum
KW  - counting numbers
KW  - counting practice
KW  - culture
KW  - diagrammatic constructions
KW  - diagrams
KW  - elementary mathematics
KW  - exemplars
KW  - frameworks
KW  - geometrical proof
KW  - historians
KW  - hypotheses
KW  - intuitionistic arithmetic
KW  - logic
KW  - mathematical activity
KW  - mathematical knowledge
KW  - mathematical objects
KW  - mathematical practice
KW  - mathematics
KW  - measuring practices
KW  - metamathematics
KW  - methodological platonism
KW  - natural numbers
KW  - number theory
KW  - objectivity
KW  - ordinal numbers
KW  - philosophers
KW  - postulational mathematics
KW  - practice
KW  - purely arithmetical proof
KW  - real numbers
KW  - scientific practice
KW  - semantic entities
KW  - set theory
KW  - sets
KW  - simple infinity
KW  - symbols
KW  - systematic links
KW  - technical practice
N1  - 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; restricted access
N2  - 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
UR  - https://doi.org/10.1515/9781400874002?locatt=mode:legacy
UR  - https://www.degruyter.com/isbn/9781400874002
UR  - https://www.degruyter.com/document/cover/isbn/9781400874002/original
ER  -