Mathematical Knowledge and the Interplay of Practices / José Ferreirós.
Material type:
TextPublisher: Princeton, NJ : Princeton University Press, [2015]Copyright date: ©2016Edition: Pilot project. eBook available to selected US libraries onlyDescription: 1 online resource (360 p.) : 6 line illusContent type: - 9780691167510
- 9781400874002
- Knowledge, Theory of
- Mathematics -- Philosophy
- SCIENCE / Philosophy & Social Aspects
- Axiom of Choice
- Axiom of Completeness
- Continuum Hypothesis
- Elements
- Euclidean geometry
- FrameworkЁgent couples
- Georg Cantor
- Greek geometry
- J. H. Lambert
- Kenneth Manders
- Peano Arithmetic
- Philip S. Kitcher
- Riemann Hypothesis
- Sir Isaac Newton
- ZermeloІraenkel axiom system
- advanced mathematics
- agents
- arbitrary infinity
- arbitrary set
- arithmetical knowledge
- axioms
- basic arithmetic
- certainty
- classical arithmetic
- cognition
- complementarity
- complex numbers
- conceptual understanding
- continuum
- counting numbers
- counting practice
- culture
- diagrammatic constructions
- diagrams
- elementary mathematics
- exemplars
- frameworks
- geometrical proof
- historians
- hypotheses
- intuitionistic arithmetic
- logic
- mathematical activity
- mathematical knowledge
- mathematical objects
- mathematical practice
- mathematics
- measuring practices
- metamathematics
- methodological platonism
- natural numbers
- number theory
- objectivity
- ordinal numbers
- philosophers
- postulational mathematics
- practice
- purely arithmetical proof
- real numbers
- scientific practice
- semantic entities
- set theory
- sets
- simple infinity
- symbols
- systematic links
- technical practice
- 510.1 23
- QA8.4
- online - DeGruyter
| Item type | Current library | Call number | URL | Status | Notes | Barcode | |
|---|---|---|---|---|---|---|---|
eBook
|
Biblioteca "Angelicum" Pont. Univ. S.Tommaso d'Aquino Nuvola online | online - DeGruyter (Browse shelf(Opens below)) | Online access | Not for loan (Accesso limitato) | Accesso per gli utenti autorizzati / Access for authorized users | (dgr)9781400874002 |
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 online access with authorization star
http://purl.org/coar/access_right/c_16ec
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.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023)