Mathematical Knowledge and the Interplay of Practices (eBook)

Jose Ferreiros (Autor)

eBook Download: EPUB

2015
360 Seiten
Princeton University Press (Verlag)
978-1-4008-7400-2 (ISBN)

Infos

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, Jose Ferreiros 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, Ferreiros 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. Ferreiros 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.

Autor

José Ferreirós is professor of logic and philosophy of science at the University of Seville in Spain. He is the author of Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics and the coeditor of The Architecture of Modern Mathematics: Essays in History and Philosophy.

Produkt-Details

• Erscheint lt. Verlag: 22.12.2015
• Zusatzinfo: 6 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Themenwelt: Sozialwissenschaften ► Soziologie ► Spezielle Soziologien
• Schlagworte: Actual infinity • Addition • advanced mathematics • Agents • algebraic number theory • Analytic number theory • arbitrary infinity • arbitrary set • arithmetic • arithmetical knowledge • Axiom • axiomatic system • Axiom of choice • Axiom of Completeness • axiom of infinity • Axioms • basic arithmetic • Bernhard Riemann • Bolzano–Weierstrass theorem • Calculation • Cardinality • category theory • Certainty • classical arithmetic • Classical Logic • classical mathematics • Cognition • cognitive science • complementarity • Complex Analysis • complex number • complex numbers • Conceptual Understanding • conjecture • Continuum • Continuum Hypothesis • Contradiction • counterexample • Counting • counting numbers • counting practice • Culture • Cumulative hierarchy • descriptive set theory • Diagram (category theory) • diagrammatic constructions • Diagrams • dichotomy • Elaboration • Elementary mathematics • Elements • Emergence • Epistemology • Euclidean Geometry • Euclidean space • Exemplars • existential quantification • Explanation • First-Order Logic • Formal science • Foundations of mathematics • Frameworks • FrameworkЁgent couples • Frege (programming language) • geometrical proof • Geometry • Georg Cantor • Gottlob Frege • Greek geometry • Hermann Weyl • historians • hypotheses • hypothesis • idealization • inference • Infinitesimal • Integer • intuitionistic arithmetic • irrational number • J. H. Lambert • Kenneth Manders • Logic • mathematical activity • Mathematical Analysis • Mathematical Induction • Mathematical Knowledge • Mathematical Logic • mathematical objects • mathematical practice • Mathematical Proof • Mathematical Theory • mathematician • Mathematics • Measurable cardinal • Measure (mathematics) • Measurement • measuring practices • metamathematics • methodological platonism • Morphism • Natural number • natural numbers • Notation • Number Theory • Objectivity • ordinal numbers • peano arithmetic • Peano axioms • Philip S. Kitcher • Philosopher • Philosophers • philosophy of mathematics • philosophy of science • polynomial • postulational mathematics • Practice • Prime number • Principle • Proof theory • Proportionality (mathematics) • purely arithmetical proof • Pure Mathematics • Quantifier (logic) • Quantity • Rational number • real number • Real Numbers • Requirement • result • Riemann hypothesis • Riemann surface • Science • scientific practice • Scientist • semantic entities • Semantics • Sets • set theory • simple infinity • Sir Isaac Newton • Subset • Summation • Symbols • systematic links • technical practice • Theorem • theory • The Philosopher • Topological space • Topology • Variable (mathematics) • Well-order • Well-ordering theorem • Zermelo–Fraenkel set theory • ZermeloІraenkel axiom system
• ISBN-10: 1-4008-7400-9 / 1400874009
• ISBN-13: 978-1-4008-7400-2 / 9781400874002