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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.

Mathematics --- Philosophy. --- Logic of mathematics --- Mathematics, Logic of --- 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.