José Ferreirós – författare
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4 produkter
4 produkter
431 kr
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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, 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.
Del 66 - Archimedes
Richness of the History of Mathematics
A Tribute to Jeremy Gray
Inbunden, Engelska, 2023
2 188 kr
Skickas inom 10-15 vardagar
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines.
Del 66 - Archimedes
Richness of the History of Mathematics
A Tribute to Jeremy Gray
Häftad, Engelska, 2024
2 188 kr
Skickas inom 10-15 vardagar
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines.
Labyrinth of Thought
A History of Set Theory and Its Role in Modern Mathematics
Häftad, Engelska, 2007
801 kr
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Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of Georg Cantor, it analyzes his work and the emergence of transfinite set theory within the broader context of the rise of modern mathematics. The text has a tripartite structure. Part 1, The Emergence of Sets within Mathematics, surveys the initial motivations for a mathematical notion of a set within several branches of the discipline (geometry, algebra, algebraic number theory, real and complex analysis), emphasizing the role played by Riemann in fostering acceptance of the set-theoretic approach. In Part 2, Entering the Labyrinth, attention turns to the earliest theories of sets, their evolution, and their reception by the mathematical community; prominent are the epoch-making contributions of Cantor and Dedekind, and the complex interactions between them. Part 3, In Search of an Axiom System, studies the four-decade period from the discovery of set-theoretic paradoxes to Gödel’s independence results, an era during which set theory gradually became assimilated into mainstream mathematics; particular attention is given to the interactions between axiomatic set theory and modern systems of formal logic, especially the interplay between set theory and type theory. A new Epilogue for this second edition offers further reflections on the foundations of set theory, including the "dichotomy conception" and the well-known iterative conception.