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Carregando... Lectures on the Philosophy of Mathematics (edição: 2021)de Joel David Hamkins (Autor)
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Hamkins writes exceptionally clearly and manages to give robust but succinct explanations for often complex ideas. There are fairly extensive exercises accompanying each chapter...
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations. Não foram encontradas descrições de bibliotecas. |
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Google Books — Carregando... GênerosClassificação decimal de Dewey (CDD)510.1Natural sciences and mathematics Mathematics General Mathematics Philosophy And PsychologyClassificação da Biblioteca do Congresso dos E.U.A. (LCC)AvaliaçãoMédia:
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That is not to say that this book is flawless, just that the flaws can't cancel out its merits. Some comments:
(1) The biggest flaw I see is that the intended audience level varies wildly. I could give many specific examples. One that springs to mind is that after spending 10 pages presenting the core concepts of undergraduate real analysis from scratch, the book makes passing reference to the Lebesgue measure of a certain set, as if no explanation is needed as to what Lebesgue measure is.
(2) There are occasional infelicities that somehow survived proof-reading. For example, on page 70, we read: "The curve therefore begins at the point c(0); it travels along the curve as time t progresses; and it terminates at the point c(1)." Apparently, the curve travels along itself!
(3) There are some repetitions but not too many. For example, on page 108 we are told: "Hilbert had listed the continuum hypothesis as the very first on his famous list of twenty-three open problems at the beginning of the twentieth century, problems that guided so much of the future of mathematical research." Then on page 285 we are told: "Hilbert gave a stirring speech at the dawn of the twentieth century, identifying the mathematical problems that would guide mathematics for the next century, and the very first problem on Hilbert's list was Cantor's continuum hypothesis." ( )