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Lectures on the Philosophy of Mathematics de…
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Lectures on the Philosophy of Mathematics (edição: 2021)

de Joel David Hamkins (Autor)

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251913,174 (5)1
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.… (mais)
Membro:cpg
Título:Lectures on the Philosophy of Mathematics
Autores:Joel David Hamkins (Autor)
Informação:The MIT Press
Coleções:Five Star, Books, Sua biblioteca
Avaliação:*****
Etiquetas:Philosophy of Mathematics

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Lectures on the Philosophy of Mathematics de Joel David Hamkins

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This is a remarkably well-written, interesting book. Almost every person interested in mathematics, including professional mathematicians, would enjoy reading it. So much writing on the philosophy of mathematics gets bogged down in minutiae, so that essentially only professional philosophers could possibly appreciate it. This is not that sort of book. General-interest math books this good are few and far between.

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." ( )
  cpg | Apr 3, 2021 |
Hamkins writes exceptionally clearly and manages to give robust but succinct explanations for often complex ideas. There are fairly extensive exercises accompanying each chapter...
adicionado por devogon | editarDanny Yee's book reviews, Danny Yee (Sep 3, 2021)
 
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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.

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510.1Natural sciences and mathematics Mathematics General Mathematics Philosophy And Psychology

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