Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics

By Joel David Hamkins

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice.

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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.

Hamkins shows, for example, how number systems set the stage for discussions of such philosophical issues as platonism, logicism, and the nature of abstraction. Consideration of the rise of rigor in the calculus leads to a discussion of whether the indispensability of mathematics in science offers grounds for mathematical truth. Sophisticated technical developments in set theory give rise to a necessary engagement with deep philosophical concerns, including the criteria for new mathematical axioms. Throughout, Hamkins offers a clear and engaging exposition that is both accessible and sophisticated, intended for readers whose mathematical backgrounds range from novice to expert.

Paperback

$45.00 X ISBN: 9780262542234 352 pp. | 7 in x 9 in

Endorsements

  • An engaging introduction to philosophical issues that arise within mathematics, explained with mathematical examples that don't require much background to understand.  Hamkins is a prominent set-theorist with a strong philosophical bent, and an exceptionally good expositor. The book is extremely readable, and has insightful discussions of a wide variety of topics. I recommend it highly.

    Hartry Field

    Silver Professor of Philosophy, New York University

  • “An engaging introduction to philosophical issues that arise within mathematics, explained with mathematical examples that don't require much background to understand.  Hamkins is a prominent set-theorist with a strong philosophical bent, and an exceptionally good expositor. The book is extremely readable, and has insightful discussions of a wide variety of topics. I recommend it highly.”