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PROOF AND OTHER DILEMMAS: MATHEMATICS AND PHILOSOPHY

PROOF AND OTHER DILEMMAS: MATHEMATICS AND PHILOSOPHY

PROOF AND OTHER DILEMMAS: MATHEMATICS AND PHILOSOPHY

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Proof and Other Dilemmas: Mathematics and Philosophy
edited by Bonnie Gold and Roger Simons

Has the advent of computers changed the nature of mathematical knowledge? Should it? Is the importance of proof decreasing? Is there an empirical aspect to mathematics after all? To what extent is mathematics socially constructed? Is mathematics the "science of patterns?" Recently emerging questions like these are discussed in this book along with some recent thinking about classical questions. During the first 75 years of the 20th century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionism, logicism, and Platonism). This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philosophers of mathematics, summarize the discussion in that community during the last 35 years.

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  • Brand name: MAA
  • Editors: Bonnie Gold and Roger Simons
  • ISBN:9780883855676
  • 320pp.
  • Hardcover
  • 2008
  • Series: Spectrum
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