A Mathematical Prelude to the Philosophy of Mathematics

Authors: Pollard, Stephen

  • Offers hundreds of exercises that are highly relevant in the teaching of philosophy of mathematics
  • Presents the mathematical and philosophical background to those exercises
  • Supplements primary texts used for philosophy of mathematics courses
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05816-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-3-319-05815-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 21, 2016
  • ISBN 978-3-319-34833-9
  • Free shipping for individuals worldwide
About this Textbook

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

About the authors

Stephen Pollard has been on the faculty of Truman State University since 1985. He received his B.A. from Haverford College in 1979 and his Ph.D. from the University of Texas in 1983. His research and publications deal primarily with logic and the philosophy of mathematics, but his interests also include classical Greek philosophy, American pragmatism and the philosophy of science. Pollard is the author of Philosophical Introduction to Set Theory (Notre Dame, 1990), co-translator of The Continuum by Herman Weyl (Dover, 1994), co-author of Closure Spaces and Logic (Kluwer, 1996) and translator/editor of Essays on the Foundations of Mathematics by Moritz Pasch (Springer, 2010). His papers have appeared in Analysis, Erkenntnis, Logique et Analyse, The Monist, Notre Dame Journal of Formal Logic, Noûs, Philosophical Studies, Philosophia Mathematica, Synthese and other journals.

Reviews

“This book provides some mathematical background for undergraduate students of philosophy who want to study philosophy of mathematics. It provides mathematical training using a lot of elementary exercises.” (Reinhard Kahle, Mathematical Reviews, January, 2016)

“There have been many books on the philosophy of mathematics, but I do not think that many books aim to prepare students properly for the subject, which is what Pollard wants to do. … For readers like me, who know some basic number theory and analysis, as well as basic logic and computability theory, Pollard’s book will be a stimulating and novel experience.” (John Stillwell, Studia Logica, Vol. 104, 2016)

“The aim of the book is to give students opportunities to recreate some mathematics that will illuminate important readings in the philosophy of mathematics. … The book contains 298 exercises in the mentioned areas supported by explanatory materials. Each chapter ends by solutions of odd-numbered exercises as well as references. … The book can serve as a supplement to primary texts chosen by instructors.” (Roman Murawski, zbMATH, Vol. 1294, 2014)

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Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05816-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-3-319-05815-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 21, 2016
  • ISBN 978-3-319-34833-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
A Mathematical Prelude to the Philosophy of Mathematics
Authors
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05816-0
DOI
10.1007/978-3-319-05816-0
Hardcover ISBN
978-3-319-05815-3
Softcover ISBN
978-3-319-34833-9
Edition Number
1
Number of Pages
XI, 202
Topics