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Defending the Axioms: On the Philosophical Foundations of Set Theory Hardcover – March 15, 2011

ISBN-13: 978-0199596188 ISBN-10: 0199596182 Edition: 1st

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Product Details

  • Hardcover: 150 pages
  • Publisher: Oxford University Press; 1 edition (March 15, 2011)
  • Language: English
  • ISBN-10: 0199596182
  • ISBN-13: 978-0199596188
  • Product Dimensions: 0.6 x 5.6 x 8.4 inches
  • Shipping Weight: 10.4 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,724,791 in Books (See Top 100 in Books)

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Reviewed in Mathematical Reviews


About the Author


Penelope Maddy is Distinguished Professor of Logic and Philosophy of Science at the University of California, Irvine. She is the author of Naturalism in Mathematics (OUP, 1997), Realism in Mathematics (OUP, 1992), and Second Philosophy (OUP, 2007).

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I found this book a thoroughly enjoyable read. The author gives an excellent overview of the different forms of evidence in set theory and outlines two possible philosophies about the nature of the practice, suggesting that it is indeterminate which one of them is correct. I felt the author made a convincing case for her views about the correct methodologies for set theory. I found myself resisting the conclusion that it is indeterminate whether Thin Realism or Arealism is correct, thinking rather that she had merely shown that it is indeterminate which one we have most reason to believe in.
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