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Naturalism in Mathematics Hardcover – February 26, 1997

ISBN-13: 978-0198235736 ISBN-10: 0198235739 Edition: 1st
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Editorial Reviews

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"Maddy's knowledge of early and contemporary set theory, and of philosophically significant parts of the history of mathematics generally, is impressively wide and deep, and her discussions of these matters are illuminating and rewarding. She writes in a clear, forthright and challenging style. Her book is eminently readable, instructive, and thought-provoking."--The Journal of Symbolic Logic


About the Author


Penelope Maddy is Professor of Philosophy at the University of California, Irvine, having previously held positions at the University of Illinois, Chicago, and the University of Notre Dame, Indiana.
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Product Details

  • Hardcover: 254 pages
  • Publisher: Oxford University Press; 1 edition (February 26, 1997)
  • Language: English
  • ISBN-10: 0198235739
  • ISBN-13: 978-0198235736
  • Product Dimensions: 5.5 x 0.9 x 8.6 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #4,833,570 in Books (See Top 100 in Books)

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19 of 21 people found the following review helpful By John Paul Jaubert on December 6, 2005
Format: Paperback
Well, I'm a little reluctant to write a review for this book for a few reasons. Firstly, it will only have a very narrow readership. I take it that it's meant to be read as part of the curricula of an upper undergraduate or graduate course on philosophy of mathematics. Only philosophers and mathematicians might read it, with the former possibly not understanding significant portions of it, and the latter possibly scoffing at the very project which the book represents. Secondly, I'm in the first camp (the philosophers) so I'm not the best reviewer but I'll give it a try anyway.

To begin, it's not a text. Don't come to the book thinking to take away something more in the way of *knowledge* than you came to it with. It's purpose is to contribute to a broader sort of understanding than that. You'll get the most out of it if you already come armed with a good acquaintance with the developments in set and model theory that have gone on since the '60's right up to the time of the book's publication.

Maddy's earlier book, Realism in Mathematics, was an elaboration and defense of the on-again-off-again unfashionable view (or family of views) according to which mathematical objects (numbers, sets, transfinites and other infinites, functions, their values, etc.) all exist in some more-or-less robust sense. This book can be variously interpreted as something of a minor retreat from or else a clarification of that realism (or both).

The book pays special attention to Godelian and Quinean arguments for realistic views according to which, to be distortingly brief, we should robustly believe in at least some mathematical objects because we must necessarily *act as if* we do in the very doing of mathematics.
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5 of 12 people found the following review helpful By Viktor Blasjo on June 26, 2009
Format: Hardcover
The "naturalism" that Maddy espouses reduces philosophers to lapdogs. Current mathematical practice is glorified as the highest and only court in which every question is to be settled: "look not to traditionally philosophical matter about the nature of mathematical entities, but to the needs and goals of mathematics itself" (p. 191). She pretends that this does not preclude a critical outlook (p. 181), but obviously the only type of criticism that can be offered by such a philosopher is a critique within the doctrinal framework itself (i.e., what amounts to debates between commissars at the Kremlin) rather than critiques of the framework itself. Consider for example Poincaré's critique of logicism. Since Poincaré's philosophical critique was that of an outsider who did not participate in this research, Maddy presumably thinks it appropriate to dismiss it without even listening to the arguments. Such arrogance is hardly very healthy.

The most important trait that Maddy inherits from her masters the mathematicians is their intolerance. Consider for example how Gödel's "realism" (i.e., Platonism) is rejected.

"A Gödelian realism along these lines has been subject to considerable philosophical criticism, most prominent being the simple objection that we have not been given a convincing account of this mathematical intuition." (p. 92-93).

Thus the "considerable philosophical criticism" amounts to this: we like to think that we know a lot of stuff. The idea that mathematical intuition plays a role is rejected not for any actual arguments against it (of which there are none) but because it violates this axiom.
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