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Platonism and Anti-Platonism in Mathematics

3.0 out of 5 stars 2 customer reviews
ISBN-13: 978-0195143980
ISBN-10: 0195143981
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Editorial Reviews

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"excellent book...exceptionally clear, insightful, and useful critical survey"--The Review of Modern Logic "Platonism and anti-platonism in mathematics is an impressive work. Balaguer presents forceful arguments for the viability of both FBP and fictionalism, and against the feasibility of any substantially different Platonist or anti-Platonist position. ... an admirable achievement."--The Bulletin of Symbolic Logic


About the Author

Mark Balaguer is Professor in the Department of Philosophy at California State University, Los Angeles. He is the author of " Platonism and Anti-Platonism in Mathematics "and " Free Will as an Open Scientific Question" (MIT Press).
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Product Details

  • Paperback: 240 pages
  • Publisher: Oxford University Press (July 19, 2001)
  • Language: English
  • ISBN-10: 0195143981
  • ISBN-13: 978-0195143980
  • Product Dimensions: 8.9 x 0.8 x 5.7 inches
  • Shipping Weight: 15.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #2,282,285 in Books (See Top 100 in Books)

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By Joao Leao on May 21, 2004
Format: Paperback
This is a remarkably forceful and ambitious book but a very
worthy read nonetheless. Balaguer is clearer in his arguments than about any other contemporary philosopher I have read on the subject! He does however make a few discernable mistakes and shows a surprising lack of depth is some of his tangential examinations as pointed by some of his reviewers (I am thinking of Colyvan and Zalta whose review of this book can be found on the web). Also, out of breath as I was, by the time I finished this book, I cannot say I feel persuaded by its thesis with respect to the indescernability between Fictionalism and Platonism. This is mostly because he means to accomplish it through a nominalization of Quantum Mechanics which I find not just blatantly flawed but ultimately indefensible (but I will address why I think so in a review of Hatry Field's book on Fictionalism since my qualms start with his own approach to this program. With David Malament I doubt QM can be nominalized or fictionalized.). Still Balaguer's notion of Full-Bloodied Platonism, the peculiar point-of-view he develops and embraces in this work is extremely interesting and challenging: it comes down to the notion that all "broadly possible" mathematical structures exist. This happens to be, though Balaguer seems anaware of it, a thesis currently arrived at by physical cosmologists speculating about the "Multiverse" (see Mark Tegmark's recent Scientific American article on "Parallel Worlds")! When different lines of speculation arrive at the same concepts there is some hint of historical consensus one tends to suspect a metaphysical corner where we are all about to get stuck for a while! On the other hand I cannot help to remark how simplistic and misleading is the language in which philosophers insist in carrying their arguments!
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To my mind, the author was trying to prove two things:

a) that he is smarter than Kurt Godel, and anyone else who has thought about the problem, and

b) that the correct answer to Platonism vs Fictionalism is "who knows or cares?"

I was unconvinced by the former and underwhelmed by the latter. On internalising the latter, I was unable to finish the book. Perhaps the rest is better, or perhaps I was expecting something else. Or perhaps, being not even as smart as Godel, I am just not clever enough. Who knows, who cares?
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