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Science Without Numbers: A Defence of Nominalism Hardcover – December, 1980

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Product Details

  • Hardcover: 144 pages
  • Publisher: Princeton Univ Pr (December 1980)
  • Language: English
  • ISBN-10: 0691072604
  • ISBN-13: 978-0691072609
  • Product Dimensions: 8.8 x 5.8 x 0.7 inches
  • Shipping Weight: 7.2 ounces
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,798,693 in Books (See Top 100 in Books)

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61 of 64 people found the following review helpful By S. Guha on October 30, 2000
Format: Hardcover
Why review an out-of-print book? Because some are just too good to pass up. I am currently working through the "heavy" section of "Science Without Numbers", wherein Hartry Field shows how to do Newtonian gravitational physics without abstracta. This book is a brilliant and *highly* unorthodox defence of mathematical nominalism, the view that there are no abstract mathematical objects. While subtle in execution, the basic ideas behind Field's approach are straightforward (though probably his gifts of exposition make them seem simpler than they are).
The traditional problem of the nominalist, or would-be nominalist, is to account for the truth of mathematical statements, apparently about abstract objects like numbers and sets, without supposing that there really are any such objects. Not so for Field; he sidesteps that issue entirely by showing that it makes no difference, so far as *applications* of mathematics are concerned, whether mathematical theories are true or false--what is really necessary is that they be consistent and satisfy a few other weak conditions. If consistency (plus these other conditions) are satisfied, then the mathematical theory will be *conservative* whether or not it is true. This means that any inferences made from nominalistic claims--claims that don't entail that there are abstracta--to other nominalistic claims with the aid of the theory are such that the conclusion is formally entailed by the nominalistic premises *alone*. So, if your concern is to make inferences about the concrete world from premises about the concrete world, you can use any math you like (all good mathematical theories are conservative, as Field demonstrates), because the ultimate *conclusions* you draw will in fact be entailed by nominalistic claims alone.
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