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Mathematics and Mind (Logic and Computation in Philosophy) 1st Edition

4.0 out of 5 stars 1 customer review
ISBN-13: 978-0195079296
ISBN-10: 0195079299
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Editorial Reviews

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"The volume contains extremely interesting papers of high quality on the philosophy of mathematics. The book is compact, and a number of central philosophers of mathematics are discussed in detail."--Modern Logic


"It includes several papers worthy of careful study."--Journal of Symbolic Logic


About the Author

George is Professor of Philosophy at Amherst College.
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Product Details

  • Series: Logic and Computation in Philosophy
  • Hardcover: 216 pages
  • Publisher: Oxford University Press; 1 edition (September 8, 1994)
  • Language: English
  • ISBN-10: 0195079299
  • ISBN-13: 978-0195079296
  • Product Dimensions: 6.2 x 0.9 x 9.5 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #2,518,780 in Books (See Top 100 in Books)

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Format: Hardcover
While I have no intention of reviewing this book in full, I was prompted by Hallett's pleasant chapter on "Hilbert's Axiomatic Method and the Laws of Thought" to propose the following somewhat idiosyncratic reconstruction of Hilbert's "formalism."

Step 1 is to observe that mathematics is fundamentally cognitive, and otherwise non-contentual. This is proved from experience. The proof consists in pointing out the following fact:

"Mathematics is an indivisible whole, an organism whose ability to live is governed by the connection between its parts. No matter how various is the stuff of mathematical knowledge in its details, we recognise very clearly the sameness of the logical tools, the close relations between idea formation across the whole of mathematics, and the innumerable analogies between its distinct domains." (Hilbert, pp. 167-168)

Or the same more poetically:

"A problem, even when it originates in the world of outer phenomena, is like a young rice plant, which can only thrive and bear fruit when it is carefully grafted onto an old stem according to the rules of art of the gardener, the stem here being the secure treasury of mathematical knowledge." (Hilbert, p. 167)

These plain facts of mathematical experience are nothing short of miracles on certain philosophies of mathematics. We recall that Frege, for example, blinded by epistemological dust, stipulated a profound dichotomy between arithmetic, which supposedly is given by logic alone, and geometry, which supposedly depends on experience (pp. 162-165). We should like to see a proponent of such a view try to explain the rudimentary phenomenological observations above.
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