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Gödel's Theorem in Focus (Philosophers in Focus) Revised ed. Edition

3.0 out of 5 stars 1 customer review
ISBN-13: 978-0415045759
ISBN-10: 0415045754
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About the Author

Stuart G. Shanker is Distinguished Research Professor of Philosophy and Psychology at York University, Toronto where he is also President of the Council for Early Child Development and Director of the Milton and Ethel Harris Research Initiative.
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Product Details

  • Paperback: 272 pages
  • Publisher: Routledge; Revised ed. edition (February 22, 1990)
  • Language: English
  • ISBN-10: 0415045754
  • ISBN-13: 978-0415045759
  • Product Dimensions: 5.4 x 0.6 x 8.5 inches
  • Shipping Weight: 12.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #3,087,840 in Books (See Top 100 in Books)

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Format: Paperback
The most interesting part of the book is the discussion of Gödel's "Platonism." One is "struck by the great contrast between the deep platonist convictions Gödel held concerning the objective basis of mathematics and the special caution he exercised in revealing these convictions" (p. 96). In fact, Gödel made only "one public statement of a philosophical character in the period directly following his thesis work," namely: "Gödel openly criticized the view which took consistence as the criterion for existence ... '[Assuming the consistence of classical mathematics] one can even give examples of propositions ... which are really contentually true ... but are unprovable in the formal system of classical mathematics.' Hence, the negations of such statements could be adjoined to form a consistent system containing false statements; thus consistency would not guarantee existence in the intended sense." (pp. 102-103). "it should be noted that the heuristic principle of my construction of undecidable number theoretic propositions in the formal systems of mathematics is the highly transfinite concept of 'objective mathematics truth' as opposed to that of 'demonstrability'" (p. 107). However, "in consequence of the philosophical prejudices of our times ... a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless" (p. 107).

The book's main objective, however, is "to divest [Gödel's theorem] of its false metaphysical pretensions" (p. 235), as witnessed, for example, by the fact that the article on Gödel's own convictions is shorter than that by his hardcore enemy Detlefsen, who proclaims that all is fine and well with Hilbert's Programme.
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