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The Infinite (Problems of Philosophy) Paperback – March 9, 2001

ISBN-13: 978-0415252850 ISBN-10: 0415252857 Edition: 2nd

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Product Details

  • Series: Problems of Philosophy
  • Paperback: 268 pages
  • Publisher: Routledge; 2 edition (March 9, 2001)
  • Language: English
  • ISBN-10: 0415252857
  • ISBN-13: 978-0415252850
  • Product Dimensions: 5.4 x 0.7 x 8.5 inches
  • Shipping Weight: 14.1 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,599,499 in Books (See Top 100 in Books)

Editorial Reviews

Review

'Moore's book points to deep and unresolved issues in the philosophy of mathematics, and even deeper issues in general philosophy ... It deserves serious study by both mathematicians and philosophers.' - Thomas Tymoczko, Philosophia Mathematica

'[Moore's treatment of] the problems with which the history of thought about the infinite confronts us today ... shows that questions concerning the nature and existence of the infinte are still very much alive ... The importance of [his] book lies ... in its highly stimulating account of the nature of infinity and its bold defence of finitism.' - W.L.Craig, International Philosophical Quarterly

About the Author

A. W. Moore is Tutorial Fellow in Philosophy at St. Hugh's College, Oxford. --This text refers to an out of print or unavailable edition of this title.

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Customer Reviews

4.2 out of 5 stars
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Most Helpful Customer Reviews

13 of 13 people found the following review helpful By J. Rantschler on September 23, 2005
Format: Paperback
Moore's book, The Infinite, is written in two parts. The first is a very thorough discussion on the history of the idea of infinity in both its mathematical and metaphysical aspects, as he calls them, and how later discoveries in the mathematics of the infinite (calculus and Cantor) influenced its metaphysics. The second part is an attempt at a defense of a certain philosophy of infinity, "finitism," influenced by Wittgenstein. Part I,the longer of the two, is such an excellent introduction (worth five stars) that it more than mitigates the occasionally incoherent chapters of Part II.

Moore discusses the history of infinity mostly in terms of paradoxes and how, in different periods of history, philosophers tried to solve them. The major themes of the paradoxes are "the infinitely small," "the infinitely large," "the one and the many," and "thought about infinity." The paradoxes are analyzed in the different periods, which would alternately emphasize either the mathematical aspect of infinity (boundlessness, as in Lucretius rather than modern mathematics, uncompletability) or the metaphysical aspect (completeness, unity, perfection). The ideas of everyone from the pre-Socratics to Quine are on display in this first part, and the discussion is in-depth and understandable.

The most disappointing part of the book comes in the discussion of the continuum hypothesis. After mentioning Skolem and Goedel and how, together, they show that set theory can neither show that it is true nor show that it is false that the size of the of real numbers is equal to the size of the power set of the natural numbers in Part I, he promises to discuss them more in Part II.
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27 of 31 people found the following review helpful By Nikita B. Katz on December 31, 1999
Format: Paperback
This is a perfect book with which to grow impatient and ultimately to reject.
It is highly competent (no factual errors) and could be read by people with no prior exposure to any kind of Deep Thought (clear style, lots of diagrams). It succeeds in condensing the problems and treatments of the Infinite down to easy to grasp outlines; it explains and systematizes what usually appears as hopelessly arcane (LS theorem, Go:del's results, the antinomies of the infinite etc.)
The book fails (as nearly all do) in its attempt of a clear presentation of Cantor's legacy: from the diagonal procedure to the continuum hypothesis. Another omission is an outline of the 'journey to Omega' (current views on Sets that are bigger than ZF axioms can support).
The last three chapters are devoted to a 'defense of finitism'. The mere intent to defend something that is much more intuitive than any of Cantor's results is suspicious. Alas, the hidden tension (how can a finite creature create and use infinite concepts /or the concept of the infinite/) is simply deflated (not 'solved') possibly due to the author's tacit attachment to Kantianism.
Wittgenstein's name is mentioned often, disappointingly, he is also presented as a closeted Kantian (from failure to construct infinite numbers via succession procedure in Tractatus, alleged abandonment of the metaphysical infinity to the later discovery of nonsensical nature of (attempted) language-games concerned with infinity).
AW Moore's work deserves a high rating; partially because of the low quality of other authors' attempts to present the Infinite to the general public.
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8 of 8 people found the following review helpful By Pierre B. on January 5, 2009
Format: Paperback
The opening history is informative, interesting and useful. One learns much about Aristotle's conception of the infinite; Cantor's rival conception and the numerous positions between them. There are helpful and helpfully brief explanations of ordinals, the LS theorem and the Goedel results. However, the parts of the book in which the author presents his own positive view are a mixed bag: this reader found them to be only partially illuminating and highly repetitive. One wants to know much more about what it is to be "shown" something which, when one tries to say it, is strictly speaking false--and mere invocations of Wittgenstein aren't all that helpful here. One wonders whether the author really knew what he meant by this idea. I found the repetitive final chapters dragged, and in places bordered on the tedious.
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