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The Infinite (Problems of Philosophy) 2nd Edition

4.1 out of 5 stars 7 customer reviews
ISBN-13: 978-0415252850
ISBN-10: 0415252857
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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 a Professor of Philosophy at the University of Oxford and Tutorial Fellow of St Hugh's College, Oxford. He is the author of three previous books: The Infinite (1990); Points of View (1997); and Noble in Reason, Infinite in Faculty: Themes and Variations in Kant's Moral and Religious Philosophy (2003). He is also the editor or co-editor of several anthologies, and his articles and reviews have appeared in numerous other scholarly publications.
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Product Details

  • Series: Problems of Philosophy
  • Paperback: 268 pages
  • Publisher: Routledge; 2 edition (March 11, 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: 4.1 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #825,441 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

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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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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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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Format: Kindle Edition
This book first sparked my interest in metaphysics and the philosophy of mathematics as an undergraduate. It is accessible to non-specialists and provides a delightful history of the concept of the infinite in western philosophy. The coverage of figures such as Aristotle, Kant, Wittgenstein on this topic is very good, as is the attention to Cantor and Brouwer. A bit more attention to Hilbert would be desirable. It is a broad sweeping essay on the history of an idea such as is seldom found today. It is not suitable for detailed scholarly work in the history of philosophy or philosophy of mathematics given its broad sweep. Nonetheless, it is a marvelous introduction to this topic in metaphysics and mathematics. Moreover, the last third of the book presents the development of the author's own Wittgensteinian finitist point of view. Whether one agrees with AW Moore's position at the end or not, it would be hard to find a better book at this level of accessibility.
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