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The Infinite (Problems of Philosophy) Paperback – 25 Jan 2001

5.0 out of 5 stars 4 customer reviews

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Product details

  • Paperback: 296 pages
  • Publisher: Routledge; 2 edition (25 Jan. 2001)
  • Language: English
  • ISBN-10: 0415252857
  • ISBN-13: 978-0415252850
  • Product Dimensions: 13.8 x 1.7 x 21.6 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 639,694 in Books (See Top 100 in Books)
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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

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Format: Paperback
This book is excellent. If you have ever tried to get your head round the concept of infinity and failed miserably then you need this book. It covers many areas, from the history of infinity to its relevance in modern mathematics and philosophy. It does this in a very entertaining fashion, never stooping to professorial pomposity or becoming dry and 'academic'. Read this book. Then read it again. Then maybe you'll get some sleep.
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Format: Paperback
I last read a philosophy book in the 1960s when I did a degree that included it. At the time the orthodoxy seemed to be that the business of philosophy was to clear up various verbal tangles which only philosophers were silly enough to get into in the first place. I did not find this activity inspiring. In sharp contrast I found this book enlightening and highly enjoyable.

For me the delights were many. The book deals with an undeniably important concept (infinity obviously); it grounds its discussion in the history of the subject from the time it was approached by Anaximander, through Aristotle, Plotinus, mediaeval thinkers, Leibniz, Kant and their successors , and on to Cantor, Brouwer, Wittgenstein and other more modern work; it treats seriously philosophers such as Heidegger and Hegel whom I was taught to consider pretentious windbags; it outlines the relevant paradoxes and technical work including Godel's proof and considers their implications; and it treats seriously both the mathematical and emotional aspects of infinity - our struggles with the idea of 'a set of all sets' and our yearnings for some 'infinite' background against which to set our finite lives.

As a lay person I cannot judge the book's technical merit. But if any other lay person is intrigued by the idea of infinity, I cannot think there can be a clearer or more compelling introduction to both the concept and perhaps philosophy as it now is.
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Format: Paperback Verified Purchase
Moore succeeds in an area that is notoriously difficult for the vast majority of writers on a subject that itself cannot be easily grasped let alone written about. He is technically proficient enough with the most complex of pure mathematical propositions to be able to present them with care and simplicity, and a good enough philosopher to be able to capture key concepts. On top of all that, he is a patient and articulate writer who pulls it all together in a book that may well be the best single modern treatment of the subject of infinity.

Clegg's book, which I have also reviewed, is an alternative (and very good) approach, as is the work by Kaplan and Kaplan, but overall, Moore's book is the most complete.
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very good
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Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)

Amazon.com: 4.1 out of 5 stars 7 reviews
3 of 3 people found the following review helpful
5.0 out of 5 stars One of the best overviews 2 Dec. 2012
By Anne - Published on Amazon.com
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.
16 of 16 people found the following review helpful
4.0 out of 5 stars A Nice Discussion on the Philosophy of Infinity 23 Sept. 2005
By J. Rantschler - Published on Amazon.com
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. In fact, he devotes a chapter to each in Part II, but they are the least coherent chapters in the book and focus on the philosophy to the detriment of the mathematics.

This is not to say that all the chapters in Part II are equally bad. Chapters 10 and 14 are quite good, and 13 and 15 are nearly adequate. In comparison to the precision and clarity of Part I, however, pushing through to the end is chore.

This is definitely a book to read, and probably a good book to buy if you like solid discussion about a very difficult subject that's presented clearly.
10 of 10 people found the following review helpful
3.0 out of 5 stars A mixed bag 5 Jan. 2009
By Pierre B. - Published on Amazon.com
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.
28 of 32 people found the following review helpful
4.0 out of 5 stars Thorough yet disappointing 31 Dec. 1999
By Nikita B. Katz - Published on Amazon.com
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.
4.0 out of 5 stars Subtle Handling of Eternal Dilemmas 10 April 2015
By Andrew Langridge - Published on Amazon.com
Format: Kindle Edition
A.W. Moore's masterly study demonstrates how a proper appreciation of the infinite is crucially important in deciding the limits of our knowledge and providing meaning for our lives. After an illuminating historical exposition of the key debates from the Ancient Greeks to the present day, Moore advances his view that our radically finite lives are aspects of an infinite whole. This is something that we are shown, not something that we can know. We cannot fully grasp the infinite (despite Cantor's best efforts), but self-conscious introspection invites us to apply a-priori Ideas of the infinite to reality. For example, continuous lines and shapes are really self-contained wholes but can be treated by mathematicians as if they were sets of infinitesimal points. What I find remarkable is that Aristotle had already solved many of the problems through advancement of the 'potential' infinite.
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