- 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)
- See Complete Table of Contents
The Infinite (Problems of Philosophy) Paperback – 25 Jan 2001
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'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
Top Customer Reviews
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.
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.
Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)
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.
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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