A.W. Moore
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Customer Reviews:
Total reviews: 3
Average rating: 4.0 of 5
Thorough yet disappointing 4 out of 5 stars.
18 of 20 people found this review helpful.
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.
Editorial Review:
This historical study of the infinite covers all its aspects from the mathematical to the mystical. Anyone who has ever pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of the subject. Beginning with an entertaining account of the main paradoxes of the infinite, including those of Zeno, A.W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein.