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The Infinite : PROBLEMS OF PHILOSOPHY THEIR PAST AND PRESENT - A. W. Moore

The Infinite

PROBLEMS OF PHILOSOPHY THEIR PAST AND PRESENT

Paperback

Published: 25th January 2001
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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 recognise 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. Recent technical work is examined in the light of Cantor's remarkable discovery that infinity comes in degrees: some infinite sets are much bigger than others. Moore also gives a crisp sketch of Godel's celebrated proof, his clear presentation enabling the non-mathematical reader to grasp deep mathematical issues. Drawing on these technical results and on the early work of Wittgenstein, Moore outlines his own original account of the infinite. He argues that there are fundamental links between the infinite and the ineffable. In a final chapter on human finitude, these and other links are traced out, and the book concludes with a moving discussion of death and the poignancy of human finitude.

'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

Preface to the Second Editionp. xi
Prefacep. xx
Introduction Paradoxes of the Infinitep. 1
The Historyp. 15
Early Greek Thoughtp. 17
Aristotlep. 34
Medieval and Renaissance Thoughtp. 45
The Calculusp. 57
The Rationalists and the Empiricistsp. 75
Kantp. 84
Post-Kantian Metaphysics of the Infinitep. 96
The Mathematics of the Infinite, and the Impact of Cantorp. 110
Reactionsp. 131
Infinity Assessedp. 145
Transfinite Mathematicsp. 147
The Löwenheim-Skolem Theoremp. 159
Gödel's Theoremp. 172
Saying and Showingp. 186
Infinity Assessed. the History Reassessedp. 201
Human Finitudep. 218
Glossaryp. 234
Bibliographyp. 250
Indexp. 261
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780415252850
ISBN-10: 0415252857
Series: PROBLEMS OF PHILOSOPHY THEIR PAST AND PRESENT
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 296
Published: 25th January 2001
Publisher: Taylor & Francis Ltd
Country of Publication: GB
Dimensions (cm): 21.2 x 13.8  x 2.2
Weight (kg): 0.4
Edition Number: 2
Edition Type: New edition