The infinite
Author(s)
Bibliographic Information
The infinite
（The problems of philosophy : their past and present）
Routledge, 1991
- : pbk
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Note
Bibliography: p. 250-260
Includes index
Description and Table of Contents
Description
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.
Table of Contents
History 1. Early Greek thought 2. Aristotle 3. Medieval and Renaissance thought 4. The Calculus 5. The Rationalists and the Empiricists 6. Kant 7. Post-Kantian Metaphysics of the Infinite 8. The Mathematics of the Infinite, and the impact of Cantor Reactions Part 2: Infinity Assessed 10. Transfinite Mathematics 11. The Lowenheim-Skolem Theorem 12. Godel's Theorem 13. Saying and Showing 14. Infinity assessed. The History re-assessed 15. Human Finitude
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