| Description |
1 online resource (xii, 268 pages) : illustrations |
| Series |
The Problems of philosophy |
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Problems of philosophy (Routledge (Firm))
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| Contents |
Cover; The Infinite; Copyright; Contents; Preface to the Second Edition; Preface; Introduction: Paradoxes of the Infinite; 1 Paradoxes of the infinitely small; 2 Paradoxes of the infinitely big; 3 Paradoxes of the one and the many; 4 Paradoxes of thought about the infinite; Part One: The History; 1. Early Greek Thought; 1 Anaximander and to apeiron; 2 The Pythagoreans; 3 The Eleatics; 4 Plato; 5 Early Greek mathematics; 2. Aristotle; 1 Preliminaries; 2 The problem; 3 The solution: the potential infinite and the actual infinite; 4 Application of the solution; 5 A remaining difficulty |
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3. Medieval and Renaissance Thought1 The Greek legacy: reactions and developments; 2 Aquinas; 3 Later developments: the mathematically infinite; 4 Nicholas of Cusa. The end of the Renaissance; 4. The Calculus; 1 The fundamental principles of the calculus; 2 A brief history of the calculus; 3 Taking stock; 5. The Rationalists and the Empiricists; 1 The rationalists; 2 The empiricists; 6. Kant; 1 The background: an outline of Kant's philosophy; 2 The metaphysically infinite and the mathematically infinite; 3 The infinitude of the world. The antinomies; 4 The infinitude of reason |
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7. Post-Kantian Metaphysics of the Infinite1 Hegel; 2 Currents of thought in post-Hegelian metaphysics of the infinite I: the 'metaphysically big'; 3 Currents of thought in post-Hegelian metaphysics of the infinite II: the 'metaphysically small'; 4 Currents of thought in post-Hegelian metaphysics of the infinite III: the existentialists; 5 Nietzsche; 8. The Mathematics of the Infinite, and the Impact of Cantor; 1 Bolzano; 2 Turn-of-the-century work on the foundations of mathematics; 3 The main elements of Cantor's theory. Its early reception; 4 The theory of ordinals. The Burali-Forti paradox |
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5 Cantor's attitude to the paradoxes6 Later development: axiomatization; 9. Reactions; 1 Intuitionism; 2 Finitism; 3 Wittgenstein; 4 Current thought; Part Two: Infinity Assessed; 10. Transfinite Mathematics; 1 The iterative conception of a set. The paradox of the Set of all Sets; 2 Ordinals as sets; 3 Cardinals. Measuring infinite sets; 4 The continuum hypothesis; 5 Further thoughts on the infinite by addition and the infinite by division; 11. The Löwenheim-Skolem Theorem; 1 An introduction to the Löwenheim-Skolem theorem. Reactions and counter-reactions |
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2 The solution to Skolem's paradox. Scepticism and relativism3 Scepticism and relativism rebutted; 4 Meaning and understanding. The Löwenheim-Skolem theorem finally defused; 5 A lingering paradox; 12. Gödel's Theorem; 1 Introduction: the Euclidean paradigm; 2 A sketch of the proof of Gödel's theorem; 3 Hilbert's programme; 4 The human mind and computers; 5 Self-consciousness; 6 Meaning and understanding; 13. Saying and Showing; 1 The saying/showing distincton in the Tractatus; 2 The very idea of a saying/showing distinction; 3 Wittgenstein's early views on the infinite |
| Summary |
Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical |
| Analysis |
Infinity |
| Bibliography |
Includes bibliographical references (pages 250-260) and index |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
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Print version record |
| Subject |
Infinite.
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infinity.
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Infinite
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Unendlichkeit
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Philosophie
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Oneindigheid.
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| Form |
Electronic book
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| ISBN |
0203415884 |
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9780203415887 |
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