Opposition and paradoxes : philosophical perplexities in science and mathematics

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Opposition and paradoxes : philosophical perplexities in science and mathematics

John L. Bell

Broadview Press, c2016

  • : pbk

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Since antiquity, opposed concepts such a s t he One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and Paradoxes, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell not only motivates abstract conceptual thinking about the paradoxes at issue, he also offers a compelling introduction to central ideas in such otherwise-di cult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life-he would, if he had infinite time, never complete the work, although no individual part of it would remain unwritten ... Or imagine an English professor who time-travels back to 1599 to offer a printing of Hamlet to William Shakespeare, so as to help the Bard overcome writer's block and author the play which will centuries later inspire an English professor to travel back in time ... These and many other of the book's paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty of many of our most basic concepts.

目次

Acknowledgements What Is This Book About? Chapter I: The Continuous and the Discrete Continuity and Discreteness The Pythagorean School and Incommensurable Magnitudes Atomism The Stoics and the Continuum Theory of Matter Zeno's Paradoxes Contemporary Versions of Zeno's Paradoxes: Supertasks Infinitesimals Chapter II: Oppositions and Paradoxes in Mathematics: Set Theory and the Infinite Set Theory and the One/Many Opposition Paradoxes of the Infinite Uncountable Infinities Set-Theoretic Antinomies The Axiom of Choice Chapter III: The Strange Universe of Non-Euclidean Geometry Hyperbolic Geometry Riemannian Geometry Chapter IV: Puzzles and Paradoxes of Time Travel Time Travel into the Past: Branching Timelines Temporal Loops Time Travel into the Future The Future Time Viewer Two-Dimensional Time Temporal Interdicts Time Travel as a Physical Possibility Chapter V: Puzzles and Paradoxes of Relativity Theory Special Relativity Spacetime Faster-than-Light Particles in Special Relativity: Tachyons General Relativity: The Principle of Equivalence Black Holes Chapter VI: Puzzles and Paradoxes in Quantum Physics Waves vs. Particles Heisenberg's Uncertainty Principle and Bohr's Principle of Complementarity Quantum Tunneling The Riddle of Polarization Schroedinger's Cat Paradox Interpretations of Quantum Theory The EPR Paradox and Nonlocality Chapter VII: Cosmic Enigmas The Beginnings of Cosmology Steady-State vs. Big Bang The Problem of the Origin of the Universe Dark Matter, Dark Energy, and Cosmic Acceleration The Argument from Design vs. the Multiverse A Philosophical Coda Appendix 1: Paradoxes in Logic and Language The Liar Paradox The Liar, the Truth-Teller, and the Dice Man Curry's Paradox The Grelling-Nelson Paradox Berry's Paradox Richard's Paradox The Paradox of the Heap Appendix 2: Reflections on the Constant and the Changing Appendix 3: Oppositions in Kant's Philosophy Appendix 4: The Principle of Microstraightness, Nilpotent Infinitesimals, and the Differential Calculus Further ReadingList of OppositionsList of ParadoxesIndex

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