Opposition and paradoxes : philosophical perplexities in science and mathematics
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Bibliographic Information
Opposition and paradoxes : philosophical perplexities in science and mathematics
Broadview Press, c2016
- : pbk
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Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
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
by "Nielsen BookData"