Oppositions and paradoxes : philosophical perplexities in science and mathematics / John L. Bell.

Format:

Book

Author/Creator:

Bell, J. L. (John Lane), author.

Language:

English

Subjects (All):

Paradoxes.

Opposition, Theory of.

Science--Philosophy.

Science.

Mathematics--Philosophy.

Mathematics.

Physical Description:

xiv, 195 pages : illustrations ; 23 cm

Distribution:

Tonawanda, NY : Broadview Press, [2016]

Place of Publication:

Peterborough, Ontario : Broadview Press, [2016]

Summary:

"Since antiquity, opposed concepts such as the 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-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous 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 and he would, if he had infinite time, presumably 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 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 paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts."-- Provided by publisher.

Contents:

Chapter I The Continuous and the Discrete 1

Continuity and Discreteness 1

The Pythagorean School and Incommensurable Magnitudes 5

Atomism 8

The Stoics and the Continuum Theory of Matter 9

Zeno's Paradoxes 10

Contemporary Versions of Zeno's Paradoxes: Supertasks 14

Infinitesimals 16

Chapter II Oppositions and Paradoxes in Mathematics: Set Theory and the Infinite 21

Set Theory and the One/Many Opposition 21

Paradoxes of the Infinite 28

Uncountable Infinities 31

Set-Theoretic Antinomies 39

The Axiom of Choice 41

Chapter III The Strange Universe of Non-Euclidean Geometry 45

Hyperbolic Geometry 45

Riemannian Geometry 53

Chapter IV Puzzles and Paradoxes of Time Travel 57

Time Travel into the Past: Branching Timelines 58

Temporal Loops 66

Time Travel into the Future 71

The Future Time Viewer 72

Two-Dimensional Time 75

Temporal Interdicts 77

Time Travel as a Physical Possibility 78

Chapter V Puzzles and Paradoxes of Relativity Theory 81

Special Relativity 81

Spacetime 88

Faster-than-Light Particles in Special Relativity: Tachyons 90

General Relativity: The Principle of Equivalence 92

Black Holes 95

Chapter VI Puzzles and Paradoxes in Quantum Physics 103

Waves vs. Particles 103

Heisenbergs Uncertainty Principle and Bohr's Principle of Complementarity 109

Quantum Tunneling 112

The Riddle of Polarization 113

Schrodinger's Cat Paradox 116

Interpretations of Quantum Theory 118

The EPR Paradox and Nonlocality 122

Chapter VII Cosmic Enigmas 125

The Beginnings of Cosmology 125

Steady-State vs. Big Bang 128

The Problem of the Origin of the Universe 134

Dark Matter, Dark Energy, and Cosmic Acceleration 138

The Argument from Design vs. the Multiverse 139

A Philosophical Coda 144.

Notes:

Includes bibliographical references and index.

ISBN:

9781554813025

1554813026

OCLC:

932169588