Opposition and Paradoxes: Philosophical Perplexities in Science and Mathematics

ISBN-13: 9781554813025 / Angielski / Miękka / 2016 / 216 str.

John Bell

Opis

In Oppositions and Paradoxes, John L. Bell uses conceptual puzzles and paradoxes as a window into fundamental concepts of mathematics and physics.

Spis treści

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
Schrödinger’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