Oppositions and Paradoxes
Philosophical Perplexities in Science and Mathematics
  • Publication Date: April 18, 2016
  • ISBN: 9781554813025 / 1554813026
  • 216 pages; 6" x 9"

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Oppositions and Paradoxes

Philosophical Perplexities in Science and Mathematics

  • Publication Date: April 18, 2016
  • ISBN: 9781554813025 / 1554813026
  • 216 pages; 6" x 9"

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, but 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 — he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or think of an office mailbox labelled “mail for those with no mailbox”—if this is a person’s mailbox, how can they possibly have “no mailbox”? These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts.

For an excerpt from Oppositions and Paradoxes, please see our blog post: The Paradox of the Heap, from John L. Bell’s Oppositions and Paradoxes.

Comments

“Who else but John Bell could write a book like this one? One of the leading logicians of our day, Bell uses the role of conceptual oppositions and the paradoxes to which they occasionally give rise to take readers on a whirlwind tour through great swaths of the history of human thought. The sophisticated discussion of deep and difficult topics is highly digestible thanks to Bell wearing his expertise lightly and presenting things with dollops of his clever—and sometimes silly—humour.” — David DeVidi, University of Waterloo

“Bell is a master of simplicity and clarity, while sacrificing nothing of accuracy and erudition. His enthusiasm for his subject is palpable and infectious. Oppositions and Paradoxes is a pleasure to read.” — Graham Priest, CUNY Graduate Center

“John L. Bell is the true philosophical heir of Bertrand Russell, and his new book, Oppositions and Paradoxes, exemplifies all the best traits in Russell’s legacy. His presentation of philosophical paradoxes and perplexities in logic, mathematics, and physics is a model of lucidity and economy, and his analysis of these problems is secure and sane. Oppositions and Paradoxes is readily accessible and a sure path into some of philosophy’s greatest themes.” — Bradley Bassler, University of Georgia

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 Reading
List of Oppositions
List of Paradoxes
Index

John L. Bell is Professor of Philosophy at Western University and a Fellow of the Royal Society of Canada.