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Opposition and Paradoxes

Philosophical Perplexities in Science and Mathematics

John L. Bell (author)

ISBN: 9781554813025

Publication Date: Apr 2016

Format: Paperback

Explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, John L. 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.

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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.


"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

Illustrations 20 illustrations
Pages 216
Dimensions 229 x 152 x 10
Date Published 30 Apr 2016
Publisher Broadview Press
Subject/s Philosophy of science   Philosophy: metaphysics & ontology   Philosophy of mathematics  

What Is This Book About?

Chapter I: The Continuous and the Discrete

Continuity and Discreteness
The Pythagorean School and Incommensurable Magnitudes
The Stoics and the Continuum Theory of Matter
Zeno's Paradoxes
Contemporary Versions of Zeno's Paradoxes: Supertasks

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
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

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

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