Research Catalog

Title

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

Author

Bell, J. L. (John Lane)

Publication

• Peterborough, Ontario : Broadview Press, [2016]
• Tonawanda, NY : Broadview Press, [2016]
• ©2016

Items in the Library & Off-site

Details

Description

xiv, 195 pages : illustrations; 23 cm

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."--

Subject

• Paradoxes
• Opposition, Theory of
• Science > Philosophy
• Mathematics > Philosophy

Bibliography (note)

• Includes bibliographical references and index.

Contents

Acknowledgements -- What is this book about? 1 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. 2 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. 3 The strange universe of non-Euclidean geometry : Hyperbolic geometry -- Riemannian geometry. 4 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. 5 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. 6 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. 7 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.

Call Number

JFE 16-9527

ISBN

• 9781554813025
• 1554813026

OCLC

932169588

Author

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

Title

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

Publisher

Peterborough, Ontario : Broadview Press, [2016]

Distributor

Tonawanda, NY : Broadview Press, [2016]

Copyright Date

©2016

Type of Content

text

Type of Medium

unmediated

Type of Carrier

volume

Bibliography

Includes bibliographical references and index.

Research Call Number

JFE 16-9527