Zeno’s Paradoxes of Motion



Because of their extreme subtlety and profundity, there is little of value that can be said in a short space about Zeno’s four paradoxes of motion.1 Accordingly, this introduction will be limited to brief comments upon the selections and will end by considering the relevance that the problems they discuss have to the main question of the previous sections—the objectivity of temporal becoming.


Infinite Number Finite Time Temporal Order Infinite Sequence Physical Time 
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  1. For a discussion of the historical Zeno and the subsequent treatments of his paradoxes see: F. Cajori, “The History of Zeno’s Arguments on Motion,” American Mathematical Monthly, 23 (1915)Google Scholar
  2. Cajori, “The Purpose of Zeno’s Arguments on Motion,” Isis, 3 (1920-1921)Google Scholar
  3. Zeno of Elea, text, with tr. and notes by H. D. P. Lee, Cambridge University Press, Cambridge, 1936Google Scholar
  4. C. B. Boyer, The Concepts of the Calculus, Hafner, New York, 1949Google Scholar
  5. G. Vlastos, “Zeno’s Race Course,” Journal of the History of Philosophy, 4 (1966)Google Scholar
  6. Vlastos, “Zeno,” in The Encyclopedia of Philosophy, P. Edwards, ed., Collier, New York, 1967Google Scholar
  7. W. C. Salmon’s Introduction to Zeno’s Paradoxes, Salmon, ed., Bobbs-Merrill, New York, 1967.Google Scholar
  8. What I have termed the “Metaphysical Replies” to Zeno are in: H. Bergson, Time and Free Will, tr. by R. L. Pogson, George Allen & Unwin, London, 1910Google Scholar
  9. Bergson, An Introduction to Metaphysics, tr. by T. E. Hulme, G. P. Putnam’s Sons, New York, 1912Google Scholar
  10. W. James, Some Problems of Philosophy, Longmans, Green, London, 1911Google Scholar
  11. A. N. Whitehead, Process and Reality, Macmillan, New York, 1929Google Scholar
  12. A. Edel, “Aristotle’s Theory of the Infinite,” New York, 1934, not publ.Google Scholar
  13. J. O. Wisdom, “Why Achilles Does Not Fail to Catch the Tortoise,” M, 50 (1941)Google Scholar
  14. A. P. Ushenko, “Zeno’s Paradoxes,” M, 55 (1946)Google Scholar
  15. H. R. King, “Aristotle and the Paradoxes of Zeno,” JP, 46 (1949). Criticisms of these various metaphysical replies are in: A. O. Lovejoy, “The Problem of Time in Modern French Philosophy,” PR, 21 (1912)Google Scholar
  16. R. M. Blake, “The Paradoxes of Temporal Process,” JP, 23 (1926)Google Scholar
  17. G. Santayana, Winds of Doctrine, Charles Scribner’s Sons, New York, 1926Google Scholar
  18. B. Russell, A History of Western Philosophy, Simon & Schuster, New York, 1945, chapter on “Bergson”Google Scholar
  19. A. Grünbaum, “Relativity and the Atomicity of Becoming,” Review of Metaphysics, 4 (1950).Google Scholar
  20. The problem of completing an infinite number of tasks, which is central to the Thomson article, is discussed by the following authors: Weyl, Philosophy of Mathematics and Natural Science, cited earlier in fullGoogle Scholar
  21. H. B. Smith, “Mr. Blake and the Paradox of Zeno,” JP, 34 (1923)Google Scholar
  22. Max Black, “Achilles and the Tortoise,” A, 11 (1951), reprinted with new comments and other articles on Zeno in Problems of Analysis, Cornell University Press, Ithaca, N.Y., 1954Google Scholar
  23. R. Taylor, “Mr. Black on Temporal Paradoxes,” A, 12 (1951)Google Scholar
  24. J. O. Wisdom, “Achilles on a Physical Race Course,” A, 13 (1952)Google Scholar
  25. Taylor, “Mr. Wisdom on Temporal Paradoxes,” A, 13 (1952)Google Scholar
  26. L. E. Thomas, “Achilles and the Tortoise,” A, 13 (1952)Google Scholar
  27. A. Grünbaum, “Messrs. Black and Taylor on Temporal Paradoxes,” A, 13 (1952)Google Scholar
  28. J. Watling, “The Sum of an Infinite Series,” A, 13 (1952)Google Scholar
  29. J. M. Hinton and C. B. Martin, “Achilles and the Tortoise,” A, 14 (1954)Google Scholar
  30. G. Ryle, “Achilles and the Tortoise,” in Dilemmas, cited earlier in fullGoogle Scholar
  31. D. S. Shwayder, “Achilles Unbound,” JP, 52 (1955)Google Scholar
  32. G. E. L. Owen, “Zeno and the Mathematicians,” PAS, 58 (1957-1958)Google Scholar
  33. Whitrow, The Natural Philosophy of Time, cited earlier in fullGoogle Scholar
  34. P. Benacerraf, “Tasks, Super-tasks, and the Modern Eleatics,” JP, 59 (1962)Google Scholar
  35. E. TeHennepe, “Language Reform and Philosophical Imperialism: Another Round with Zeno,” A, 23 (1963)Google Scholar
  36. C. S. Chihara, “On the Possibility of Completing an Infinite Process,” PR, 74 (1965)Google Scholar
  37. and Vlastos, “Zeno’s Race Course,” cited earlier in full.Google Scholar
  38. For a discussion of the mathematical continuum and its relevance to Zeno’s paradoxes see: B. Russell, The Principles of Mathematics, cited earlier in fullGoogle Scholar
  39. Russell, Our Knowledge of the External World, Open Court, Chicago, 1914.Google Scholar

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© Richard M. Gale 1968

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