Atomism and Infinite Divisibility

Chapter 4

Notes and References

  1. John Burnet, Greek Philosophy: Thales to Plato, (London: Macmillan, 1914; reprint, New York: St Martin's Press 1968), p. 69. text
  2. David J. Furley, Two Studies in the Greek Atomists, (Princeton: Princeton University Press, 1967), p. 57. text
  3. Burnet, p. 76. text
  4. David Gallop, Parmenides of Elea, (Toronto: University of Toronto Press, 1984), p. 8. text
  5. Burnet, p. 77. text
  6. Cyril Bailey, The Greek Atomists and Epicurus, (New York: Russell & Russell, 1964), pp. 118-9. text
  7. Gordon H. Clark, Thales to Dewey: A History of Philosophy, (Boston: The Riverside Press, 1957), p. 35. text
  8. C. J. F. Williams, Aristotle's De Generatione Et Corruptione, (Oxford: Clarendon Press, 1982). text
  9. W. D. Ross, Aristotle's Physics, (Oxford: Clarendon Press, 1960). text
  10. J. L. Ackrill, Aristotle's Categories and De Interpretatione, (Oxford: Clarendon Press, 1963). text
  11. Ackrill qualifies his use of 'quantity' in the translation. "Quantity: The Greek is a word that serves both as an interrogative and as an indefinite adjective (Latin quantum).", p. 77. text
  12. Aristotle, "Metaphysics", trans. W. D. Ross, in The Basic Works of Aristotle, ed. Richard McKeon (New York: Random House, 1941). text
  13. It is generally believed today that the universe is "finite and unbounded" with its closure remaining an open question. According to Heinz R. Pagels, Perfect Symmetry: The Search for the Beginning of Time, (New York: Bantam Books, 1986), p. 146, text
  14. Today most scientists maintain that the universe evolved from a hot, dense gas of quantum particles which subsequently expanded rapidly -- an explosion called the "hot big bang".
  15. If the universe is "closed", the expansion will eventually stop and reverse -- yielding a finite universe. If the universe is "open", the expansion will continue, as Aristotle would say, without being gone through. The resulting universe will be finite at any moment in time, although it continues to expand. It would be at most "potentially" infinite. text

  16. Ross, p. 542. text
  17. Georg Cantor, Contribution to the founding of the Theory of Transfinite Numbers, trans. Philip E. B. Jourdain, (n.p., England: Open Court Publishing Company, 1915; reprint ed., New York: Dover Publications, 1955). text
  18. Williams, pp. 69-70. text
  19. 17. Harold H. Joachim, Aristotle on Coming-to-be & Passing-away, (Oxford, England: The Clarendon Press, 1922), p. 79. text
  20. Ackrill, p. 91. text
  21. Jonathan Lear, "Aristotelian Infinity", Proceedings of the Aristotelian Society 80, (1979/80): 199-200. text
  22. Williams, p. 74. text
  23. David Bostock, "Aristotle, Zeno and the Potentially Infinite", Proceedings of the Aristotelian Society 73, (1972-3): 37-51. text
  24. Bostock, p. 46. text
  25. Elliott Mendelson, Introduction to Mathematical Logic 2nd. ed., (New York: D. Van Norstrand, 1979): p. 9. text