Into the Stratosphere

  • Calvin C. Clawson


We have discussed many ideas in mathematics, and particularly ideas that have not yet been rigorously proven by mathematicians. For example, we don’t know if an infinity of twin primes exist, if either the Goldbach Conjecture or Riemann hypothesis is true. Many of us believe that given enough time and work, all these questions can be answered. Yet, is that the case? Given a statement in mathematics, can we say it is always possible to either prove or disprove it?


Transformation Rule Logical Rule Riemann Hypothesis Symbolic Statement Vienna Circle 
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End Notes

  1. 1.
    John Locke, An Essay Concerning Human Understanding (CD: DeskTop BookShop) (Indianapolis: WeMake CDs, Inc., 1994).Google Scholar
  2. 2.
    J.M. Dubbey, Development of Modern Mathematics (New York: Crane, Russak & Company, 1970), p. 112.MATHGoogle Scholar
  3. 3.
    Rudy Rucker, Infinity and the Mind (New York: Bantam Books, 1982), p. 177.MATHGoogle Scholar
  4. 4.
    James R. Newman, “The Foundations of Mathematics,” in The World of Mathematics (New York: Simon and Schuster, 1956), p. 1616.Google Scholar
  5. 5.
    Dubbey, Development of Modern Mathematics, p. 113.Google Scholar
  6. 6.
    Rucker, Infinity and the Mind, p. 169.Google Scholar
  7. 7.
    Ernest Nagel and James R. Newman, Gödel’s Proof (New York: New York University Press, 1958), p. 3.MATHGoogle Scholar
  8. 8.
    Most of the following terminology and examples are taken from the Nagel and Newman book, Gödel’s Proof. Google Scholar
  9. 9.
    Ibid, p. 68.Google Scholar
  10. 10.
    Ian Stewart, The Problems of Mathematics (New York: Oxford University Press, 1987), p. 218.MATHGoogle Scholar
  11. 11.
    John D. Barrow, Pi in the Sky (New York: Little, Brown and Company, 1992), p. 122.MATHGoogle Scholar
  12. 12.
    Rucker, Infinity and the Mind, p. 176.Google Scholar
  13. 13.
    Barrow, Pi in the Sky, p. 117.Google Scholar
  14. 14.
    Ibid, p. 123.Google Scholar
  15. 15.
    Rucker, Infinity and the Mind, p. 181.Google Scholar
  16. 16.
    Barrow, Pi in the Sky, p. 261.Google Scholar
  17. 17.
    Douglas R. Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern (New York: Basic Books, Inc., 1985).Google Scholar
  18. 18.
    Kathleen Freemen, Ancilla to The Pre-Socratic Philosophers (Cambridge, MA: Harvard University Press, 1966), p. 9.Google Scholar
  19. 19.
    Hofstadter, Metamagical Themas, pp. 11–13.Google Scholar
  20. 20.
    Ibid, p. 14.Google Scholar
  21. 21.
    Nagel and Newman, Gödel’s Proof, p. 97.Google Scholar
  22. 22.
    Thomas Paine, Age of Reason (CD: DeskTop BookShop) (Indianapolis: WeMake CDs, Inc., 1994).Google Scholar

Copyright information

© Calvin C. Clawson 1996

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  • Calvin C. Clawson

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