The berry paradox

  • G. J. Chaitin
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 461-461)


Positive Integer Liar Paradox Universal Turing Machine Algorithmic Information Theory Usual Axiom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. -G. J. Chaitin, Information, Randomness & Incompleteness, second edition, World Scientific, 1990. Errata: on page 26, line 25, “quickly that” should read “quickly than”; on page 31, line 19, “Here one” should read “Here once”; on page 55, line 17, “RI, p. 35” should read “RI, 1962, p. 35”; on page 85, line 14, “1. The problem” should read “1. The Problem”; on page 88, line 13, “4. What is life?” should read “4. What is Life?”; on page 108, line 13, “the table in” should read “in the table in”; on page 117, Theorem 2.3(q), “H c (s,t)” should read “H c(s/t)”; on page 134, line 7, “#{n H(n)≤n}≤2 n“ should read “#{k H (k)≤n}≤2 n”; on page 274, bottom line, “n 4p+4” should read “n 4p′+4”.Google Scholar
  2. -G. J. Chaitin, Algorithmic Information Theory, fourth printing, Cambridge University Press, 1992. Erratum: on page 111, Theorem Io(q), “H c(s,t)” should read “H c (s/t)”.Google Scholar
  3. -G. J. Chaitin, Information-Theoretic Incompleteness, World Scientific, 1992. Errata: on page 67, line 25, “are there are” should read “are there”; on page 71, line 17, “that case that” should read “the case that”; on page 75, line 25, “the the” should read “the”; on page 75, line 31, “−log2 p−log2 q” should read “−plog2 p−qlog2 q”; on page 95, line 22, “This value of” should read “The value of”; on page 98, line 34, “they way they” should read “the way they”; on page 99, line 16, “exactly same” should read “exactly the same”; on page 124, line 10, “are there are” should read “are there”.Google Scholar

Recent Papers

  1. -G. J. Chaitin, “On the number of n-bit strings with maximum complexity,” Applied Mathematics and Computation 59 (1993), pp. 97–100.zbMATHCrossRefMathSciNetGoogle Scholar
  2. -G. J. Chaitin, “Randomness in arithmetic and the decline and fall of reductionism in pure mathematics,” chao-dyn/9304002, Bulletin of the European Association for Theoretical Computer Science No. 50 (June 1993), pp 314–328.zbMATHGoogle Scholar
  3. -G. J. Chaitin, “The limits of mathematics—Course outline & software,” chao-dyn/9312006 IBM Research Report RC-19324, 127 pp., December 1993.Google Scholar
  4. -G. J. Chaitin, “Randomness and complexity in pure mathematics,” International Journal of Bifurcation and Chaos 4 (1994), pp. 3–15.zbMATHCrossRefMathSciNetGoogle Scholar
  5. -G. J. Chaitin, “Responses to ‘Theoretical Mathematics...',” Bulletin of the American Mathematical Society 30 (1994), pp. 181–182.Google Scholar
  6. -G. J. Chaitin, “The Limits of Mathematics,” chao-dyn/9407003 IBM Research Report RC-19646, July 1994, 270 pp.Google Scholar
  7. -G. J. Chaitin, “The Limits of Mathematics IV”, chao-dyn/9407009, IBM Research Report RC-19671, July 1994, 231 pp.Google Scholar
  8. -G. J. Chaitin, “The Limits of Mathematics (Extended Abstract),” chaodyn/9407010, IBM Research Report RC-19672, July 1994, 7 pp.Google Scholar

See Also

  1. -M. Davis, “What is a computation?,” in L.A. Steen, Mathematics Today, Springer-Verlag, 1978.Google Scholar
  2. -R. Rucker, Infinity and the Mind, Birkhäuser, 1982.Google Scholar
  3. -T. Tymoczko, New Directions in the Philosophy of Mathematics, Birkhäuser, 1986.Google Scholar
  4. -R. Rucker, Mind Tools, Houghton Mifflin, 1987.Google Scholar
  5. -H. R. Pagels, The Dreams of Reason, Simon & Schuster, 1988.Google Scholar
  6. -D. Berlinski, Black Mischief, Harcourt Brace Jovanovich, 1988.Google Scholar
  7. -R. Herken, The Universal Turing Machine, Oxford University Press, 1988.Google Scholar
  8. -I. Stewart, Game, Set & Math, Blackwell, 1989.Google Scholar
  9. -G. S. Boolos and R. C. Jeffrey, Computability and Logic, third edition, Cambridge University Press, 1989.Google Scholar
  10. -J. Ford, “What is chaos?,” in P. Davies, The New Physics, Cambridge University Press, 1989.Google Scholar
  11. -J. L. Casti, Paradigms Lost, Morrow, 1989.Google Scholar
  12. -G. Nicolis and I. Prigogine, Exploring Complexity, Freeman, 1989.Google Scholar
  13. -B.-O. Küppers, Information and the Origin of Life, MIT Press, 1990.Google Scholar
  14. -J. L. Casti, Searching for Certainty, Morrow, 1991.Google Scholar
  15. -J. A. Paulos, Beyond Numeracy, Knopf, 1991.Google Scholar
  16. -L. Brisson and F. W. Meyerstein, Inventer L'Univers, Les Belles Lettres, 1991. (English edition in press)Google Scholar
  17. -J. D. Barrow, Theories of Everything, Oxford University Press, 1991.Google Scholar
  18. -D. Ruelle, Chance and Chaos, Princeton University Press, 1991.Google Scholar
  19. -T. Nørretranders, Mærk Verden, Gyldendal, 1991.Google Scholar
  20. -M. Gardner, Fractal Musci, Hypercards and More, Freeman, 1992.Google Scholar
  21. -P. Davies, The Mind of God, Simon & Schuster, 1992.Google Scholar
  22. -J. D. Barrow, Pi in the Sky, Oxford University Press, 1992.Google Scholar
  23. -N. Hall, The New Scientist Guide to Chaos, Penguin, 1992.Google Scholar
  24. -H.-C. Reichel and E. Prat de la Riba, Naturwissenschaft und Weltbild, Hölder-Pichler-Tempsky, 1992.Google Scholar
  25. -I. Stewart, The Problems of Mathematics, Oxford University Press, 1992.Google Scholar
  26. -A. K. Dewdney, The New Turing Omnibus, Freeman, 1993.Google Scholar
  27. -A. B. Çambel, Applied Chaos Theory, Academic Press, 1993.Google Scholar
  28. -K. Svozil, Randomness & Undecidability in Physics, World Scientific, 1993.Google Scholar
  29. -J. L. Casti, Complexification, HarperCollins, 1994.Google Scholar
  30. -M. Gell-Mann, The Quark and the Jaguar, Freeman, 1994.Google Scholar
  31. -T. Nørretranders, Verden Vokser, Aschehdoug, 1994.Google Scholar
  32. -S. Wolfram, Cellular Automata and Complexity, Addison-Wesley, 1994.Google Scholar
  33. -C. Calude, Information and Randomness, Springer-Verlag, 1994.Google Scholar
  34. -J. L. Casti and A. Karlqvist, Cooperation and Conflict in General Evolutionary Processes, Wiley, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • G. J. Chaitin
    • 1
  1. 1.IBM Research DivisionYorktown HeightsUSA

Personalised recommendations