Abstract Chaitin’s theorem and its methodological consequences
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09.04.2013
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Abstract forms of Kolmogoroff’s complexity, Chaitin and G_del’s theorems are stated. They are used to analyze numerous methodological issues: Kant’s Third antinomy, Parkinson’s law of committee, cooperative creative activity, multilanguage programming, benevolence to other’s views, dilemma of deism–atheism.
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Непейвода Н. Abstract Chaitin’s theorem and its methodological consequences // Логические исследования / Logical Investigations. 2013. Т. 19. C. 166-183.
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Литература
Chaitin, G.J., Information-theoretic limitations of formal systems, J. of the ACM 21:403–424.
Kleene, S.C., Introduction to metamathematics, Princeton, NJ: Van Nostrand, 1964.
Chaitin, G., Meta Math!: The Quest for Omega, Pantheon Books, 2005.
Chaitin, G., Mathematics, Complexity and Philosophy, Editorial Midas, 2011.
Chaitin, G., Randomness in arithmetics, Scientific American 9:56–68, 1988.
Kritchman, S. and R. Raz, The Surprise Examination Paradox and the Second Incompleteness Theorem, Notices of the American Mathematical Society, 57(11):1454—1458, 2010.
Raatikainen, P., On interpreting Chaitin’s incompleteness theorem, Journal of Philosophical Logic 27:569–586, 1998.
Kant, I., The Critique of Pure Reason. http://www.gutenberg.org/ebooks/4280
Aschbacher, M., The status of the classification of the finite simple groups, Notices of the American Mathematical Society 51:736–740, 2004.
Kleene, S.C., Introduction to metamathematics, Princeton, NJ: Van Nostrand, 1964.
Chaitin, G., Meta Math!: The Quest for Omega, Pantheon Books, 2005.
Chaitin, G., Mathematics, Complexity and Philosophy, Editorial Midas, 2011.
Chaitin, G., Randomness in arithmetics, Scientific American 9:56–68, 1988.
Kritchman, S. and R. Raz, The Surprise Examination Paradox and the Second Incompleteness Theorem, Notices of the American Mathematical Society, 57(11):1454—1458, 2010.
Raatikainen, P., On interpreting Chaitin’s incompleteness theorem, Journal of Philosophical Logic 27:569–586, 1998.
Kant, I., The Critique of Pure Reason. http://www.gutenberg.org/ebooks/4280
Aschbacher, M., The status of the classification of the finite simple groups, Notices of the American Mathematical Society 51:736–740, 2004.