Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2012 | 1(3/4) | 43--58
Tytuł artykułu

Abstract Incompleteness Theorems and Their Influence in Methodology

Treść / Zawartość
Warianty tytułu
Języki publikacji
Kolmogoroff's complexity, Chaitin and Gödel's incompleteness theorems are considered commonly relatively to a fixed coding of objects and to a standard notion of algorithms. In essence all they are independent from almost all properties of concrete theories, algorithms and codings. So stable and general results are to have deep methodological, philosophical and even theological consequences. Here we consider their abstract form and speculations which can be derived from them and partially from modern computer science, IT practice and physics. Main ones are the following: A new proof of Kant's Third antinomy and of Parkinson's Law of committee, relations to cooperative creative activity, multi-language programming, benevolence to other's views, dilemma of deismatheism, and finally methodological approach to theology.(original abstract)
Opis fizyczny
  • Institute of Program Systems RAS Pereslavl-Zalessky, Russia
  • 1. Nepejvoda N. N. Chaitin's theorem as a source of methodological consequences. 2012 ISBN978-5-288-05315-3, pp. 212-222.
  • 2. Nepejvoda N. N. Abstract variants of Godel and Chaitin theorems. Will be published in DAN RAS, 2012.
  • 3. Chaitin, G. J. Information-theoretic limitations of formal systems, J. of the ACM 21, pp. 403-424.
  • 4. Kleene S. C. Introduction to metamathematics. Amazon, 2009, ISBN: 978-0923891572.
  • 5. G. Chaitin. Meta Math!: The Quest for Omega. Pantheon Books, 2005.
  • 6. G. Chaitin. Mathematics, Complexity and Philosophy, Editorial Midas, 2011.
  • 7. G. Chaitin. Randomness in arithmetics. Scientific American, 1988, No 9, pp. 56-68.
  • 8. Shira Kritchman and Ran Raz. The Surprise Examination Paradox and the Second Incompleteness Theorem, Notices of the AMS 57, N11 (2011).
  • 9. PANU RAATIKAINEN. ON INTERPRETING CHAITIN'S INCOMPLETENESS THEOREM. Journal of Philosophical Logic 27: 569-586, 1998.
  • 10. I. Kant. The Critique of Pure Reason.
  • 11. A. A. Poзoв. Дeпopтация (Koнфeдepация мeганeзия -1)
  • 12. M. Aschbacher, The status of the classification of the finite simple groups, Notices Amer. Math. Soc. 51 (2004), pp. 736-740.
  • 13. Calvino, Italo. Cosmicomics (trans. William Weaver). London: Picador, 1993.
  • 14. G. Chaitin. The Search for the Perfect Language. Dicta & Contradicta, 2009 (can be accessed by
  • 15. Benedictus de Spinoza. Ethica. _De_Deo.
  • 16. Heпeйвoда H. H. Пpикладная лoгика. Hoвocибиpcк, 2000, 565 c.
  • 17. E.W. Dijkstra Go To Statement Considered Harmful. Communications of the ACM, Vol. 11, No. 3, March 1968, pp. 147-148.
  • 18. R. Penrose The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989, ISBN 0-14-014534-6.
  • 19. Nepejvoda N. N. Уpoки кoнcтpуктивизма (Lessons of constructivism). LAP, Saarbrücken, 2011. ISBN: 978-3-8443-5181-1 78p.
  • 20. Thomas Aquinas. Summa Theologica
  • 21. Nicolas Cusanus. De docta ignorantia.
Typ dokumentu
Identyfikator YADDA

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.