|
Vol: 51(65) No: 4 / December 2006 Information Machine and the Gödelian Case Marius Crisan Department of Computers and Software Engineering, “Politehnica” University of Timisoara, 300223 Timisoara, Romania, phone: (+40) 256-403254, e-mail: crisan@cs.upt.ro, web: http://www.cs.utt.ro/~crisan Keywords: information machine, Gödel’s incompleteness theorem, provability, artificial intelligence, cognitive modeling. Abstract The paper discusses the concept of information machine applied to the Gödelian case. The information machine based model of truth recognition process can account for the non-computability characteristic of human decision upon mathematical truth. An analysis of the meaning of Gödel\'s theorem implications is made, revealing the importance of differentiating between the truth and provability predicates. References [1] E. T. Jaynes. “The Evolution of Carnot\'s Principle,” in Maximum-Entropy and Bayesian Methods in Science and Engineering, Vol. 1, G. J. Erickson and C. R. Smith (eds.), Kluwer, Dordrecht, 1988, pp. 267-282. [2] M. Crisan. “Establishing The Information Machine Concept,” Scientific Bulletin of “Politehnica” University of Timisoara, Transactions on Automatic Control and Computer Science Vol.50 (64), 2005, pp. 55-61. [3] C. Adami and N. J. Cerf. “Complexity, computation, and measurement,” in T. Toffoli, M. Biafore, and J. Leao (ed.), PhysComp96, New England Complex Systems Institute (1996), 7-11. [4] J. Machta. “Entropy, Information, and Computation,” Am. J. Phys. 67 (12), December 1999, pp. 1074-1077. [5] J.R. Lucas. “The Implications of Gödel\'s Theorem,” Talk given to the Sigma Club on February 26th, 1998. (http://users.ox.ac.uk/~jrlucas) [6] K. Gödel. “Collected Works,” III, ed. Feferman, Oxford, 1995, p. 310. [7] A. Tarski. \"The Concept of Truth in Formalized Languages\" in Corcoran, J., ed., Logic, Semantics and Metamathematics. Indianapolis: Hackett, 1983. The English translation of Tarski\'s 1936 Der Wahrheitsbegriff in den formalisierten Sprachen. [8] G.J. Chaitin. “Randomness and Gödel’s Theorem,” Mondes en Développement, No. 54-55, 1986, pp. 125-128. [9] G.J. Chaitin. “The Berry Paradox,” Complexity 1:1, 1995, pp. 26-30. [10] E. Nagel and J.R. Newman. \"Gödel\'s Proof,\" New York University Press, N.Y. 1958. [11] J.R. Lucas. “Minds, Machines and Gödel,” Philosophy, XXXVI, 1961, pp. 112-127. [12] A. Turing. \"Computing Machinery and Intelligence\'\'. First published in Mind, 49, 1950, reprinted in Alan Ross Anderson, Minds and Machines, Englewood Cliffs, N.J., 1964, pp.4-30. [13] D.R. Hofstadter. “A conversation with Eistein’s brain.” In The Mind’s I (ed. D.R. Hofstadter and D.C. Dennet), Basic Books, Inc., Penguin Books, Ltd., Harmondsworth, Middx., 1981. [14] G.L. Bowie. “Lucas’ number is finally up.” J. of Philosophical Logic, 11, 1982, pp. 279-285. [15] R. Penrose. “The Emperor\'s New Mind-Concerning Computers, Minds and The Laws of Physics,” Oxford University Press, 1989. [16] R. Penrose. \"Shadows of the Mind,\" Oxford University Press, 1994. [17] D. McCullough. \"Can Humans Escape Gödel?\" Psyche: an interdisciplinary journal of research on consciousness, 2(1), Jan., 1995. [18] D.J. Chalmers. \"Minds, Machines, and Mathematics,\" Psyche: an interdisciplinary journal of research on consciousness, 2(9), June, 1995. [19] S. Bringsjord and H. Xiao. “A Refutation of Penrose’s New Gödelian Case Against the Computational Conception of Mind,” 1997. |