Gödel's theorem and information

Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.

[1]  B. Russell.  Mathematical Logic as Based on the Theory of Types , 1908 .

[2]  G. Hardy,et al.  What is Mathematics? , 1942, Nature.

[3]  Emil L. Post.  Recursively enumerable sets of positive integers and their decision problems , 1944 .

[4]  E. Bell.  Mathematics: Queen and Servant of Science , 1952 .

[5]  Albert Einstein,et al.  Ideas and Opinions , 1954 .

[6]  G. Pólya.  Heuristic Reasoning in the Theory of Numbers , 1959 .

[7]  W. R. Stahl.  Self-Reproducing Automata , 2015, Perspectives in biology and medicine.

[8]  Martin Davis,et al.  The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions , 2004 .

[9]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[10]  G. J. Chaltin,et al.  To a mathematical definition of 'life' , 1970, SIGA.

[11]  M. Levin,et al.  MATHEMATICAL LOGIC FOR COMPUTER SCIENTISTS , 1974 .

[12]  Gregory J. Chaitin,et al.  Information-Theoretic Limitations of Formal Systems , 1974, JACM.

[13]  Gregory J. Chaitin,et al.  Information-theoretic computation complexity , 1974, IEEE Trans. Inf. Theory.

[14]  Gregory J. Chaitin,et al.  Information-Theoretic Computational Complexity , 1974 .

[15]  G. Chaitin.  Randomness and Mathematical Proof , 1975 .

[16]  G. Chaitin.  A Theory of Program Size Formally Identical to Information Theory , 1975, JACM.

[17]  F. Browder.  Mathematical developments arising from Hilbert problems , 1976 .

[18]  J. Schwartz,et al.  A note on monte carlo primality tests and algorithmic information theory , 1978 .

[19]  S. Ulam,et al.  Mathematics and logic , 1979 .

[20]  G. Chaitin,et al.  TOWARD A MATHEMATICAL DEFINITION OF “ LIFE ” , 1979 .

[21]  D. Hofstadter,et al.  Godel, Escher, Bach: An Eternal Golden Braid , 1979 .

[22]  Douglas R. Hofstadter,et al.  Godel, Escher, Bach: An Eternal Golden Braid. , 1980 .

[23]  Edith Schonberg,et al.  Higher level programming : introduction to the use of the set-theoretic programming language SETL , 1981 .

[24]  Stephen Wolfram,et al.  SMP - A Symbolic Manipulation Program , 1981, SYMSAC '81.

[25]  H. Wilf.  The Disk with the College Education. , 1982 .

[26]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[27]  K. Gödel.  Philosophy of mathematics: What is Cantor's continuum problem? , 1984 .