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Gödel's Theorem and Information
, 1982
"... 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 tr ..."
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Cited by 53 (6 self)
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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.
Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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Cited by 45 (7 self)
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
Fisher’s Instrumental Approach to Index Numbers. Supplement to the History of Political Economy
"... ‘If contradictory attributes be assigned to a concept, I say, that mathematically the concept does not exist. ’ (Hilbert 1902, 448) ‘Sometimes control with a single lens is impossible since some incompatible features are required and a compromise becomes necessary calling for further judgement on th ..."
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Cited by 2 (0 self)
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‘If contradictory attributes be assigned to a concept, I say, that mathematically the concept does not exist. ’ (Hilbert 1902, 448) ‘Sometimes control with a single lens is impossible since some incompatible features are required and a compromise becomes necessary calling for further judgement on the part of the designer as to which error should be reduced and to what degree. ’ (Bracey 1960, 18) 1.
the journals Mathematical Inequalities and Applications and Journal of Mathematical Inequalities centered on a
"... their book on inequalities [4] “To G. H. Hardy, ..."