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  1. Randomness by Design.William A. Dembski - 1991 - Noûs 25 (1):75-106.
    “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.”1 John von Neumann’s famous dictum points an accusing finger at all who set their ordered minds to engender disorder. Much as in times past thieves, pimps, and actors carried on their profession with an uneasy conscience, so in this day scientists who devise random number generators suffer pangs of guilt. George Marsaglia, perhaps the preeminent worker in the field, quips when he asks his (...)
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  • On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of (...)
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  • Algorithmic Information Theory and Undecidability.Panu Raatikainen - 2000 - Synthese 123 (2):217-225.
    Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.
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  • On Explicating the Concept the Power of an Arithmetical Theory.Jörgen Sjögren - 2008 - Journal of Philosophical Logic 37 (2):183 - 202.
    In this paper I discuss possible ways of measuring the power of arithmetical theories, and the possiblity of making an explication in Carnap's sense of this concept. Chaitin formulates several suggestions how to construct measures, and these suggestions are reviewed together with some new and old critical arguments. I also briefly review a measure I have designed together with some shortcomings of this measure. The conclusion of the paper is that it is not possible to formulate an explication of the (...)
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  • Incompleteness, Complexity, Randomness and Beyond.Cristian S. Calude - 2002 - Minds and Machines 12 (4):503-517.
    Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.
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  • Exploring Randomness.Panu Raatikainen - 2001 - Notices of the AMS 48 (9):992-6.
    Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.
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  • The Source of Chaitin's Incorrectness.Don Fallis - 1996 - Philosophia Mathematica 4 (3):261-269.
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  • Kolmogorov Complexity and Characteristic Constants of Formal Theories of Arithmetic.Shingo Ibuka, Makoto Kikuchi & Hirotaka Kikyo - 2011 - Mathematical Logic Quarterly 57 (5):470-473.
    We investigate two constants cT and rT, introduced by Chaitin and Raatikainen respectively, defined for each recursively axiomatizable consistent theory T and universal Turing machine used to determine Kolmogorov complexity. Raatikainen argued that cT does not represent the complexity of T and found that for two theories S and T, one can always find a universal Turing machine such that equation image. We prove the following are equivalent: equation image for some universal Turing machine, equation image for some universal Turing (...)
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  • Models and the Dynamics of Theory-Building in Physics. Part I—Modeling Strategies.Gérard G. Emch - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):558-585.
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  • Models and the Dynamics of Theory-Building in Physics. Part I—Modeling Strategies.Gérard G. Emch - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):558-585.
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