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Philosophical Applications of Kolmogorov's Complexity Measure

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  • Itzhak Gilboa

Abstract

Kolmogorov has defined the complexity of a sequence of bits to be the minimal size of (the description of) a Turing machine which can regenerate the given sequence. This paper contains two notes on possible applications of this complexity notion to philosophy in general and the philosophy of science in particular. The first presents simplicism--a theory prescribing that people would tend to choose the simplest theory to explain observations, where "simple" is defined by (a version of) Kolmogorov's measure. The second suggests a reinterpretation of a simple observation, saying that reality is almost surely too complex to understand, terms such as "good" and "evil" almost surely too complex to define, and so forth.

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  • Itzhak Gilboa, 1990. "Philosophical Applications of Kolmogorov's Complexity Measure," Discussion Papers 923, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:923
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    Cited by:

    1. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2012. "Fact-Free Learning," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 8, pages 185-210, World Scientific Publishing Co. Pte. Ltd..
    2. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Knowledge and Planning," Discussion Papers 1127, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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