Entropy 2011, 13(6), 1076-1136; doi:10.3390/e13061076

A Philosophical Treatise of Universal Induction

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Received: 20 April 2011; in revised form: 24 May 2011 / Accepted: 27 May 2011 / Published: 3 June 2011
(This article belongs to the Special Issue Kolmogorov Complexity)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.
Keywords: sequence prediction; inductive inference; Bayes rule; Solomonoff prior; Kolmogorov complexity; Occam’s razor; philosophical issues; confirmation theory; black raven paradox
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MDPI and ACS Style

Rathmanner, S.; Hutter, M. A Philosophical Treatise of Universal Induction. Entropy 2011, 13, 1076-1136.

AMA Style

Rathmanner S, Hutter M. A Philosophical Treatise of Universal Induction. Entropy. 2011; 13(6):1076-1136.

Chicago/Turabian Style

Rathmanner, Samuel; Hutter, Marcus. 2011. "A Philosophical Treatise of Universal Induction." Entropy 13, no. 6: 1076-1136.

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