A Philosophical Treatise of Universal Induction

Por • 30 sep, 2011 • Sección: Filosofía

Samuel Rathmanner and Marcus Hutter

Research School of Computer Science, Australian National University, Corner of North and Daley Road, Canberra ACT 0200, Australia

* Author to whom correspondence should be addressed.

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)

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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.

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

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