  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.
