The Foundations of Solomonoff Prediction
Summary
R.J. Solomonoff's theory of Prediction assembles notions from information theory, confirmation theory and computability theory into the specification of a supposedly all-encompassing objective method of prediction. The theory has been the subject of both general neglect and occasional passionate promotion, but of very little serious philosophical reflection. This thesis presents an attempt towards a more balanced philosophical appraisal of Solomonoff's theory.
Following an in-depth treatment of the mathematical framework and its motivation, I shift attention to the proper interpretation of these formal results. A discussion of the theory's possible aims turns into the project of identifying its core principles, and a defence of the primacy of the unifying principle of Universality supports the development of my proposed interpretation of Solomonoff Prediction as the statement, to be read in the context of the philosophical problem of prediction, that in a universal setting, there exist universal predictors.
The universality of the setting is grounded in the central assumption of computability: while this assumption is not uncontroversial as a constraint on the world, I argue that it is hardly a constraint at all if we restrict attention to all possible competing prediction methods. This is supported by a new, more refined convergence result.