Don't choose theories: Normative inductive reasoning and the status of physical theories

Abstract

Evaluating theories in physics used to be easy. Our theories provided very distinct predictions. Experimental accuracy was so small that worrying about epistemological problems was not necessary. That is no longer the case. The underdeterminacy problem between string theory and the standard model for current possible experimental energies is one example. We need modern inductive methods for this problem, Bayesian methods or the equivalent Solomonoff induction. To illustrate the proper way to work with induction problems I will use the concepts of Solomoff induction to study the status of string theory. Previous attempts have focused on the Bayesian solution. And they run into the question of why string theory is widely accepted with no data backing it. Logically unsupported additions to the Bayesian method were proposed. I will show here that, by studying the problem from the point of view of the Solomonoff induction those additions can be understood much better. They are not ways to update probabilities. Instead, they are considerations about the priors as well as heuristics to attempt to deal with our finite resources. For the general problem, Solomonoff induction also makes it clear that there is no demarcation problem. Every possible idea can be part of a proper scientific theory. It is just the case that data makes some ideas extremely improbable. Theories where that does not happen must not be discarded. Rejecting ideas is just wrong.