Title:
A conception of Bayesianism for open hypothesis systems
Abstract:
Although the long-term objectivity of Bayesian inference from subjective priors is well established in complete hypothesis systems by convergence-to-truth theorems, its validity becomes questionable in open hypothesis systems, where known hypotheses form an incomplete sample space and susceptible to awareness growth. In such systems, Bayesian inference process may lead to “convergence without truth”: in the absence of the true hypothesis, the Bayesian posterior will tend to confirm a false view. Another long-standing challenge for Bayesianism in the open systems is how to assign credence to new hypotheses as the awareness grows. This is recognized as the "accommodation problem" of the "problem of new theory". This project aims to address these problems by developing an "open hypothesis-system Bayesianism". I propose a two-phase mechanism to account for the update of the credence. When no new theory emerges, the credence undergoes an incremental updating phase driven by Bayes' theorem. Here I adopt a dynamical perspective, according to which the posterior credence evolves continuously over time. A radical update phase is incurred when a theory revision takes place. This two-phase scenario indicate a possible underlying connection with Kuhn's theory of scientific paradigms and revolutions. As a case study, I will explicitly focus on the famous problem of Mercury's perihelion precession: how people's credence shifted from Newtonian gravity to general relativity as the latter was recognized to solve the puzzle. Finally, I will explore the possibility of extracting scaling laws in citation networks as indicators of Bayesian convergence in scientific practice.