Theory Choice, Theory Change, and Inductive Truth-Conduciveness

(I) Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. (II) Diachronic norms of theory change, as studied in belief revision, restrict how one should change one's current beliefs in light of new information. (III) Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning (III), we explicate inductive truth conduciveness in terms of optimally direct convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning (I), we explicate Ockham's razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning (II), we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary (and in some cases, sufficient) for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between (I), (II), and (III).