A Principled Analysis of Consistency of an Abstract Principal Principle

Abstract

The paper takes the Abstract Principal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of both classical an non-classical (quantum) probability measure spaces. It is proved that the Abstract Principal Principle is weakly and strongly consistent both in the classical and non-classical cases. It is argued that it is desirable to strengthen the Abstract Principal Principle by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined, and the strong consistency of the Abstract Principal Principle is interpreted as necessary for a non-omniscient Bayesian agent to be able to have rational degrees of belief in all epistemic situations. We give a proof of weak consistency of the Stable Abstract Principal Principle in the framework of classical probability theory, a proof which is different from the proof in Bana (Philos Sci, 2016, forthcoming). Formulation and investigation of the status of a Stable Abstract Principal Principle in quantum probability spaces remains for further study.