The Theory of Fallible Probability and The Dynamics of Degrees of Belief

TL;DR

This paper develops a comprehensive theory of fallible probability and belief dynamics, proposing improvements over existing models, resolving key issues, and providing a new framework for updating and confirming beliefs.

Contribution

It introduces an enhanced theory of probability dynamics that replaces Jeffrey's probability kinematics and addresses longstanding problems in belief updating.

Findings

Proposes an improved probability dynamics framework

Resolves the problem of New Explanation of Old Evidence

Refutes the Principle of Reflection

Abstract

This monograph is an account of the theory of fallible probability and of the dynamics of degrees of belief. It discusses the first order subjective theory in which first order degrees of belief are expressed by subjective probabilities and are updated by conditionalization (Bayes, 1764; Ramsey, 1926), gives an improved exposition of the greater part of the author's theory of Probability Dynamics (Nathan, 2006) which should replace the so-called Probability Kinematics (Jeffrey, 1965), resolves the problem of New Explanation of Old Evidence (Jeffrey, 1995), provides a Theory of Confirmation, and refutes the Principle of Reflection (Van Fraassen, 1984).