Bayes's Two Arguments for The Rule of Conditioning

Abstract

The introductory section of Thomas {B}ayes's famous essay on probability contains two arguments for what we now call the rule of conditioning. The first argument, which leads to {B}ayes's third proposition, can be made rigorous if we use rooted trees to represent the step-by-step determination of events. The second argument, which leads to {B}ayes's fifth proposition, does not stand up to scrutiny.