Two Mistakes Regarding the Principal Principle

This paper examines two mistakes regarding David Lewis’ Principal Principle that have appeared in the recent literature. These particular mistakes are worth looking at for several reasons: The thoughts that lead to these mistakes are natural ones, the principles that result from these mistakes are untenable, and these mistakes have led to significant misconceptions regarding the role of admissibility and time. After correcting these mistakes, the paper discusses the correct roles of time and admissibility. With these results in hand, the paper concludes by showing that one way of formulating the chance–credence relation has a distinct advantage over its rivals. 1. Introduction 2. Background 2.1. The chance function 2.2. The chance–credence relation 2.3. Assumptions 3. Assessing the First Mistake 3.1. The first mistake 3.2. Motivating the first mistake 3.3. Why the first mistake is problematic 3.4. Consequences of the first mistake 4. The Role of Admissibility 4.1. Crystal balls 4.2. Usefulness 4.3. The strength of PP1 4.4. Lewis and admissibility 5. Assessing the Second Mistake 5.1. The second mistake 5.2. Motivating the second mistake 5.3. Why the second mistake is problematic 5.4. The role of time 6. Assessing the Chance–Credence Relation 6.1. Take I: Lewis' grounding argument 6.2. Take II: general grounding arguments 6.3. The winner