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. Introduction2. Background 2.1. The chance function2.2. The chance–credence relation2.3. Assumptions3. Assessing the First Mistake 3.1. The first mistake3.2. Motivating the first mistake3.3. Why the first mistake is problematic3.4. Consequences of the first mistake4. The Role of Admissibility 4.1. Crystal balls4.2. Usefulness4.3. The strength of PP14.4. Lewis and admissibility5. Assessing the Second Mistake 5.1. The second mistake5.2. Motivating the second mistake5.3. Why the second mistake is problematic5.4. The role of time6. Assessing the Chance–Credence Relation 6.1. Take I: Lewis' grounding argument6.2. Take II: general grounding arguments6.3. The winner Introduction Background 2.1. The chance function2.2. The chance–credence relation2.3. Assumptions The chance function The chance–credence relation Assumptions Assessing the First Mistake 3.1. The first mistake3.2. Motivating the first mistake3.3. Why the first mistake is problematic3.4. Consequences of the first mistake The first mistake Motivating the first mistake Why the first mistake is problematic Consequences of the first mistake The Role of Admissibility 4.1. Crystal balls4.2. Usefulness4.3. The strength of PP14.4. Lewis and admissibility Crystal balls Usefulness The strength of PP1 Lewis and admissibility Assessing the Second Mistake 5.1. The second mistake5.2. Motivating the second mistake5.3. Why the second mistake is problematic5.4. The role of time The second mistake Motivating the second mistake Why the second mistake is problematic The role of time Assessing the Chance–Credence Relation 6.1. Take I: Lewis' grounding argument6.2. Take II: general grounding arguments6.3. The winner Take I: Lewis' grounding argument Take II: general grounding arguments The winner
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