Correcting credences with chances

Lewis’s Principal Principle is widely recognized as a rationality constraint that our credences should satisfy throughout our epistemic life. In practice, however, our credences often fail to satisfy this principle because of our various epistemic limitations. Facing such violations, we should correct our credences in accordance with this principle. In this paper, I will formulate a way of correcting our credences, which will be called the Adams Correcting Rules and then show that such a rule yields non-commutativity between conditionalizing and correcting. With the help of the notion of ‘accuracy’, then, I attempt to provide a vindication of the Adams Correcting Rule and show how we can respond to the non-commutativity in question.