Categorical Versus Graded Beliefs

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief.The possibility Inflatables for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List.The nature, relevance, and Hair Color implications of the tension are explained and assessed.