Categorical versus graded beliefs
Résumé
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 for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem. The nature, relevance, and implications of the tension are explained and assessed. A more technical elaboration can be found in Dietrich and List (2018, 2021).
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