According to probabilistic theories of higher cognition, beliefs come in degrees. Here, we test this idea by studying how people make predictions from uncertain beliefs. According to the degrees-of-belief theory, people should take account of both high- and low-probability beliefs when making predictions that depend on which of those beliefs are true. In contrast, according to the all-or-none theory, people only take account of the most likely belief, ignoring other potential beliefs. Experiments 1 and 2 tested these theories in explanatory reasoning, and found that people ignore all but the best explanation when making subsequent inferences. Experiment 3A extended these results to beliefs fixed only by prior probabilities, while Experiment 3B found that people can perform the probability calculations when the needed probabilities are explicitly given. Thus, people’s intuitive belief system appears to represent beliefs in a ‘digital’ (true or false) manner, rather than taking uncertainty into account.