Contemporary epistemology offers us two very different accounts of our epistemic lives. According to Traditional epistemologists, the decisions that we make are motivated by our desires and guided by our beliefs and these beliefs and desires all come in an all-or-nothing form. In contrast, many Bayesian epistemologists say that these beliefs and desires come in degrees and that they should be understood as subjective probabilities and utilities.
What are we to make of these different epistemologies? Are the Tradionalists and the Bayesians in disagreement, or are their views compatible with each other? Some Bayesians have challenged the Traditionalists: Bayesian epistemology is more powerful and more general than the Traditional theory, and so we should abandon the notion of all-or-nothing belief as something worthy of philosophical analysis. The Traditionalists have responded to this challenge in various ways. I shall argue that these responses are inadequate and that the challenge lives on.