It has become standard practice in philosophy to follow Richard Foley (1992) in distinguishing between an epistemology of belief and an epistemology of degrees of belief. The former distinguishes among three doxastic attitudes: belief, disbelief (i.e., believing something not to be the case), and suspension of belief. Key to the latter epistemology is the idea that beliefs come in various strengths, where the strength of a belief can be measured on a continuous scale (typically, the unit interval but that is a matter of convention). Many have hoped that because the two epistemologies appear to differ only in assuming a different granularity while looking at the same attitude – that of belief – there must be some way to connect them. Finding one or more bridge principles between these epistemologies seems a worthy endeavor indeed, for given such principles, we might be able to derive truths about the notion of categorical belief from insights about the notion of graded belief, or vice versa.