Representation theorems have been developed and appealed to in the service of three philosophical projects: in preference-based attempts to define credences, in the measurement of credences, and in arguments for probabilism. State-based theorems have played a particularly prominent role here, due in part to their strong uniqueness results. However, these theorems have a common defect which renders them unsuitable for such purposes; in short, they do not allow us to assign probabilities to enough propositions, or to the right kinds of propositions, to plausibly found any of these projects.