published on March 15, 2017
Imprecise Probability and Higher Order Vagueness
There is a trade-off between specificity and accuracy in accounts of belief. Descriptions of agents in the tripartite account, which recognizes three doxastic attitudes—belief, disbelief, and suspension—are accurate, but not specific. The orthodox Bayesian account, which requires real-valued credences, is specific, but often inaccurate. I argue that a popular attempt to fix the Bayesian account by using sets of functions is also inaccurate; it suffers from a problem analogous to higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse a principle with the surprising consequence that the trade-off between accuracy and specificity is in-principle unavoidable. However, we can nonetheless improve on both the tripartite and existing Bayesian accounts. I construct a new framework that allows descriptions that are much more specific than those of the tripartite account and yet remain, unlike existing Bayesian accounts, perfectly accurate.