Defences of Williamson’s Anti-Luminosity Argument (ALA) that employ doxastic propagation principles—i.e., rules by which cases of beliefs and/or dispositions to believe are inferred from other such cases—risk running into sorites. Since these principles are explainable by an ineffective capacity to phenomenally discriminate between two adjacent cases, luminist rejections of the ALA can halt sorites by denying doxastic propagation, thereby reaffirming these discriminative capacities as appropriately effective. One potent method of resisting the luminist involves recharacterizing discriminative capacities in terms of a (...) distinction between beliefs and their underlying dispositions to reinstate the plausibility of doxastic propagation. To this effect, I propose a novel coarse-grained approach favouring the ALA that leverages a modal analysis of the belief/ disposition distinction. This motivates a sharp threshold between belief and absent belief that neither succumbs to sorites nor begs the question against the luminist. The upshot of this approach is substantial: by conferring a dialectical advantage to the anti-luminist, the luminist is held to highly problematic positions, regarding the trivialisation of safety and the relationship between beliefs and dispositions, if they deny the coarse-grained approach at many of its components. (shrink)