In this paper I consider one of the influential challenges to the notion that perceptual experience might be completely conceptually structured, a challenge that rests on the idea that conceptual structure cannot do justice to the fineness of grain of perceptual experience. In so doing, I canvass John McDowell’s attempt to meet this challenge by appeal to the notion of demonstrative concepts and review some criticisms recently leveled at McDowell’s deployment of demonstrative concepts for this purpose by Sean D. Kelly. (...) Finally, I suggest that, though Kelly’s criticisms might challenge McDowell’s original presentation of demonstrative concepts, a modified notion of demonstrative concept is available to the conceptualist that is proof against Kelly’s criticisms. (shrink)