This chapter, specially written for a Philosophy and Phenomenological Research book symposium on the Stephen Schiffer’s The Things We Mean, is focused on Schiffer’s proposal there concerning the most central and important question about vagueness: namely, what, specifically, something’s being a borderline case of a vague expression consists in. Schiffer argues for a new kind of approach, according to which vagueness is constitutively a psychological phenomenon, grounded in a supposedly distinctive propositional attitude taken by practitioners of vague discourse: vagueness-related partial belief (VPB), contrasting in ways Schiffer details with standard partial belief (SPB). Two principal problems are raised for this proposal. First, on Schiffer’s account, VPB looks to be characteristic of a wider range of kinds of indeterminacy besides the targeted soritical vagueness. Second, there is an awkward dilemma arising over whether or why a thinker could not, as a matter of psychological contingency, adopt a VPB towards a precise proposition.