Republic IX 583c-585a presents something surprisingly unusual in ancient accounts of pleasure and pain: an argument in favour of the view that there are three relevant hedonic states: pleasure, pain, and an intermediate. The argument turns on the proposal that a person’s evaluation of their current state may be misled by a comparison with a prior or subsequent state. The argument also refers to ‘pure’ and anticipated pleasures. The brief remarks in the Republic may appear cursory or clumsy in comparison with the Philebus, but this appearance is misleading. Rather, they are part of a neat dialectical argument against a potentially troubling set of opponents. Socrates’ use of a topological analogy at 584d3-585a7 rounds off this section by clarifying and illustrating his position, preparing the ground for the final explanation of the pleasantness of the philosophical life at 585a-587c.