Quine rejects Peirce's theory of truth because, among other things, its notion of a limit of a sequence of theories is defective in that the notion of a limit depends on that of nearer than which is defined for numbers but not for theories. This paper shows that the missing definition of nearer than applied to theories can be supplied from within Quine's own epistemology. The upshot is that either Quine's epistemology must be rejected or Peirce's pragmatic theory of truth is partially vindicated.