 According to a platonist about arithmetic, the truth of the sentence ‘7 is prime’ entails the existence of an abstract object, the number 7. This object is abstract because it has no spatial or temporal location, and is causally inert. A platonic realist about arithmetic will say that the number 7 exists and instantiates the property of being prime independently of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false (hence the name ‘error-theory’). Platonists divide on their account of the epistemology of arithmetic: some claim that our knowledge of arithmetical fact proceeds by way of some quasi-perceptual encounter with the abstract realm (Gödel 1983), while others have attempted to resuscitate a qualified form of Frege’s logicist project of grounding knowledge of arithmetical fact in knowledge of logic (Wright 1983, Hale 1987, Hale and Wright 2001).