In this paper we consider how boundedly rational agents learn rational expectations. The assumption that agents are boundedly rational is made operational by imposing computability constraints on the economy: all equilibrium price functions or forecasts of future equilibrium prices are required to be computable. Computable functions are defined, as in the computer science literature, as functions whose values can be calculated using some finite algorithm. The paper examines two learning environments. In the first, agents have perfect information about the state of nature. In this case, the theory of machine inference can be applied to show that there is a broad class of computable economies whose rational expectations equilibria can be learned by inductive inference. In the second environment, agents do not have perfect information about the state of nature. In this case, a version of Godel's incompleteness theorem applicable to the theory of computable functions yields the conclusion that rational expectations equilibria cannot be learned.