Connectivism, which has been argued to be a new learning theory, has emerged in the field of online learning during the last decade. On the World Wide Web at least, connectivism promises to establish learning spaces similar to those that Ivan Illich imagined in "Deschooling Society", through so-called massive online open courses (MOOCs). In this paper, we critically examine the theoretical postulates of connectivism and identify three important psychological and epistemological problems, namely the lack of a solution to the learning paradox, the underconceptualization of interaction and the inability to explain concept development. Some of the theoretical deficiencies in question may explain certain learning problems experienced by participants in MOOCs. The paper concludes that, although MOOCs are a worthwhile experience and ought to be continued, connectivism as a learning theory has significant theoretical problems and should be profoundly revised if it is to explain and foster learning in such environments.