Arguments in favor of anti-representationalism in cognitive science often suffer from a lack of attention to detail. The purpose of this paper is to fill in the gaps in these arguments, and in so doing show that at least one form of anti-representationalism is potentially viable. After giving a teleological definition of representation and applying it to a few models that have inspired anti-representationalist claims, I argue that anti-representationalism must be divided into two distinct theses, one ontological, one epistemological. Given the assumptions that define the debate, I give reason to think that the ontological thesis is false. I then argue that the epistemological thesis might, in the end, turn out to be true, despite a potentially serious difficulty. Along the way, there will be a brief detour to discuss a controversy from early twentieth century physics.