In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I (...) will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities. (shrink)