According to the currently dominant view, cognitive science is a study of mind and intelligence focused on computational models of knowledge in humans. It is described in terms of symbol manipulation over formal language. This approach is connected with a variety of unsolvable problems, as pointed out by Thagard. In this paper, I argue that the main reason for the inadequacy of the traditional view of cognition is that it detaches the body of a human as the cognizing agent from the higher-level abstract knowledge generation. It neglects the dynamical aspects of cognitive processes, emotions, consciousness, and social aspects of cognition. It is also uninterested in other cognizing agents such as other living beings or intelligent machines. Contrary to the traditional computationalism in cognitive science, the morphological computation approach offers a framework that connects low-level with high-level approaches to cognition, capable of meeting challenges listed by Thagard. To establish this connection, morphological computation generalizes the idea of computation from symbol manipulation to natural/physical computation and the idea of cognition from the exclusively human capacity to the capacity of all goal-directed adaptive self-reflective systems, living organisms as well as robots. Cognition is modeled as a layered process, where at the lowest level, systems acquire data from the environment, which in combination with the already stored data in the morphology of an agent, presents the basis for further structuring and self-organization of data into information and knowledge.