Starting from the observation that small children can count more objects than numbers—a phenomenon that I am calling the “lifeworld dependency of cognition”—and an analysis of finger calculation, the paper shows how learning can be explained as the development of cognitive systems. Parts of those systems are not only an individual's different forms of knowledge and cognitive abilities, but also other people, things, and signs. The paper argues that cognitive systems are first of all semiotic systems since they are dependent on signs and representations as mediators. The two main questions discussed here are how the external world constrains and promotes the development of cognitive abilities, and how we can move from cognitive abilities that are necessarily connected with concrete situations to abstract knowledge.