Endo-observers can be described and classified on the basis of a novel two-dimensional scheme. One axis stands for the observer's style of knowledge acquisition, whereas the other axis corresponds to the observer's style of knowledge representation. In this way several problems concerning the relation between the endo-observer and the exo-system can be studied more systematically. Among other things, it is shown that there are two complementarity relations which restrict the observer's capacity of information gain: a duality between structure and dynamics (an increased information gain on the structure of the endo-system implies a reduced information gain on its dynamics, and vice versa), and a duality between the predictive and the explanatory power of a model. Connections with the problem of hermeneutics are outlined.