Nomothetical theoretical models, including those in psychology are judged according to general criteria among which that of predictability is one of the most important. That is a nomothetic model should be capable of predicting future events and paths of processes successfully. It is claimed that such models base their predictions upon empirical generalizations of normal courses of events, and not upon models of developmental mechanisms. In the present article the question is raised whether or not predictability can in principle be achieved. A simple model of longitudinal cognitive growth is presented based on the logistic growth equation. It is argued that this model produces good theoretical reconstructions of empirical cognitive growth sequences. It is shown that the behavior of growth processes based on the logistic assumption is nevertheless very complicated, and sensitive to differences in parameters that are well beyond our possibilities of psychological measurement. Some examples of unpredictability are presented. It is argued that a model of psychological development should be a model of a dynamics describing ranges of individual processes. Such processes are characterized by intrinsic prediction horizons which are not reducable to influences of free will or major random factors.