The evolution of belief systems has always been a focus of cognitive research. In this paper, we delineate a new model describing belief systems as a network of statements considered true. Testing the model with a small number of parameters enabled us to reproduce a variety of well-known mechanisms ranging from opinion changes to development of psychological problems. The self-organizing opinion structure showed a scale-free degree distribution. The novelty of our work lies in applying a convenient set of definitions allowing us to depict opinion network dynamics in a highly favorable way, which resulted in a scale-free belief network. As an additional benefit, we listed several conjectural consequences in a number of areas related to thinking and reasoning.