Beyond their linguistic and rhetorical uses, the mental epistemic verbs to knowand to believe reveal a basic conceptual system for human intentionality and the theory of representational mind. Numerous studies, particularly in the field of child development, have been devoted to the conditions under which knowledge and belief are acquired. Upstream of this empirical approach, this paper proposes a topological model of the conceptual structure underlying the linguistic use of to know and to believe. A cusp model of catastrophe theory (...) is chosen to model the formation of epistemic states. Its main characteristic is considering to believe as an intermediate state which lacks stability and presents the delayed effect of hysteresis. The attribution of mental states to the other (viewpoint of the third person) is obtained by the crossing of first and third person knowledge and belief, which gives rise to new categories (to know if and to falsely believe) and closes the system. Another merging of the beliefs of persons A and B, using the butterfly catastrophe, provides a model of interpersonal belief appreciated by an independent observer along a potential evolving from agreement to disagreement. (shrink)