In order to address these issues, the modal structuralist puts forward a general framework. The main idea is that although mathematics is concerned with the study of structures, this study can be accomplished by focusing only on possible structures, and not actual ones. Thus, the modal interpretation is not committed to actual mathematical structures; there is no commitment to their existence as objects or to any objects that happen to ‘constitute’ these structures. In this way, the ontological commitment to them is avoided: the only claim is that the structures in question are possible. In order to articulate this point, the modal-structural interpretation is formulated in a second-order modal language based on S5. However, to prevent commitment to a set-theoretical characterization of the modal operators, Hellman takes these operators as primitive (1989, pp. 17, and 20–23).