 As Hellman makes clear, his goal is to develop a form of “structuralism without structures” (Hellman 1996), since the existence of abstract structures, postulated by Resnik and Shapiro, is replaced by the modal aspects of his position (and corresponding assumptions about necessity and possibility). In fact, Hellman’s position is meant to be a form of nominalism, i.e., to eliminate the appeal to any kind of abstract entity (not only abstract structures but also sets etc.). Yet it is also not meant to rely on possibilia, i.e., possible objects existing in some shadowy sense. This leads Hellman to a specific understanding of the modalities at issue. They are meant to be basic, i.e., the relevant possibilities and necessities are not reducible to anything further. On the other hand, they are specified precisely in terms of laws of modal logic (those of the system S5).