  As with concretism and abstractionism, combinatorialism provides  reasonably clear definitions of possible worlds and existence in a  world and is noteworthy for its attempt to avoid what might be  thought of as the metaphysical excesses of the two competing views.  In contrast to concretism, combinatorialism is staunchly actualist:  instead of an infinity of alternative physical universes, each with  its own unique inhabitants existing as robustly as the inhabitants of the actual world, the worlds of combinatorialism are simply  rearrangements of the universals and particulars of the actual world; and commitment even to them might be avoided if some version  of fictionalism is tenable. Likewise, in contrast to abstractionism's  rather rich and unrestrained ontology of SOAs, combinatorialism's  states of affairs are comparatively modest. Moreover, in contrast to  nearly all versions of abstractionism, combinatorialism shares with  concretism the virtue of a reductive theory of modality: Modal  statements, ultimately, are true or false in virtue of how things  stand with respect to worlds that are themselves defined in non-modal terms. 