 According to actualist representationism, which is also known under Lewis’s tendentious label ersatzism, a possible world is an actual maximally consistent representation of how the universe could possibly have been, and the actual world is the representation of how the universe actually is. A representation r is maximally consistent if and only if r is consistent and for any representation r′, either r &amp; not-r′ is not consistent or r &amp; r′ is not consistent (assuming the appropriate conceptions of the negation and conjunction of representations). Different actualist representationists employ different actual items to play the role of the maximally consistent representations, such as sentences, propositions, states of affairs, properties, etc. (Adams 1974, Armstrong 1989, Bigelow and Pargetter 1990, Carnap 1947, Cresswell 1972, Forrest 1986, Hintikka 1962, Jeffrey 1965, Lycan 1979, Lycan &amp; Shapiro 1986, Plantinga 1974, 1987, Prior &amp; Fine 1977, Quine 1968, Roper 1982, Skyrms 1981, Stalnaker 1976). Note that the notion of consistency of a representation is not ultimately eliminated in actualist representationism. Most actualist representationists accept consistency as a modal notion, for they doubt it can be reduced to a non-modal notion, such as a proof-theoretic notion or a model-theoretic notion. If those actualist representationists are right and consistency is indeed a modal notion, then actualist representationism is not a reductionist theory of modality. This, however, should not automatically be taken to be a serious challenge to actualist representationism, for a thoroughly reductionist theory of modality may or may not be feasible. Not even every possibilist realist believes in thorough reduction; cf. modal–dimensionalists.