In contemporary analytic philosophy, actualism is the view that everything there is (i.e., everything that has being, in the broadest sense) is actual. Another phrasing of the thesis is that the domain of unrestricted quantification ranges over all and only actual existents.
The denial of actualism is possibilism, the thesis that there are some entities that are merely possible: these entities have being but are not actual and, hence, enjoy a "less robust" sort of being than do actually existing things. An important, but significantly different notion of possibilism known as modal realism was developed by the philosopher David Lewis." On Lewis's account, the actual world is identified with the physical universe of which we are all a part. Other possible worlds exist in exactly the same sense as the actual world; they are simply spatio-temporally unrelated to our world, and to each other. Hence, for Lewis, "merely possible" entities—entities that exist in other possible worlds—exist in exactly the same sense as do we in the actual world; to be actual, from the perspective of any given individual x in any possible world, is simply to be part of the same world as x.
Consider the statement "Sherlock Holmes exists." This is a false statement about the world, but is usually accepted as representing a possible truth. This contingency is usually described by the statement "there is a possible world in which Sherlock Holmes exists". The possibilist argues that apparent existential claims such as this (that "there are" possible worlds of various sorts) ought to be taken more or less at face value: as stating the existence of two or more worlds, only one of which (at the most) can be the actual one. Hence, they argue, there are innumerably many possible worlds other than our own, which exist just as much as ours does.
Most actualists will be happy to grant the interpretation of "Sherlock Holmes' existence is possible" in terms of possible worlds. But they argue that the possibilist goes wrong in taking this as a sign that there exist other worlds that are just like ours, except for the fact that we are not actually in them. The actualist argues, instead, that when we claim "possible worlds" exist we are making claims that things exist in our own actual world which can serve as possible worlds for the interpretation of modal claims: that many ways the world could be (actually) exist, but not that any worlds which are those ways exist other than the actual world around us.