Suppose that we interpret necessity as truth in all possible worlds, possibility as truth in some possible world, and truth simpliciter, naturally, as truth in the actual world. Suppose that we take this interpretation seriously, not merely accepting it as a useful instrument, but believing that it reflects the very meanings of "necessary", "possible", and "true". Then we are committed, in some sense, to there being many possible worlds, and at the same time, to the idea that just one world, our world, is actual. And this is an apparent contradiction, for what is being if not actuality? Of the many solutions to this puzzle, I shall be concerned with the one offered by actualists. Actualism is the view that there are in general no nonactual objects, and in particular no nonactual possible objects. Those actualists who believe in possible worlds, which certainly seem to be nonactual possibles, take them instead to be existing abstract entities. These abstract entities are chosen in such a way that just one of them corresponds, in an appropriate sense, to reality. For example, Alvin Plantinga says that worlds are maximal possible states-of-affairs, only one of which, the actual world, obtains.1 In this way, actualists can maintain both that all possible worlds have being, in the sense that they exist, but that one is distinguished as actual, in the sense that it alone corresponds to reality. Thus our initial puzzle is solved. I shall argue, however, that at a deeper level, actualism is not compatible with standard possible worlds semantics. According to the standard semantics, a statement 'It is possible that A' is true if and only if there is a possible world which includes the state-of-affairs expressed by A. The statement "It is possible that Socrates have chosen exile" is true, for instance, if and only if there is a possible world which includes the state-of-affairs of Socrates' choosing exile, a truth-condition that is not at all unreasonable. Difficulty is encountered, however, in the interpretation of statements containing iterated modal operators, such as "It is possible that there have been a man