A Problem for Actualism About Possible Worlds

Abstract

T he notion of a possible has many uses in the formal philosophy of language. Its primary use, of course, is in the interpretation of sentences about necessity and possibility. A proposition is necessary if and only if it is true in all possible worlds; possible if and only if true in some possible world. One advantage of the possible worlds interpretation is its extensionality. The intensional notions of necessity and possibility are replaced by quantifiers over possible worlds. The language in which these quantifiers appear, sometimes called world theory, can be given an ordinary Tarski semantics. A second advantage of the possible worlds interpretation is purely heuristic. It just seems to help our modal thinking to imagine other possible worlds. However, the nature of possible worlds is the subject of a familiar controversy, the dispute between actualism and possibilism. One common position in this controversy, which I shall call atomistic actualism, seems to me the most plausible. Nevertheless, I shall show that it is open to serious objection. It fails to provide an adequate interpretation for certain modal sentences, assuming that we adopt standard rules of interpretation. Thus we must either reject atomistic actualism, even though, as I shall argue in the next section, the alternatives are not attractive, or reject the standard semantics, despite its practical successes.