possible worlds alternative worlds in terms of which one may think of possibility. The idea of thinking about possibility in terms of such worlds has played an important part, both in Leibnizian philosophical theology and in the development of modal logic and philosophical reflection about it in recent decades. But there are important differences in the forms the idea has taken, and the uses to which it has been put, in the two contexts.
Leibniz used it in his account of creation. In his view God’s mind necessarily and eternally contains the ideas of infinitely many worlds that God could have created, and God has chosen the best of these and made it actual, thus creating it. (Similar views are found in the thought of Leibniz’s contemporary, Malebranche.) The possible worlds are thus the complete alternatives among which God chose. They are possible at least in the sense that they are logically consistent; whether something more is required in order for them to be coherent as worlds is a difficult question in Leibniz interpretation. They are complete in that they are possible totalities of creatures; each includes a whole (possible) universe, in its whole spatial extent and its whole temporal history (if it is spatially and temporally ordered). The temporal completeness deserves emphasis. If ‘the world of tomorrow’ is ‘a better world’ than ‘the world of today,’ it will still be part of the same ‘possible world’ (the actual one); for the actual ‘world,’ in the relevant sense, includes whatever actually has happened or will happen throughout all time. The completeness extends to every detail, so that a milligram’s difference in the weight of the smallest bird would make a different possible world. The completeness of possible worlds may be limited in one way, however. Leibniz speaks of worlds as aggregates of finite things. As alternatives for God’s creation, they may well not be thought of as including God, or at any rate, not every fact about God. For this and other reasons it is not clear that in Leibniz’s thought the possible can be identified with what is true in some possible world, or the necessary with what is true in all possible worlds. That identification is regularly assumed, however, in the recent development of what has become known as possible worlds semantics for modal logic (the logic of possibility and necessity, and of other conceptions, e.g. those pertaining to time and to morality, that have turned out to be formally analogous). The basic idea here is that such notions as those of validity, soundness, and completeness can be defined for modal logic in terms of models constructed from sets of alternative ‘worlds.’ Since the late 1950s many important results have been obtained by this method, whose best-known exponent is Saul Kripke. Some of the most interesting proofs depend on the idea of a relation of accessibility between worlds in the set. Intuitively, one world is accessible from another if and only if the former is possible in (or from the point of view of) the latter. Different systems of modal logic are appropriate depending on the properties of this relation (e.g., on whether it is or is not reflexive and/or transitive and/or symmetrical). The purely formal results of these methods are well established. The application of possible worlds semantics to conceptions occurring in metaphysically richer discourse is more controversial, however. Some of the controversy is related to debates over the metaphysical reality of various sorts of possibility and necessity. Particularly controversial, and also a focus of much interest, have been attempts to understand modal claims de re, about particular individuals as such (e.g., that I could not have been a musical performance), in terms of the identity and nonidentity of individuals in different possible worlds. Similarly, there is debate over the applicability of a related treatment of subjunctive conditionals, developed by Robert Stalnaker and David Lewis, though it is clear that it yields interesting formal results. What is required, on this approach, for the truth of ‘If it were the case that A, then it would be the case that B’, is that, among those possible worlds in which A is true, some world in which B is true be more similar, in the relevant respects, to the actual world than any world in which B is false. One of the most controversial topics is the nature of possible worlds themselves. Mathematical logicians need not be concerned with this; a wide variety of sets of objects, real or fictitious, can be viewed as having the properties required of sets of ‘worlds’ for their purposes. But if metaphysically robust issues of modality (e.g., whether there are more possible colors than we ever see) are to be understood in terms of possible worlds, the question of the nature of the worlds must be taken seriously. Some philosophers would deny any serious metaphysical role to the notion of possible worlds. At the other extreme, David Lewis has defended a view of possible worlds as concrete totalities, things of the same sort as the whole actual universe, made up of entities like planets, persons, and so forth. On his view, the actuality of the actual world consists only in its being this one, the one that we are in; apart from its relation to us or our linguistic acts, the actual is not metaphysically distinguished from the merely possible. Many philosophers find this result counterintuitive, and the infinity of concrete possible worlds an extravagant ontology; but Lewis argues that his view makes possible attractive reductions of modality (both logical and causal), and of such notions as that of a proposition, to more concrete notions. Other philosophers are prepared to say there are non-actual possible worlds, but that they are entities of a quite different sort from the actual concrete universe – sets of propositions, perhaps, or some other type of ‘abstract’ object. Leibniz himself held a view of this kind, thinking of possible worlds as having their being only in God’s mind, as intentional objects of God’s thought.
See also COUNTERFACTUALS , KRIPKE SEMANTICS , MODAL LOGI. R.M.A.