1.1Introduction
Modality concerns what might or must be the case. We use modal expressions such as ‘might’, ‘must’, and cognates in a variety of ways, however. One can truthfully say, for example, that the neither yet proved nor disproved Goldbach’s conjecture (that every natural number greater than two is the sum of two primes) might be true, even if the conjecture is false and hence, in a metaphysical sense, necessarily so. What one means here is that the conjecture is compatible with our evidence, since we have neither proven nor disproven it.
Modal expressions are typically intensional (with an ‘s’). An expression α is intensional just in case the substitution of extensionally equivalent expressions under the scope of α need not preserve truth. For instance, even though ‘8’ and ‘the number of planets’ have the same extension, ‘Necessarily, 8 is greater than 1’ and ‘Necessarily, the number of planets is greater than 1’ do not share their extension (i.e. truth-value). However, while many modal notions are intensional, not all are. Consider e.g. the de re modal relation expressed by ‘it is necessary of x that it be such that A’, where A is to be replaced by a declarative statement. Thus, even though the expressions ‘modal’ and ‘intensional’ are sometimes used interchangeably, modality and intensionality are not equivalent.
How best are we to analyze modality and intensionality? The most popular strategy since the mid-twentieth century is to employ possible worlds. Reference to possible worlds dates back at least to Leibniz (see Mates, 1968), but they do not assume their familiar role until the 1940s when Rudolf Carnap (Carnap, 1946) gave an analysis of modal operators resembling a modern treatment in terms of quantification over what we would now call possible worlds. Such an analysis, often called possible worlds semantics, was later generalized throughout the 1940s and 1950s independently by a number of logicians, including Saul Kripke and Jaakko Hintikka, and is now the standard treatment for a wide variety of intensional notions including modality. An impressive number of intensional notions have been given possible worlds analyses, only some of which include: conditionality, causation, knowledge, de se belief, intrinsicality, dispositionality, aboutness or subject matter, supervenience and dependence, truthmaking, the laws of nature, essence, property, propositional and intentional content, fictional worlds, and truth in fiction. The use of possible worlds in linguistics, logic, and computer science has also seen enormous success. The fact that possible worlds talk has become common parlance in many areas of contemporary analytic philosophy, and other fields, raises important questions concerning their ontological status and the explanatory value they afford.
Rather than answering the question What are possible worlds? I wish to discuss what I think is a more tractable question, namely, What what theoretical roles are possible worlds supposed to play, and are they cut out to play those roles?1
The question is tractable because we can simply look and see to what purposes possible worlds have been put and whether possible worlds analyses have survived the test of time, or whether they have been succeeded by superior analyses which either do away with worlds altogether or else demote them to a lesser role.
In giving a partial answer to the question, we will begin by looking at traditional possible worlds analyses of intensional and modal concepts (Section 1.2). We will then look at three possible worlds analyses that have played an important role in their perceived success, viz. the analyses of (i) modality and possibilities in counterpart theory (Section 1.3), (ii) belief contents (Section 1.4), and (iii) conditionals (Section 1.5).
