Page 378 - Encyclopedia of Philosophy of Language

Formal Semantics
allowed at all, should be analyzed in terms of harmless modes of expression. Yet, possible worlds have been fruitfully used in mathematics, logical semantics, and even in science. For this reason philosophers such as Kripke, Lewis, and Stalnaker, among others, have concerned themselves with the issue of whether poss- ible worlds are as real as the actual one, or whether they are abstract alternatives to the real world they might represent.
1. History
A famous use of possible worlds is by Leibniz (1646- 1716) in his Monadology and Theodicy. Facts are con- tingent; they could have been otherwise. So, he poses the question, why are the present facts realized and no others? In particular, if God in his infinite wisdom chose this world to exist, why is it so much worse than we can imagine? Leibniz answered these questions in
the Monadology, §53-55:
(53) Now, as there is an infinity of possible universes in the ideas of God, and as only one of them can exist, there must be a sufficient reason for God's choice, which determines him to one rather than another.
(54) And this reason can only be found in the fitness or in the degrees of perfection that these worlds contain, each possible world having the right to a claim to exis- tence to the extent of the perfection it enfolds.
(55) And this is the cause of the existence of the best: that his wisdom makes it known to God, his Goodness makes him choose it, and his power makes him produce it.
In the late twentieth century, most philosophers would find Leibniz's solution an amazingly clever tale, but no more than that: a tale. Also, some of his fol- lowers used it to justify a superficial 'optimism,' which brings along an ethical inertia in a world full of trag- edies and disasters. This aspect of the doctrine is ridi- culed by Voltaire (1694-1778) in his Candide. It tells the story of a young optimist who is raised in the most beautiful and delightful of all possible mansions, the country seat of Baron Thunder-ten-tronck. Candide remains indifferent to a terrible amount of anguish, mainly suffered by others, for the metaphysico- theologo-cosmolo-nigologist Pangloss taught him that all is for the best in the best of all possible worlds.
2. Philosophy
The interest in possible worlds does not survive for theological or ethical reasons. Most rational human activities—suchasanticipation offutureevents,inves- tigation and explanation, fiction—involve a con- sideration of alternatives to the ways things are. This is reflected in the distinctively modal flavor of parts of speech and some of the relations between them: counterfactual conditionals, modal adverbs, and auxiliaries, and implication, among other things. Until
the 1960s, the semantics of these expressions was opaque. But the development of possible world sem- antics, made famous by the young Kripke, clarified the semantics of modal expressions by means of 'the same set-theoretic techniques of model theory that proved so successful when applied to extensional logic' (Kripke 1980: 19).
In possible world semantics, one takes the notions of a 'possible world' and an 'accessibility' or a 'simi- larity' relation among them as primitives. Prop- ositions are defined as sets of possible worlds. The truth of a sentence in a world may depend on what is the case in the worlds which are accessible from or similar to that world.
In taking possible worlds and the relations among them as primitives, the claim is not that no more could or need be said about them, but that it is fruitful to work at 'a certain level of abstraction, a level that brings out what is common in a certain range of other- wise uncommon activities' (Stalnaker 1984: 57). This is not unlike the use of individuals in extensional sem- antics. Despite its more familiar appearance, the gen- eral notion of an 'individual' seems as elusive as that of a 'possible world.' To elucidate, for example, the relation of consequence for a first-order logic—the only significant aspect of individuals is that they have properties or may be related to each other. The eluci- dation could even be so successful that many people are happy to adopt the instrumentalist view. On this view, the primitive notions are seen as convenient fictions which help to make a workable and per- spicuous theory. However, with respect to possible world semantics, the instrumentalist view is rarely defended. Instead, one finds different forms of realism,
which are discussed under the headings 'real worlds' and 'abstract worlds'below.
3. Real Worlds
'I believe there are possible worlds other than the one we happen to inhabit.' This statement gives a flavor of the modal realism defended by David Lewis (1973, 1986). According to him, possible worlds are the objects we existentially quantify over when holding, as many of us do, that there are many ways things could have been. Lewis's position can be summarized in four theses (cf. Lewis 1973: 84-86; Stalnaker 1984: 45):
(i) Possible worlds exist, (ii) Other possible worlds are things of the same sort as the actual world, (iii) The indexical analysis of the adjective 'actual' is the correct analysis, (iv) Possible worlds cannot be reduced to any- thing more basic.
The third thesis should be understood as saying that the phrase 'the actual world' is always used by speak- ers to single out the world they are in. In absence of a further specification of what kind of entities 'possible
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