Possible Worlds Semantics

The use of possible worlds as a part of a semantic theory of natural language is based on the t ruth-conditional theory of meaning, that is, that the meaning of a sentence in a language is constituted by the conditions under which that sentence is true. On this view, to know the meaning of a sentence is to know what the world would have to be like if that sentence were true. If the way the world is construed as the actual world, then other ways the world could be may be thought of as alternative possible but nonactual worlds. Knowing how the world would be if a particular sentence were true does not require knowledge of whether it is true, because in a given world w, a person need not know in w that w is the actual world. Thus, if I know the meaning of "Wellington is the capital of New Zealand," I do not have to know whether in fact it is the capital, but I do have to know what it would be like for it to be the capital. In possible worlds terms I have to know of any given world w, whether w is a world in which the sentence is true or whether w is a world in which it is false, but I do not have to know whether w is the actual world. To know which world is actual would be to be omniscient.

Our language has to be able to talk about things that may not exist. In a sentence that has become rather famous in the semantical literature, "Someone seeks a unicorn," there need be no particular unicorn that is being sought, and so in some way the idea of a unicorn, a creature that does not actually exist, has to be involved in the content of that sentence -- a sentence, moreover, that all of us understand.

Possible worlds semantics is used in compositional theories of meaning, where the meaning of a complex sentence is to be obtained from the meaning of its parts (see COMPOSITIONALITY). It developed from the languages of MODAL LOGIC where the meaning of "p is true by necessity" (written Lp or  p) is obtained from the meaning of p by specifying the worlds in which Lp is true given the worlds in which p is. To be specific, Lp is true in w provided p is true in every w' possible relative to w. Dual to necessity is possibility. "It is possible that p" (written Mp or p) is true at a world w if p itself is true in at least one w' possible relative to w. A more elaborate example is found in the semantics of counterfactual sentences. Where p   q means that if p were the case, then q would be too, then (on one account) q is true in a world w iff there is a world w' in which p and q are both true that is more similar to w than any world in which p is true but q is not. In studying these as logics it is customary (depending on which logic is being studied) to set up first a structure in which relations are given to specify that one world is or is not possible relative to another, or that a world w1 is further from a world w 2 than a world w3 is. But for studying natural language we cannot assume that any particular words like "possibly" are in any way special.

Typically, an implementation of possible worlds semantics for a language will require the language to be specified by a system of rules that give the LOGICAL FORM of every sentence. Then values are assigned to the simple symbols of a sentence in logical form in such a way that a set of indices (worlds, times, speaker, and whatever else is involved in the meaning of the sentence) emerges as the meaning of the final sentence. Thus in the sentence "Possibly Felix lives," the name "Felix" will have a person Felix as value, the verb "lives" will have as its value an operation that associates with an individual (in this case Felix) the set of worlds (and times) at which that individual lives; the adverb "possibly" will have as its value an operation that associates with a set of worlds (in this case the set of worlds in which it is the case that Felix lives) another set of worlds, in fact all the worlds from which the worlds in the first set are possible. The final sentence will then be true in a world w if there is a world w' possible relative to w, such that w' is in the set assigned to "Felix lives," that is, in the set of worlds in which Felix lives.

To deal with tensed languages worlds can be thought of as worlds at times. More neutrally these are called "semantical indices." Possible worlds semantics requires supplementation by generalizing such indices in various ways. Thus, to interpret "I" in a sentence like "I'd like an apple," one needs an index to supply a speaker (or someone regarded as the speaker). To interpret a sentence like "Everyone is present" one requires an index to supply a domain of people, because the sentence is presumably not intended to claim that everyone in the world is present, but only everyone in some contextually provided universe.

Possible worlds semantics abstracts from many features of linguistic behavior that have sometimes been thought important, though the extent to which this should be done can be controversial. Thus, for some possible worlds theorists the ascription of truth conditions to a sentence is intended to be completely neutral on the question of what an utterance of that sentence is being used to do. It might be being used to report a fact or issue an order or ask a question. Other theorists may be more hesitant to speak of nondeclaratives as having truth conditions. But perhaps more importantly for cognitive science, the ascription of truth conditions to a sentence is neutral on the question of just how those truth conditions are represented in the mind of a speaker. It is concerned with the question of how to categorize what constitutes a representation's having a certain content, not on the nature of the representation itself.

Possible worlds semantics as such can be neutral on the metaphysical status of possible worlds. At one extreme is the view that other possible worlds are just as real as the actual world. At another extreme is the view that possible worlds are no more than linguistic descriptions of how the world might be. For certain limited purposes, as for example in describing the language of a computer where the possibilities that can be represented are fixed and limited, it may be plausible to consider worlds to be descriptions. But it is plausible to claim that a general theory of MEANING should not presuppose any particular way of representing worlds.

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-- Max Cresswell

Further Readings

Cresswell, M. J. (1973). Logics and Languages. London: Methuen.

Cresswell, M. J. (1978). Semantic competence. In F. Guenthner and M. Guenthner-Reutter, Eds., Meaning and Translation. London: Duckworth, pp. 9-43. Reprinted in M. J. Gresswell, Semantical Essays 1988. Dordrecht: Kluwer, pp. 12 - 33.

Cresswell, M. J. (1985). Structured Meanings. Cambridge, MA: MIT Press/Bradford Books.

Cresswell, M. J. (1994). Language in the World. Cambridge: Cambridge University Press.

Lewis, D. K. (1972). General semantics. In D. Davidson and G. Harman, Eds., Semantics of Natural Language. Dordrecht: Reidel, pp. 169-218.

Lewis, D. K. (1973). Counterfactuals. Oxford: Blackwell.

Lewis, D. K. (1975). Languages and language. In K. Gunderson, Ed., Language, Mind and Knowledge. Minneapolis: University of Minnesota Press, pp. 3-35.

Lewis, D. K. (1986). On the Plurality of Worlds. Oxford: Blackwell.

Loux, M. J., Ed. (1979). The Possible and the Actual. Ithaca: Cornell University Press.

Putnam, H. (1975). The meaning of "meaning." In K. Gunderson, Ed., Language, Mind and Knowledge. Minneapolis: University of Minnesota Press, pp. 131-193. Reprinted in H. Putnam, Mind, Language and Reality (1975). Cambridge: Cambridge University Press, pp. 215 - 271.

Schiffer, S. (1987). Remnants of Meaning. Cambridge, MA: MIT Press.

Stalnaker, R. C. (1968). A theory of conditionals. In N. Rescher, Ed., Studies in Logical Theory. Oxford: Blackwell, pp. 98-112.

Stalnaker, R. C. (1978). Assertion. In P. Cole, Ed., Syntax and Semantics, vol. 9: Pragmatics. New York: Academic Press, pp. 315-332.

Stalnaker, R. C. (1984). Inquiry. Cambridge, MA: MIT Press.

Stalnaker, R. C. (1989). On what's in the head. In J. E. Tomberlin, Ed., Philosophical Perspectives 3: Philosophy of Mind and Action Theory. Atascadero, CA: Ridgeview Publishing Co., pp. 287-316.