Possible-worlds theory

The theory of possible worlds (henceforth PW), a modern adaptation of a Leibnizian concept, was originally developed by philosophers of the analytic school (Kripke, Lewis, Rescher, Hintikka) as a means to solve problems in formal semantics. In the 1970s a group of literary scholars familiar with structuralist methods (Eco, Pavel, Dolezel) discovered the explanatory power of the PW model for narrative and literary theory, especially (but not exclusively) for the areas discussed below. Critics of the PW approach to narrative (Ronen) have argued that literary worlds are not the PWs of semantic logic in any rigorous technical sense; but this objection ignores the heuristic value of cross-disciplinary metaphorical transfers. Philosophers themselves have invited the analogy by comparing PWs to ‘the book on’ or ‘the story of ’ a world.

The basis of the theory is the set-theoretical idea that reality -- the sum of the imaginable -- is a universe composed of a plurality of distinct elements. This universe is hierarchically structured by the opposition of one well-designated element, which functions as the centre of the system, to all the other members of the set. The resulting structure is known as ‘modal system’, or M-model (Kripke). The central element is commonly interpreted as ‘the actual world’, and the satellites as merely possible worlds. For a world to be possible it must be linked to the centre by a so-called ‘accessibility relation’. The boundary between possible and impossible worlds depends on the particular interpretation given to the notion of accessibility. The most common interpretation associates possibility with logical laws; every world that respects the principles of non-contradiction and the excluded middle is a PW. More controversial is the problem of the nature of the property that designates one world as actual. Two theories of actuality stand out among the various proposals. The first, proposed by Lewis, regards the concept of actual world as an indexical notion whose reference varies with the speaker. According to Lewis, ‘the actual world’ means ‘the world where I am located’, and all PWs are actual from the point of view of their inhabitants.The other theory, defended by Rescher, states that the actual world differs in ontological status from merely possible ones in that this world alone presents an autonomous existence. All other worlds are the product of a mental activity, such as dreaming, imagining, foretelling, promising, or storytelling.

The primary logical purpose of this model is to formulate the semantics of the modal operators of necessity and possibility. A proposition asserting the possibility of a state of affairs p is true when it is verified in at least one of the worlds of the system; a proposition asserting the necessity of p must be true in all the worlds; and a proposition asserting impossibility must be false in all of them. The model has also been found useful for the formulation of the truth conditions of counterfactuals and for the characterisation of the distinction between intension and extension (or sense and reference).

Possible worlds and the semantics of fiction

Before the advent of PW theory it was almost sacrilegious to mention the issue of truth in relation to literary works. Recourse to the notion of PW makes it possible to talk about the truth of the propositions asserted in fictional texts without reducing these texts to a representation of reality. In a work like Doktor Faustus by Thomas Mann, for instance, we are invited to give equal credence within the fictional world to the musicological discussions and to the conversation of the hero with the devil. But as Pavel has argued, we are also entitled to regard the musicological discussions as potentially accurate information about the real world: readers occasionally use fiction as a source of knowledge. Fictional propositions can thus be evaluated in different reference worlds. While they may be true or false of worlds that exist independently of the text in which they appear, they are automatically true of their own fictional world by virtue of a convention that grants declarative (or performative) force to fictional statements: unless its narrator is judged unreliable, the fictional text gives imaginative existence to worlds, objects, and states of affairs by simply describing them. In creating what is objectively a non-actual PW, the fictional text establishes a new actual world which imposes its laws on the reader and determines its own horizon of possibilities.

In a key article, Lewis proposed to extend his pioneering analysis of counterfactuals to the problem of the truth of statements made about (rather than found in) fiction. According to Lewis, a counterfactual statement of the form ‘if p had been the case then q would have been the case’ is true for an evaluator if the PWs in which both p and q are true are closer, on balance, to the actual world than the worlds in which p is true and q is false. A statement referring to a fictional world may be compared to an ‘if p then q’ statement in which the text specifies p and the reader provides q as an interpretation of p. The statement ‘Emma Bovary was unable to distinguish fiction from reality’ translates as: ‘if all the facts stated by Flaubert’s text about Emma Bovary were true then it would be true that she was unable to distinguish fiction from reality’. This analogy enables Lewis to formulate the truth conditions for statements about fiction in the following terms: a sentence of the form ‘in the fiction f, p’ is true when some world where f is told as known fact and p is true differs less, on balance, from the actual world than does any world where f is told as known fact and p is not true.

This analysis entails a principle which has come to be recognised as fundamental to the phenomenology of reading. Variously described as ‘the principle of minimal departure’ (Ryan), the ‘reality principle’ (Walton), and the ‘principle of mutual belief’ (Walton again), the principle states that when readers construct fictional worlds, they fill in the gaps in the text by assuming the similarity of the fictional world to their own experiential reality. This model can only be overruled by the text itself; thus, if a text mentions a blue deer, the reader will imagine an animal that resembles her idea of real deer in all respects other than the colour. The statement ‘deer have four legs’ will be true of this fictional world, but the statement ‘deer have a single horn, and it is made of pearl’ will be false, unless specified by the text.

The principle of minimal departure presupposes that fictional worlds, like the PWs postulated by philosophers, are ontologically complete entities: every proposition p is either true or false in these worlds. To the reader’s imagination, undecidable propositions are a matter of missing information, not of ontological deficiency. This view is not unanimously endorsed by theorists. The main dissenter is Dolezel, who regards incompleteness as the distinctive feature of fictional existence. He argues that by filling the gaps, the reader would reduce the ontological diversity found in fictional worlds to a uniform structure, namely the structure of the complete, Carnapian world. Dolezel further believes that a filling of gaps would neutralise the effect of the strategies of showing and hiding that regulate the disclosure of narrative information -- strategies which determine the ‘texture’ of the text and its degree of informational saturation. It is not insignificant, for instance, that visual information and the surname of the hero are suppressed in Kafka’s The Trial. This raises the question of the location of gaps: are they part of the texture of the text, or do they belong to the fictional world itself? One way or another, however, gaps can only be apprehended against a full background: the incomplete texture of the text compared to the completeness of the fictional world for the proponents of minimal departure; the incompleteness of the fictional world compared to the fullness of the real world if gaps belong to the ontological fabric of the fictional world.

Whereas Dolezel regards the imaginative domain projected by fiction as less than a complete PW, Ryan argues that this domain encompasses not just one world but an entire modal system. In contrast to modes of expression that refer to the non-actual in a hypothetical mode, such as if…then statements, fiction includes both factual and non-factual statements. The former outline a textual actual world (TAW), while the latter allude to the virtualities of the fictional system. The contrast actual/non-actual is thus reinscribed within the textual universe. Author and reader engage in an act of make-believe by which they relocate themselves as narrator and narratee in TAW. This imaginative relocation results in a reorganisation of the modal system around a new centre. Through the concept of playful recentring this proposal reconciles the indexical theory of actuality proposed by Lewis with Rescher’s absolutist view. From the point of view of the ‘actual actual world’ the worlds of fiction are discourse-created non-actual possible worlds, populated by incompletely specified individuals; but to the reader immersed in the text the TAW is imaginatively real, and the characters are ontologically complete human beings.

Possible worlds and narrative semantics

As a model for narrative semantics, PW theory is applicable to both fiction and non-fiction. The need for a semantic model that recognises different propositional modalities was recognised in the early seventies by Todorov and Bremond. Both insisted on the importance of hypothetical events for the understanding of the behaviour of characters. Every intent-driven action, for instance, aims at preventing a possible state of affairs, thus making it forever counterfactual, and at actualising another state. To capture the logic of action, narrative semantics should therefore consider both the factual events of the TAW and the virtual events contemplated by characters. The mental representations of characters can be conceived as the PWs of a modal system. Eco describes the narrative text as a ‘machine for producing PWs’ (1984: 246). He has in mind three types of worlds:

1. The PW imagined and asserted by the author, which consists of all the states presented as actual by the fabula.

2. The possible subworlds that are imagined, believed, wished (etc.) by the characters.

3. The possible subworlds that the reader imagines, believes, wishes (etc.) in the course of reading, and that the fabula either actualises or ‘counterfactualises’ by taking another fork.

The worlds of type 2 are formally described by PW theorists as sets of propositions governed by modal operators, or predicates of propositional attitude (Eco, Vaina, Dolezel). These predicates distinguish various domains of mental activity: worlds of beliefs (the epistemic system), of obligations (the deontic system), of desires (the axiological system), and of actively pursued goals and plans. The propositional content of these private worlds enters into a system of compatibilities which defines the relations of antagonism or cooperation between the characters, as well as the points of conflict in the narrative universe. The relation between hero and villain can for instance be characterised as pursuing p versus pursuing ~p. Ryan further divides the private worlds of characters into representations of existing material or mental worlds (beliefs), static model-worlds, which capture how the actual world should or will be (obligations, desires, predictions), dynamic model-worlds, or intention-worlds, which project courses of events leading to goal states (the active plans of characters), and fantasy worlds which outline new systems of reality, complete with their own actual and possible worlds (dreams, hallucinations, acts of imagination, fictions-within-fictions). Whenever a proposition in a belief or model world becomes unsatisfied in the actual world, the narrative universe falls into a state of conflict. The general goal of characters is to resolve conflict by aligning all of their private worlds with the TAW. An action, event, or property is narratively relevant (rather than purely descriptive) when it affects, through a causal chain, the relations among the worlds of the system. The plot of the narrative text captures the movement of individual worlds in the global narrative universe. It does not end when all conflicts are resolved, for conflict is a permanent state of any universe, but when all the remaining conflicts cease to be productive because their experiencer is no longer willing or able to take steps toward their resolution.

Narrative-worlds typology and genre theory

As already mentioned, the logical interpretation of possibility is not the only conceivable one. A typology of narrative worlds can be obtained by narrowing down the criteria of possibility and by varying the notion of accessibility relations. In a broad sense, possibility depends not only on logical principles but also on physical laws and material causality. Following this interpretation, narrative worlds can be classified as realistic or fantastic, depending on whether or not the events they relate could physically occur in the real world. Maître, for example, distinguishes four types of narratives: (1) Works involving largely accurate reference to actual historical events (true fiction, creative nonfiction, or roman à clefs). (2) Works dealing with imaginary states of affairs which could be actual (strongly realistic texts). (3) Works in which there is an oscillation between could-be-actual and could-never-be-actual (Todorov’s conception of the fantastic). (4) Works dealing with states of affairs which could never be actual (Todorov’s marvellous). This typology can be refined by introducing other criteria of compossibility: a world can be declared accessible from AW if it presents a common geography or history; if it is populated by the same natural species; if it is in the same stage of technological progress; if its human inventory includes the population of AW; if it may be reached without time travel, etc. Every genre defined by its content can be described through a particular set of broken and preserved relations, true fiction breaking the fewest, and nonsense verse the most. But one set of values for accessibility relations is not always sufficient to classify a textual world. Narratives may present what Pavel calls a dual or a layered ontology. In this case the domain of the actual is split into sharply distinct domains obeying distinct laws, such as the sacred and the profane, the realm of the gods and the realm of humans, or the knowable and the unknowable. The lines that divide narrative worlds may be cultural and ideological as well as strictly ontological. The deontic system can for instance describe a world (real or fictional) in which some beliefs are obligatory, others permitted, and yet others forbidden.

Poetics of postmodern narrative

Though the idea of a centred system of reality is contrary to its ideology, the postmodern imagination has found in the concepts of PW theory a productive plaything for its games of subversion and self-reflexivity. McHale characterises the transition from modernism to postmodernism as a switch from epistemological to ontological concerns. Whereas modernism was haunted by the question ‘What can I know about myself and about the world’, postmodernism asks more radically: ‘What is a world?’ ‘What makes a world real?’ ‘Is there a difference in mode of existence between textual worlds and the world(s) I live in, or are all worlds created by language?’ The ontological inquiry of postmodern literature takes a variety of forms: (1) Challenging the classical ontological model through branching plots that lead to plural actual worlds, or through the blurring of the distinction between actuality and possibility -- no world in the system assuming the role of ontological centre. (2) Thematisation of the origin of narrative worlds in mental processes and questioning of the relation creator-creature. (3) Exploitation of the relation of transworld identity through the migration of characters from one narrative universe to another. (4) Extension of the principle of minimal departure to textual worlds through postmodern rewrites (the world of the rewrite being construed as the closest possible to the world of the original). (5) Blocking of the principle of minimal departure through the creation of impossible objects, inconsistent geographies, and radically incomplete beings. (6) Recursive applications of the gesture of recentring through the Chinese box effect of fictions within fictions. (7) Entangling of diegetic levels, trompe-l’oeil effects, play with world boundaries, and what McHale calls ‘strange loops’: repeated shifts into higher narrative levels which eventually lead back to the original level. (8) Subversion of the hierarchy of accessibility relations, through the creation of hybrid worlds situated at the same time very close and very far from experiential reality (magical realism). (9) Fascination with the scenarios of counterfactual history and creation of fictional universes in which the real and the possible exchange places. (In such worlds characters may ask: ‘What would have happened if Hitler had not won the war’.) (10) Multi-stranded or parallel plots that play simultaneously in separate ontological domains, such as reality and computer-generated virtual worlds.

References and Further Reading

Dolezel, Lubomír (1998) Heterocosmica: Fiction and Possible Worlds, Baltimore: Johns Hopkins UP.
Eco, Umberto (1984) The Role of the Reader: Explorations in the Semiotics of Texts, Bloomington: Indiana UP.
Kripke, Saul (1963) ‘Semantical Considerations on Modal Logic’, Acta Philosophica Fennica, 16, 83-94.
Lewis, David (1978) ‘Truth in Fiction’, American Philosophical Quarterly, 1, 37-46.
Maître, Doreen (1983) Literature and Possible Worlds, Middlesex: Middlesex Polytechnic P.
McHale, Brian (1987) Postmodernist Fiction, New York: Methuen.
Pavel, Thomas G. (1986) Fictional Worlds, Cambridge, Mass.: Harvard UP.
Rescher, Nicholas (1979) ‘The Ontology of the Possible’, in M. Loux (ed.) The Possible and the Actual: Readings in the Metaphysics of Modality, Ithaca: Cornell UP.
Ronen, Ruth (1994) Possible Worlds in Literary Theory, Cambridge: Cambridge UP.
Ryan, Marie-Laure (1991) Possible Worlds, Artificial Intelligence, and Narrative Theory, Bloomington: Indiana UP.
Vaina, Lucia (1977) ‘Les Mondes possibles du texte’, Versus,17, 3-13.
Walton, Kendall (1990) Mimesis as Make-Believe: On the Foundations of the Representational Arts, Cambridge, Mass: Harvard UP.