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The problem of impossible fictions.

"In fiction, anything is possible." This statement appears to be such a truism about literature that its utterance seems hardly necessary. And yet the implicit assumption in this platitude is that those events and circumstances whose realization in the actual world is practically impossible are nevertheless possible in the realm of fiction. The notion of an "impossible fiction" is an ostensible oxymoron. Traditionally, according to theorists of possible-world semantics, impossible worlds are those worlds that violate the foundational principles of classical logic: the laws of noncontradiction and bivalence or the excluded middle. Such worlds, considered so radically different from the actual world we inhabit, are thought to be inaccessible. However, as Marie-Laure Ryan has noted, logical impossibility is but one conceivable form of an impossible world. Other forms include physical, causal, taxonomic, temporal, and geographic inaccessibility.(1) She writes that "genres will be defined on the basis of the number of accessibility relations linking FW (the fictional world) to the culturally predominant representation of AW (the actual world). The greater the number of accessibility relations, the shorter the distance from AW to FW" (Ryan, "Possible Worlds" 536).(2) A number of fictional works, though, are constructed taxonomically and/or physically in radically different ways from the actual world particularly in science fiction and fantasy. Though such worlds would naturally be considered as impossible, they are more often construed as highly improbable. Their eventuality is significantly minuscule but nevertheless not impossible, according to Ryan ("Possible Worlds" 538).

Not only is the transgression of taxonomic and physical norms possible in fiction, but in the development of so-called "postmodernist fiction," the once sacred laws of logic have been opened to violation as well. The logically impossible is a salient feature in the fictional universe of many works in recent literature.

A TYPOLOGY OF IMPOSSIBLE FICTIONS

In all, there are roughly five principle types of impossible fictions. One form explicitly violates the logical law of noncontradiction and might also be described as a sous-rature world, a world under "erasure." Another type is the so-called "forking-path" fiction, where more than one narrative path or possible world becomes actual at the same time. A third example is the "squaring-the-circle" fiction, where otherwise logically consistent fictions have a capacity to lead to logical paradoxes. A fourth division is the mixing or traversing of ontological levels in a fictional work, what might be called "diegetic violations." The final type of impossible fictions is that of characters inhabiting more than one fictional world: in other words, the problem of the compossibility of characters.

1. CONTRADICTIONS AND SOUS-RATURE WORLDS

An event might be described by a narrator as having taken place in a fictional work, only to be asserted subsequently as not having occurred. It cannot be the case, at the same temporal moment and in the same geographic location, that an event has occurred and not occurred. This is a transgression of the first fundamental principle of informal logic. An example might be found in Alain Robbe-Grillet's La maison de rendez-vous, where Edouard Manneret's death occurs in more than one temporal moment. Johnson hears of his murder from the police yet still manages to call on him later that evening. Kim, his murderer, finds his corpse after having killed him, only to reencounter a living Manneret waiting for her in a room. Manneret manages to be alive after having been found dead, clearly a contradiction.

In Brian McHale's useful inventory of characteristic impossibilities, he discusses what he calls sous-rature worlds, worlds under erasure, which are usually withdrawn immediately after their construction only to be reinvoked. "First one state of affairs is projected.... [T]hen that state of affairs is recalled or rescinded.... [F]inally the erased state of affairs is replayed ..." (McHale 99). This type of impossibility is similar to the transgression of the law of noncontradiction in that two contrary states of affairs are summoned simultaneously. The effect of erasure is a conspicuous effacement, leaving behind the trace of what was created. This effect has dual aspects: "destabilizing the ontology of this projected world and simultaneously laying bare the process of world construction" (McHale 101). The reader's expectation of undergoing an immersive experience in reading the text is seemingly undermined in the strategy of sous-rature, as the text instead reflects on its own construction.

One particular instance of McHale's notion of sous-rature might be noted in Robbe-Grillet's use of the interruptive "retake" in works such as Project for a Revolution in New York, which represents something similar to the cinematic intermission or the intervention of a film's director.(3) Reflecting on retake's use in the text, the narrator claims that the word "means to continue something that had been interrupted for some reason" when in fact the device serves to do the exact opposite: to discontinue the narration by interrupting it, which is rather similar to its use in the cinema (Robbe-Grillet 132). The narrator's interpretation of the "retake" is in fact counterintuitive, or contrary to its common sense understanding. After the story splits into pieces, the term appears in order to help the audience to "tell where they are," according to the narrator. McHale claims that the notion of "retake" really does not function in the manner prescribed by the narrator but instead demonstrates the "ontological instability" of the text. Thus, its use is ironic and of no assistance in understanding the narrative. But McHale misses the point of the term supposedly helping the audience to "tell where they are." He fails to see that the term functions metafictionally rather than fictionally. Where the readers are, in fact, is in a textual universe that precludes their full immersion whereas the phenomenological experience of reading a realistic novel usually elicits the absorption that Robbe-Grillet's work prevents. In a certain sense, Robbe-Grillet can be credited with having invented another kind of realistic text, as well, but one that calls attention to the experience of reading, the performative aspect of narration, as well as the intrafictional events being described. Postmodern fictions tend to draw attention to themselves as fictions whereas "realistic" ones tend not to. In this sense, postmodern fictions are more completely realistic though their transgressions of normative logical principles indicate that they be seen as less than realistic.

Kendall Walton has characterized the kind of experience associated with reading such novels as that of "appreciation without participation" (274). Certain works, like those of Robbe-Grillet, prevent audience involvement in the sense of psychological participation. Rather than being participants in an immersive game of make-believe,(4) the audience is said to occupy a stance "akin to that of an onlooker" in a spectator sport (Walton 274). Although the appreciation of such works is necessarily "distanced," they can nevertheless be "enormously provocative, entrancing, satisfying" (274-75). Walton cites the work of Italo Calvino and William Thackeray in support of this view. While rightly recognizing that postmodern fictional devices, such as those employed by Robbe-Grillet, are capable of eliciting the reader's appreciation, Walton, nevertheless, does not see the possibility that the employment of such techniques as logical impossibility and the erasure of worlds can themselves be immersive but not in the same sense as the normative narration employed in such texts as realistic or even fantastic novels. Indeed, many onlookers at sporting events are immersed in the game being viewed as psychological rather than actual participants. Such games are not ones of make-believe, yet they are no less immersive. Consequently, the analogy of spectator sports is not a very good one.

2. FORKING PATHS

Another type of impossible fiction is the so-called "forking path" variety, the simultaneous existence of more than one actual, logically consistent world. Jorge Luis Borges's "Garden of Forking Paths" is the exemplary case though John Fowles's French Lieutenant's Woman and the computer-assisted writing technique, "hypertext," serve as additional examples. Borges's story might actually be seen as a case of "pan-possibility," where not one possible world is invoked but all possible worlds enabled by the text. The "almost unfathomable Ts'ui Pen" - the author of a virtual, "chaotic" novel - chooses all possible paths, or narrative alternatives, simultaneously. In such a text, there are no possible counterfactuals since all possible alternatives are invoked. To choose all of an infinite number of narrative paths is impossible given the finite confines of a textual world. Yet such a choice is nevertheless conceivable in terms of the metalanguage used to describe it (the author chooses all possible paths simultaneously) though such a text is practically unfathomable because we could not imagine what it would look like. Borges's short story "The Garden of Forking Paths" is a metafiction on an impossible fiction, The Garden of Forking Paths, whose theme is the paradox of time. How is it possible for a book to be infinite? This is the problem Borges tries to address in constructing the story. A novel structured in a circular fashion, like Finnegans Wake, where the last line returns the reader to the beginning, is one possibility though the textual space of the book is still finite even while its temporal dimension is presumably infinite. Ts'ui Pen's text, contrary to Borges's account, is both temporally and spatially infinite, for any text that includes all counterfactual possibilities would necessarily be infinite in length.

3. "SQUARING-THE-CIRCLE" FICTIONS

A third form of impossibility might be called "squaring-the-circle" fictions, where ostensibly logically consistent fictional works nevertheless exhibit a capacity that could lead to paradoxes. One example would be time travel, a conundrum for a number of physicists and philosophers, despite efforts by H. G. Wells and others to depict such circumstances in science fiction. Michael Dummett(5) has noted a particularly troubling case of an art critic returning from the future to the twentieth century to meet a painter regarded in the critic's epoch as a magnificent artist. However, the critic sees the painter's current work as mediocre and determines that the artist has yet to paint his masterpieces. The critic shares some reproductions of this later work from a book that he possesses, and the artist, upon seeing them, covertly pilfers the book and reproduces these works from the book after the critic returns to the future in his time machine. The paradox invoked in this instance is that there are no originary masterpieces, only various reproductions. Another instance of the paradox of time travel is the example of someone who returns to a point in time prior to his birth in order to murder his father, thereby preventing his birth. This circumstance would imply that at any temporal moment during the span of this person's life, he would both exist and not exist, clearly a contradiction.

4. DIEGETIC VIOLATIONS

The transgression of ontological levels would constitute a fourth type of fictional impossibility. These might be described as paradoxical or "Escher-types" of narrative constructions or in Gerard Genette's terms, "metalepsis." In Douglas Hofstadter's parable, Achilles and the Tortoise are able to "push into" and "pop out from" Escher paintings, which in themselves constitute transgressions of ontological levels. They accomplish these intrusions in a narrative called "Djinn and Tonic," which is being read by an Achilles and a Tortoise in a story invented by Hofstadter. What has come to be called postmodernist fiction not only violates logical, physical, and taxonomic rules; it also actualizes the seeming impossibility of one world encroaching upon another. Postmodernist fiction accomplishes this feat primarily through embedded or nested narrative levels. Embedded narratives, or Chinese-box-worlds,(6) allow for the possibilities of infinite regress, trompe-l'oeil, and metalepsis to operate in the fictional world. Though the infiltration of imagined worlds into the actual world from which they are imagined is technically impossible from the standpoint of the actual world, many writers exploit this concept in the fictional world. Julio Cortazar offers a good case of metalepsis in his story "Continuity of Parks," where the hierarchy of ontological realms is transgressed as the second-order fictional level intrudes upon the first-order one, that of a person reading about the second. From the perspective of narrativity, Cortazar's text is an ontological paradox very much akin to the visual representations of Escher. On the metaphorical level, his text is an allegory of immersive reading, where the reader imagines himself as part of the story, empathically entering the undefined character that the killer plans to murder. Another example might be found, as well, in Robbe-Grillet's Project for a Revolution in New York. In this instance, the narrator hears the click of a lock and, in an empathic reverie, imagines that he, himself, has left his key on the right-hand side of a marble table next to a brass candlestick after departing from his apartment. The daydream leads him to forget or erase the circumstances that led to it (the clicking of the lock), and he concludes (rightly, as it turns out) that "there must be a table in this dim vestibule" (Robbe-Grillet 5). There is no necessary relation between the turn of a lock and the presence of the table in the room enclosed by the door with the lock. But in this text, this logical relation is assumed. A false inference is derived, leading to a conclusion that turns out to be true. The problem stems from a conflation of the embedded world of the narrator's imagination with the diegetic level of the fictional world of the text, leading him to transpose the separate spaces of his apartment and the room he hears being locked.

The various postmodern devices of infinite regress, metalepsis, and trompe-l'oeil eschew the normative expectation of denouement. The same might be said for the similar device of mise-en-abyme. What all of these techniques have in common is an overlapping of diegetic levels or the mutual encroachment of ontological domains: in short, the conception and realization of the impossible.

5. MULTIPLE-WORLDS CAST OF CHARACTERS

The last type of impossible fiction is that of composite worlds importing characters or features from several other fictional works or worlds. In his book Mulligan Stew, Gilbert Sorrentino imports the characters Ned Beaumont from Dashiell Hammett's The Thin Man and Anthony Lamont from Flann O'Brien's At Swim-Two-Birds. This device violates the principle of the "compossibility" of characters. Only with respect to a retour de personnages, found in the works of Balzac and Faulkner, for example, is it possible for characters to appear in different texts, and in these cases the author must be the same for each text where the character recurs (McHale 57). With postmodern fiction, Sorrentino's being among several examples, it is possible for characters to appear from different works by different authors. Often in postmodern fiction, these characters are experienced more as radically incomplete literary constructs than as pseudoactual beings imagined as complete.(7) Perhaps no contemporary writer has been more liberal in building a pastiche from borrowed characters as Kathy Acker. Her entire corpus is composed of such entities, but seldom are they as fleshed out as in the original texts in which they appear. Examples include the appearances of the Marquis de Sade and Arthur Rimbaud as fictional characters, a presumed biography of Henri Toulouse-Lautrec, an autobiography of Pier Paolo Pasolini, and a Don Quixote appearing in punkish, modern New York.(8) Her most recent novel, My Mother: Demonology, contains a short chapter whose characters, Kathy and Heathcliff, are imported from Emily Bronte's Wuthering Heights. The novel itself is structured on the symbiotic love relationship between the French philosopher Georges Bataille and the tragic Laure (Claire Peignot), who become fictional characters in the novel. Acker's entire fiction can be seen as one vast, singular violation of the strictures of compossibility.

LITERARY THEORISTS OF IMPOSSIBLE FICTION

Three significant literary theorists have undertaken the problem of impossible fictions and have construed the notion of the "impossible" in fiction in more or less strict ways. Lubomir Dolezel, adhering to a classical notion of modality, has the most stringent notion of impossibility in fiction. Brian McHale's view is the most liberal, permitting nearly all conceptions of the impossible as possible in the fictional world. Umberto Eco's account lies between the two, but tends toward the axis proposed by Dolezel.

1. LUBOMIR DOLEZEL

The theory of fictional worlds advanced by Dolezel would seemingly deny the fifth type of impossible fiction, that of cross-world synthetic individuals.

According to Dolezel, "fictional worlds are formed by macrostructural constraints which determine the set of their compossible constituents" (234). These "compossible constituents," themselves, are comprised of "agential domains," which are constituted by the agent's "property set, his relation network, his belief set, his action scope, etc." (234). Thus, if the fictional world is composed of one agent, then the agential domain is equivalent to the entire fictional world. Fictional worlds composed of multiple agents are therefore "a set of agential domains held together by the macrostructural conditions of the agents' compossibility" (234). By implication, the fictions of an Acker or a Sorrentino are impossible because the agents borrowed from one fictional world in order to inhabit another (Acker's Don Quixote, for example) are not semantically the same. The agential domain has changed in certain key respects even if the proper name is the same, and this is the case even if reference is made to particular aspects of the agential domain of the original text. Thus, Acker's Quixote is not the same as Cervantes's even if the fictitious Pierre Menard's is the same (word for word, though of course richer, according to Borges). The agential domain has changed even if the proper name and physical characteristics have not.

As we shall see, Dolezel's view of impossible fictional worlds is very much like that of Umberto Eco. Dolezel states that these "worlds" "include inner contradictions, or imply contradictory states of affairs" (238). The problem with such impossible fictions is that "the authenticity of fictional existence is denied by the logico-semantic structure of the world itself. Literature offers the means for constructing impossible worlds, but at the price of frustrating the whole enterprise" (239). A reader cannot make believe that an impossible fictional world exists when the author frustrates every attempt at immersive involvement by drawing attention to the text's constructedness. In the end, Dolezel sees impossible fictional worlds as an allegory of "fiction-making as a trial-and-error procedure" (239). This interpretation is too general; it does not answer the question as to what such fictions reveal about the process of making fictions. Might there be a more significant purpose than the mere allegory of fictional construction?

2. UMBERTO ECO

Depending on one's theoretical allegiances, seemingly impossible fictions might be thought to be possible ones. Some view the realization of a logical impossibility in a fictional work as an indication that this seeming impossibility has become at least fictionally possible. Eco, who does not share this view, has argued that logically impossible propositions cannot constitute worlds. In order to construct a world, one must be able to make inferences about it. In a situation in which both p & -p can be asserted, anything at all might be inferred and the construction of a world becomes exceedingly difficult. Any possible world, therefore, cannot violate the laws of noncontradiction and excluded middle. The construction of logically impossible worlds in fiction serve, in McHale's terms, as "subversive critiques of worlds and world-building" (33). However, Eco's views are more complicated than a mere rejection of the concept of possible worlds that do not comport to the necessary truths of logic. He says that worlds where causal chains are closed (A caused B; B caused C; C caused A) or where a number like 17 is no longer a prime number "can be imagined and are intuitively possible" (Eco 234). The problem for Eco is not that such worlds cannot be conceived, but that they cannot be described in adequate detail. "Such a world is in fact quoted, but it is not constructed, or - if you want - extensionally mentioned, but not intensionally analyzed" (Eco 234). It is not enough to assert that the number 17 is no longer prime. The rule for carrying out its division must be provided along with the result. But this would be impossible for Eco because it would be impossible to compare two worlds with different logical systems without severely affecting our "metasemiotic instrument." It is only possible to introduce an unanalyzed logical variance, the suspension of a logical law. Thus, Borges's "Garden of Forking Paths" would serve as an example of Eco's notion of impossibility: we can mention a garden of forking paths but we cannot realize or analyze such a text given the forms of textual presentation available to us. For a writer like Borges, on the contrary, to conceptualize an infinite number of possible worlds in the finite space of a book is to posit the simultaneous selection of an infinite number of possible worlds as a possibility rather than an impossibility. In fact, what Borges has theorized is yet another logical impossibility: a possible world comprised of all possible worlds, including itself. This possible world would necessarily be part of yet another encompassing itself and all other possible worlds ad infinitum. Necessarily, such a world (or universe) would be impossible to fathom.

According to Eco, the presence of the logically impossible in the fictional realm functions more as an allegory in forcing the reader to question the operative laws of the actual world.(9)

the proper effect of such narrative constructions ... is just that of producing a sense of logical uneasiness and of narrative discomfort. So they arouse a sense of suspicion in respect to our common beliefs and affect our disposition to trust the most credited laws of the world of our encyclopedia. They undermine the world of our encyclopedia rather than build up another self-sustaining world. (Eco 234)

It seems, though, that Eco is too reductive in ascribing the use of logically impossible worlds in fiction to an allegorical functionalism. If this were indeed the primary purpose, why would fiction writers choose to violate logical laws rather than laws of some other kind? In what manner could the transgression of logical principles impact our understanding of the actual world? Or should we take authors of such works as having some other purpose?

3. BRIAN MCHALE

The breach of the law of noncontradiction, a device often employed in postmodernist texts, what McHale mistakenly calls the prevalence of excluded middles, can be defined as the simultaneous truth and falsity of a propositional ascription of a possible world.(10) This definition does not refer to the same thing as positing an impossible intermediate value between truth and falsity, which is the actual definition of the law of excluded middle. McHale points out that the realization of two mutually exclusive possible worlds is most apparent in Fowles's The French Lieutenant's Woman. In one case, Charles and Sarah are reconciled; in the other, they are not. A sort of "hypertext" with alternative forking paths is created, leaving the reader with the choice between the two. McHale calls this case a "nonending," given the obvious position of the alternative paths in the text. Once again, textual destabilization is noted as the primary effect.

McHale's typology of fiction would not seem to permit a notion of impossible fiction. He criticizes Eco, for example, for failing "to capture the full ontological peculiarity of a world in which events apparently both do and do not happen, or in which the same event happens in two irreconcilably different ways" (McHale 106). Thus, the violation of logical principles in postmodern fiction is not merely a "subversive critique of world-building," as Eco would have it, but a full-fledged imagining of a world where the impossible would be realized and its consequences explored. Eco is said to overestimate the allegory at the expense of the ontology.

THE PHILOSOPHY OF POSSIBLE WORLDS AND IMPOSSIBLE FICTION

Having examined the limitations of literary-theoretical approaches to impossible fiction, I will now turn to one of the most important philosophical writers on the discourse of possible worlds, David Lewis. As we shall see, Lewis's conception becomes more refined in his later work and can be registered to some extent as an improvement over other discussions. His account of fiction, however, is relatively incomplete when compared to McHale's.

1. DAVID LEWIS'S DEFINITION OF IMPOSSIBLE FICTION

While McHale subscribes to a broad notion of possibility in fiction so as to encapsulate postmodern fictions that explore impossibility, David Lewis's notion of impossible fictions is too restrictive. A number of conceivable transgressions of physical, taxonomic, technological, and temporal circumstances, though, are permitted in Lewis's metaphysics even if they must be characterized as highly improbable. An impossible fiction for Lewis is one in which "there is no world where it is told as known fact rather than fiction" (Lewis, "Truth in Fiction" 45). That there are serious problems with this formulation should be readily apparent. Presumably, Lewis means that an impossible fiction is impossible because in no way could it be said to describe a possible world.(11) But what makes such a fiction impossible remains to be answered. The notion of possible worlds in fiction suggests that any fiction could be true in some possible world, providing of course that this world is indeed possible. Another problem with this view is that it hinges too much on an illocutionary definition of fiction as pretense. An author of a fictional work pretends to tell the truth in some possible world. In an impossible fiction, such a pretended telling is not possible. Why not? Lewis does not address the characteristics of impossibility beyond two equally vague attributes. First, an impossible fiction might be impossible because its plot is impossible. This assertion, of course, begs the question as to how the plot is impossible. Secondly, Lewis proposes a scenario where no one is in a position to know or tell of the events in a possible plot. Thus, "to tell it as known fact would be to know its truth and tell truly something that implies that its truth could not be known; which is impossible" (Lewis, "Truth in Fiction" 4:5). It is very difficult to imagine this case as an impossibility since an omniscient narrator who knows everything can pretty much always be posited to tell any particular story. It is important to recognize that an illocutionary impossibility, such as omniscient narration, still leaves the world described and narrated as logically intact. In most cases, a fictional text's immersive capability leads its readers to forget the fact of an omniscient narrator telling the story. We separate the narrator from the world being described. Thus, omniscient narration has nothing to do with the notion of impossible fiction.

Lewis does suggest but does not elaborate on what some possible impossible fictions might involve: a man squaring a circle, an incoherent time-travel story, or contradictions in a story or stories resulting from an author's carelessness. Thus, the law of noncontradiction creeps in as a criterion of impossible fiction. Regarding this criterion, Lewis has written elsewhere that had he not been "such a commonsensical chap .... [he] might be defending not only a plurality of possible worlds, but also a plurality of impossible worlds, whereof you speak truly by contradicting yourself" (On the Plurality of Worlds 1). In the last example of authorial carelessness, truth claims about the text(s) have a range of undecidability. Lewis cites Conan Doyle's inconsistency in locating Watson's war wound on his body. In one case, the wound is thought to be on the shoulder and in another, on the leg. It is known that Watson has a single wound, but its location might be in two different places. Terence Parsons has pointed out that if it is the case that Watson has one injury in two different places, he would necessarily be an impossible object (Parsons 184). However, it is more likely that the war wound is undecidable in terms of the places where Conan Doyle located it in various stories. Where it is decidable is with regard to the locations he did not mention: for example, the neck. The decidability can only be negative not positive. But as Lewis hints at the end of his essay, the Holmes stories are not really impossible due to the inconsistency resulting from the author's lack of caution. The reader must exercise a principle of charity in such cases, concede the mistake, and focus his attention on more decidable matters.

In his "Postscripts to 'Truth in Fiction,'" Lewis tries to improve on his earlier formulation of impossible fiction. He concedes the possibility of an inconsistent fiction, seemingly equating impossibility with the infringement of the law of noncontradiction and offers some strategies for dealing with it. In inconsistent fictions, the reader might extract consistent fictions from within the inconsistent fiction except in very difficult cases where the reader is prevented from doing this. Lewis acknowledges that in these difficult instances, part of the author's intention in constructing them is to make such extraction almost impossible. He suggests two methods for extricating the truth in fiction: the methods of intersection and union, gradually assuming a preference for the latter.

method of intersection - [at] is true in the original fiction if [at] is true in every fragment

method of union - [at] is true in the original fiction if [at] is true in some fragment.

(Lewis, "Postscripts" 277)

In the method of intersection, something gets lost; in the method of union, consistency and "closure under implication" are lost. Nevertheless, and similar to McHale's argument against Eco on this matter, the ontological peculiarity of inconsistent fiction is preserved under the method of union. In the Holmes stories once again, Watson was wounded in some accounts in the shoulder, in others in the leg, but never both since he had but one wound. The method of union acknowledges both possibilities without deciding, while respecting the specification of one wound. The principle of charity mentioned previously leads us to the same conclusion. Lewis's enumeration of the strategies for approaching inconsistent fiction serves to enhance the reader's accessibility relation to such fictional texts. Paradoxically, Lewis has helped us to construe supposedly impossible fictions as possible.

Lewis's definition of impossible fiction seems at this point (in the "Postscripts to 'Truth in Fiction'") to be fictions that transgress the law of noncontradiction. This definition is much more clear and much less circular than his earlier one in "Truth in Fiction," where an impossible fiction is one that cannot be told as true (i.e., as nonfiction) of any world. Sometimes these violations are willful on the part of the author as we see with Robbe-Grillet, and occasionally they are unintended as in the Holmes stories. Lewis cites other examples, including Isaac Asimov's The End of Eternity, which alters its conception of time travel seemingly unintentionally, thereby becoming inconsistent (Lewis, "Postscripts" 277). Time travel, itself, is not impossible for Lewis; inconsistent time-travel stories, like the one mentioned of Asimov, are. These are probably inconsistencies of the unintended variety, which seem to bother Lewis more than the intended sort. "Not all science fiction writers are clearheaded, to be sure, and inconsistent time-travel stories have often been written. But some writers have thought the problems through with great care, and their stories are perfectly consistent" (Lewis, "The Paradoxes of Time Travel" 67). Lewis, then, does not seem to want to include certain technological, temporal, spatial, physical, and perhaps taxonomic impossibilities relative to the actual world we inhabit into the category of impossible fictions. Time travel, among other inventions in science fiction, is quite possible for Lewis.

Time travel, I maintain, is possible. The paradoxes of time travel are oddities, not impossibilities. They prove only this much, which few would have doubted: that a possible world where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours.

(Lewis, "Paradoxes" 67)

2. DAVID LEWIS ON ONTOLOGICAL IMPOSSIBILITY AND ITS RELEVANCE TO FICTION

Throughout his various philosophical writings, Lewis invokes the notion of possible worlds to expand the range of theoretical insight into a host of philosophical problems. Some of the seeming possibilities he acknowledges might strike the average reader as implausibilities. In nearly all the cases that Lewis manages to conjure up, the previously mentioned criteria of physical, taxonomic, technological, and temporal norms are capable of being transgressed in a possible world while the law of noncontradiction is not.

In his essay, "Mad Pain and Martian Pain," Lewis argues that any coherent theory of mind must take into account, must not deny the possibility of, both pains potentially suffered by a madman and those endured by a Martian. Under Lewis's supposition, the madman suffers pain according to different norms of cause and effect from those of an ordinary human being. The Martian, on the other hand, suffers pain in a significantly different physical realization from that of an ordinary human being. In Lewis's example, the Martian who feels pain experiences an inflation of fluid in many small cavities in his feet, and this experience causes pain. The point of invoking this set of possible worlds is to raise problems for a materialist theory of mind that would deny other possible causal networks or physical manifestations of pain.

the lesson of mad pain is that pain is associated only contingently with its causal role, while the lesson of Martian pain is that pain is connected only contingently with its physical realization. How can we characterize pain a priori in terms of causal role and physical realization, and yet respect both kinds of contingency?

(Lewis, "Mad Pain" 123)

Lewis creates a fiction in order to ascertain a dimension of a philosophical issue in the actual world, thus bringing a new meaning to the notion of "truth in fiction." While this example is not directly relevant to his theory of fiction in general, it illustrates that his notion of a possible world extends so far as to include significant taxonomic and physical dissimilarities from the actual world in the realm of the possible. The point in doing so in this instance is to indicate that the causal link between pain and the neural state that produces it might have been different. Pain is a "nonrigid" concept (Lewis, "Mad Pain" 125). The law of noncontradiction, on the other hand, is much more rigid. What is nonrigid allies rather closely with what Lewis can conceive of as a possible alternative. The notion of possibility is rather loose. It can encompass quite distant forms of experiences or local counterfactuals. "Though some possibilities are thoroughly otherworldly, others may be found on planets within range of our telescopes. One such planet is Mars" (Lewis, "Mad Pain" 126).

In his paper, "Counterparts of Persons and their Bodies," Lewis maintains that it is logically possible for one to switch out of one's body and into another. This view appears in the context of an argument for an identity theory between persons and bodies, which has a direct relevance to the discussion of the fifth category of impossible fiction concerning compossible entities. The possibility of switching bodies poses a problem to such a theory, and Lewis's purpose in writing the paper is to address it. In this sense, the counterfactual of a person switching his body is reminiscent of Lewis's discussion of mad pain and Martian pain. A fantastic possible world is postulated in order to address limitations in a particular theory. The idea of a person switching bodies might accordingly serve as a plot scenario for a fantasy novel. Counterpart theory in general was developed to answer for quantified modal logic some fairly technical problems, which are not directly relevant to the current discussion. Specifically, the notion of counterparts denotes a possible world where beings who happen to be counterparts of beings in the actual world perform certain actions that are counter-factual to actions performed in the actual world. In other words, counterpart theory is the theory of possible worlds as it applies to persons. Persons and bodies for Lewis are aggregates of stages, which taken together comprise the unity of the person and her body. "An enduring thing and its stages exist only in one world, but may have counterparts in other worlds" (Lewis, "Counterparts" 50). This sentence implies that an enduring person cannot be said to exist and perform certain actions in several possible worlds, but that counterparts to that person can exist and perform actions in different possible worlds (Lewis, "Counterparts" 49).(12) Stages, like enduring persons, can also have counterparts. A person and his counterparts, though, must be similar. As Lewis notes, one cannot have a counterpart that is a cockatrice if one is not otherwise a cockatrice. In a science-fictional universe, however, one could imagine the possibility of counterparts that did not resemble their counterparts in the textual-actual world. The essential properties of the person and his counterparts would not necessarily be physical but perhaps traits of personality. The physical could instead be an accidental property as, for example, the fairy tale where a prince is turned into a frog. The essence of the personality remains while the physical features change.(13) The relation of physical similarity in counterpart theory seems valid but not necessary.

Lewis's discussion of counterparts seems significant in the present account because he grants that the essence of personal identity is an aggregation of properties holding between actual persons and their counterparts (Lewis, "Counterparts" 54). In this sense, identity is both singular and plural simultaneously. Yet despite admitting the possibility of an actual person having an infinite number of counterparts, Lewis wants to impose limitations on how these counterparts might appear. A counterpart of Nixon must closely resemble Nixon in at least one of his various stages of existence. The counterpart of Nixon cannot resemble an elephant or else the counterpart of Nixon would no longer be a counterpart of Nixon but instead a counterpart of an elephant. This makes sense logically, but the idea of a stable identity that cannot transgress taxonomic limitations seems rather problematic. If one can imagine all sorts of possible things in a possible world, why could not one imagine a possible world where one is an elephant?

An impossible world for Lewis, at this point, is one where the principle of noncontradiction is violated and where the counterparts of persons are dissimilar to persons in the actual world. He provides one more case - the problem of transworld identity - which relates directly to the previous discussion of Chinese boxes and embedded fictions. The phantom murderer in Cortazar's "Continuity of Parks," who pursues the reader of the text from which the murderer appears, could not, in Lewis's view, perform any action, even murder, because he has crossed an ontological boundary. A person who crosses such a boundary can never be actualized in entirety but only in certain parts. Only parts of individuals can have transworld identity, not entire persons.

Accordingly, Lewis elaborates his theory of possible individuals in the "Postscripts to 'Counterpart Theory and Quantified Modal Logic.'" This theory poses problems for the fifth type of impossible fiction, that of compossible entities. Yet this theory is problematized by the existence of fictional worlds, Kathy Acker's Don Quixote, for example, composed of characters and events from other fictional worlds (in this case, obviously, the one created by Cervantes and perhaps Borges, as well). For Lewis, a world, like a person, is an aggregate of smaller units. "A world is a large possible individual; it has smaller possible individuals as parts" (Lewis, "Postscripts to Counterpart" 39). A possible individual is part of a world; it belongs to that world. "Worlds do not overlap; unlike Siamese twins, they have no shared parts .... [N]o possible individual is part of two worlds" (Lewis, "Postscripts to Counterpart" 39). Thus, any individual inhabiting more than one world would necessarily be construed as an "impossible individual," according to this view. Lewis admits as much. But strangely, the numbers of individuals exceeds the numbers of possible individuals. He writes:

I wish to impose no restrictions on mereological summation of individuals, hence I must grant that there are individuals consisting of parts from several worlds. But such a cross-world sum is not a possible individual. There is no way for the whole of it to be actual.

(Lewis, "Postscripts to Counterpart" 39)

The notion of possible individual in Lewis's sense is predicated on the potential for that individual to be actualized in the actual world. This suggests that his notion of possibility is more restricted in this instance than the notion of possible worlds, worlds that are capable of being conceived. Cross-world individuals, which are an aggregate of parts from numerous worlds, are individuals but are not possible individuals even though they may be comprised of possible individuals. Lewis goes so far as to say that he, David Lewis, is a possible individual comprising a part of a "counterpart-interrelated sum" made up of a number of possible individuals constituting a cross-world individual. We are not aware of this cross-world individual because she is not possible, not capable of being actualized. Yet, Lewis maintains that "there are many such" cross-world individuals (Lewis, "Postscripts to Counterpart" 41). In other words, any actual person residing in our world can be seen as a part of a cross-world individual, but since this individual is comprised of a multiplicity of possible individuals from numerous possible worlds, it can never exist as a whole in the actual world. Not only can any actual person be seen as such, according to Lewis, but each one of us in the actual world is such a part of some cross-world individual.

Mereological individuals exist but they are not possible. This is an apparent paradox in Lewis's account of cross-world individuals but not an actual one. Mereological individuals, comprised of the sum of all possible counterparts, cannot be actualized in one world. In other words, Lewis conceives of a mode of existence compatible with impossibility in the sense of being nonactualizable in one world. If we elide the distinction between conceivable modes of existence and possible individuals, then mereological individuals must be seen as possible rather than impossible. We are capable of such a maneuver in a fictional world, but such worlds must be construed as possible in a broader sense than the notion of possible worlds more generally. Thus, Lewis's discussion of the impossibility of mereological individuals cannot be seen as relevant to his notion of impossible fiction. Ontological possibility is a narrower concept for Lewis than logical possibility.

CONCLUSION

It seems to me that Lewis's notion of possibility is construed far too narrowly to account for fiction, providing, of course that we view impossible fictions as fictions with impossible worlds (not tellable as true of one world or containing contradictions). However, as we have seen, Lewis acknowledges that impossible fictions exist even though they are not possible in the same way as mereological individuals exist even though they are not possible. By extension, Lewis would probably acknowledge that fictional worlds composed of mereological individuals could exist even if none have yet been written. These fictions would be impossible but would nonetheless exist. In contrast to Lewis, McHale, despite his misunderstanding of formal logic, has a more complete account of fiction generally. The concept of impossibility as a trope has been attached to any number of conceivable but unrealizable experiences in the actual world that have been nevertheless realized in the fictional and artistic worlds more generally. The trompe-l'oeils of an Escher, the transworld fictional entities of Borges and Cortazar, and the transgressions of the law of noncontradiction in Robbe-Grillet and Hofstadter readily come to mind. Such seeming impossibilities can clearly be actualized in the fictional domain. They have been fathomed, if nothing else, though perhaps only in the limited sense of being capable of being mentioned, as Eco has argued, or capable of being described in a metalanguage. In this sense, what has been considered impossible has been rendered possible at least from the standpoint of our capacity to conceptualize the impossible. It should perhaps be noted that some logicians, such as Nicholas Rescher and Robert Brandom, have argued that worlds violating the principle of noncontradiction and the excluded middle, nevertheless, exhibit aspects of consistency and should not be characterized as impossible worlds but as possible ones that happen to be nonstandard. In this instance, the notion of possibility is construed quite broadly, and the problem of describing or explaining what nonstandard worlds are like becomes a dilemma of accessibility. Nonstandard worlds, though possible, are not capable of being expressed in the language of a standard world. Assuming this "logic of inconsistency," the problem of impossibility becomes one of inexpressibility.

Our five types of impossible fiction might be reduced at this point to three general categories of impossibility. The first type (a) is a fictional world that transgresses laws of logical possibility. Such a text is scriptible, and a fictional world is capable of being construed even if such a world is not completely coherent. The fictional worlds of a Robbe-Grillet would constitute a second type (b) of impossible fiction. In such worlds, so many contradictions occur that virtually nothing can be ascertained about the fictional world. It is extremely difficult for a reader to construct or imagine such a world. A third type of impossible fiction (c) is the type that cannot be written though it might be described generally in some metalanguage. "The Garden of Forking Paths" is one such case. Of the five types discussed earlier, type one (contradictions and sous-rature worlds) could be considered (a) or (b); type two would be (a) in the example of Fowles's French Lieutenant's Woman or (c) in the case of Borges's forking path; type three (squaring-the-circle fictions) is equivalent to (a); type four (diegetic violations) seems fairly close to (a); and type five would also be an instance of (a) since agential domains are altered when fictional entities are imported into different fictional worlds. Eco and Dolezel would seem to suggest that all three types of impossible fiction are truly impossible because they thwart or prevent the construction of worlds. Lewis would admit certain contradictions so long as a certain degree of decidability is maintained. He would admit the possibility of time travel, for example, despite the implications of impossibility (type three). McHale would seem to admit all three types of impossible fiction, for fictional worlds are unlimited even if our apprehension of them in certain instances is restricted (the case of Robbe-Grillet, once again, illustrates this issue).

What is yet impossible in fiction might be seen to be that which has yet to be fathomed, yet to be conceived. This I would take to be a fourth type (d) of impossible fiction, one not actually discussed by these four theorists. Such an impossible world might consist of the actualization of included middles, the realization in the conceptual realm of values between truth and falsity. As we have seen, McHale believes that such a world has already been fictionally created, but this belief is due to his confusing the law of noncontradiction with the law of the excluded middle. A world violating the principle of the excluded middle appears to be impossible at this time because it cannot be conceived in even so much as a metalanguage (type c).(14) Such a world is an impossible world because no one yet has been able to think what such a world would be like.(15) Such a conception is probably impossible or at least highly improbable, though perhaps to note that it has not yet been conceived or to begin imagining it in a metalanguage is, in a sense, to inaugurate its eventuality in thought.

Notes

1 As might be expected, impossibility with respect to reality is significantly different from impossibility with respect to a fictional world. Certain events and circumstances that one might expect to find in fairy tales and in science fiction would be impossible to find in the real world. These would be violations of Ryan's lower-numbered accessibility relations (physical and taxonomic, for example) (Possible Worlds 31-47). Impossible fictional worlds are generally construed to violate the logical principles of noncontradiction. Such worlds are difficult for a reader to imagine and thus preclude a fully immersive experience of reading.

2 The phrase "culturally predominant representation" appears too consensual or perhaps relativistic as a formulation. Moreover, whether observation statements about the world can be said to be universally maintained or culturally conditioned is a significant metaphysical debate in philosophical circles, one not yet resolved. In any case, a particular realism about the actual world must be taken into account, especially the possibility that certain descriptions exceed the contingency of theoretical formulations. In other words, certain representations of the actual world are less cultural or arbitrary than truly reflective.

3 The first paragraph of the novel is consistent with this cinematic interpretation: "The first scene goes very fast. Evidently it has already been rehearsed several times: everyone knows his part by heart. Words and gestures follow each other in a relaxed, continuous manner, the links as imperceptible as the necessary elements of some properly lubricated machinery" (Robbe-Grillet 1). The use of this device encourages the reader to see the narrative as "constructed" rather than merely a representation of the events described.

4 It might be useful at this point to clarify what is meant by such terms as "immersion" and "make-believe." Novels, films, games, and so on are often described as having the quality of being "immersive": that is to say, capable of eliciting the reader's or viewer's attention to the point of practically excluding the recognition of anything else. Walton explains this experience with respect to a reader of Tolstoy:

The reader of Anna Karenina abandons himself to the novel and is convinced, momentarily and partially at least, of Anna's existence and of the truth of what the novel says about her. Otherwise why would he be moved by her predicament? Why would one even be interested enough to bother reading the novel? Yet it also seems that the normal appreciator does not (of course!) really believe in the fiction. (Walton 6)

Instead, the reader of Anna Karenina "makes-believe" that Anna actually exists, and the events described in Tolstoy's work actually take place. The reader of the novel suspends her everyday experience of the actual world in order to participate psychologically in the experience of the events of the novel. That someone named Anna Karenina exists is not true in the real world inhabited by the reader of Tolstoy. But it is "fictionally true" that Anna exists in the world created by Tolstoy.

5 This hypothetical case is recounted in David Deutsch and Michael Lockwood.

6 It is not the case that all Chinese-box worlds are logically impossible. The tales of the Arabian Nights would serve as one example.

7 Fictional characters are by necessity incomplete, though postmodern fictional characters tend to be more so. Completeness refers to the descriptive details provided by an author regarding a character in order to enable a reader to basically "know" him as if he were a real person. In realistic fictions, characters tend, not surprisingly, to be more complete.

8 Sade appears in the invented The Childlike Life of the Black Tarantula (Portrait). Rimbaud is the dominant character in In Memoriam to Identity. Toulouse-Lautrec is the subject of the fictional biography The Adult Life of Toulouse-Lautrec (Portrait). Pasolini writes his fictionalized autobiography My Death, My Life, by Pier Paolo Pasolini (Literal). Finally, a modernized Quixote is the central character of the surreal Don Quixote: Which Was a Dream, a dream taking place in apocalyptic Manhattan.

9 McHale mistakenly equates the law of noncontradiction with that of the excluded middle in his discussion of Eco and logical impossibility. That propositions cannot be both true and false simultaneously is not the same thing as the proposition of an intermediate value between truth and falsity.

10 It might be thought that the notion of the excluded middle might mean "neither p nor -p." This phrase, as applied to fictional worlds, refers to the incompleteness of fictional entities and those instances where ascriptions about them are undecidable, given the lack of textual evidence. We do not know, for example, how many sisters Alice has in Through the Looking-Glass. It is neither true nor false that she has two sisters, and the number of sisters she might have is irrelevant to the narrative. The problem of incompleteness or undecidability is not what I am suggesting by excluded middles in this paper. However, by definition, an excluded middle is necessarily neither p nor -p but an intermediate value between the two. In a fictional world, the appearance of an excluded middle might take the form of an intermediate value between an event both occurring and not occurring simultaneously. As we shall see, it is extremely difficult to conceive of what such a circumstance might be.

11 I leave aside here the relevant issue of the completeness of a possible versus a fictional world and, similarly, the completeness of fictional entities.

12 I use the word "exist" here in the sense that Lewis does when he talks about possible worlds as "existing."

13 If the prince were turned into a stone instead of a frog, then other problems would surface. Stones are nonliving and unconscious and the essence of personality would not be apparent in the stone as it would be in a frog. A stone could not be a true counterpart of a prince. I am indebted to Marie-Laure Ryan for this counterexample.

14 A statement of the sort, "this is a world that violates the law of excluded middle," is all that can be maintained about such a world.

15 It might be maintained, apropos of Rescher and Brandom, that a nonstandard fictional world violating the principle of the excluded middle is possible. Such a world would admit degrees of truth in certain instances. This reasoning is an example of "fuzzy" logic. It might be the case that an event neither happened nor did not happen, but only "sort of" happened.

The problem of expressing such an occurrence arises from having to describe such an event in the language of a standard world. Such nonstandard events are inaccessible from this standpoint. For this very reason, a "fuzzy fiction" could not be written in a standard language. Certain predicates in the language, such as "exists" are not compatible with the notion of intermediacy. This observation is the same as saying that such circumstances are unimaginable. I am indebted to Uri Margolin for this objection.

Works Cited

Acker, Kathy. Don Quixote: Which Was a Dream. New York: Grove, 1986.

-----. In Memoriam to Identity. New York: Grove, 1990.

-----. Literal Madness: Three Novels. New York, Grove, 1988.

-----. Portrait of an Eye. New York: Grove, 1992.

Allen, Sture, ed. Possible Worlds in Humanities, Arts and Sciences: Proceedings of Nobel Symposium 65. New York: Gruyter, 1989.

Borges, Jorge Luis. Labyrinths. Trans. Donald A. Yates and James E. Irby. New York: New Directions, 1964.

Deutsch, David, and Michael Lockwood. "The Quantum Physics of Time Travel." Scientific American Mar. 1994: 68-74.

Dolezel, Lubomir. "Possible Worlds and Literary Fictions." Allen 221-42.

Eco, Umberto. The Role of the Reader. Bloomington: Indiana UP, 1979.

Hofstadter, Douglas R. Godel, Escher, Bach: An Eternal Golden Braid. New York: Basic, 1979.

Lewis, David. "Counterpart Theory and Quantified Modal Logic." Philosophical Papers. Vol. 1. New York: Oxford UP, 1983. 26-38. 2 vols.

-----. "Counterparts of Persons and Their Bodies." Philosophical Papers. Vol. 1. New York: Oxford UP, 1983.47-54. 2 vols.

-----. "Mad Pain and Martian Pain." Philosophical Papers. Vol. 1. New York: Oxford UP, 1983. 122-29. 2 vols.

-----. On the Plurality of Worlds. Oxford: Basil Blackwell, 1986.

-----. "The Paradoxes of Time Travel." Philosophical Papers. Vol 2. New York: Oxford UP, 1986. 67-80. 2 vols.

-----. "Postscripts to 'Counterpart Theory and Quantified Modal Logic.'" Philosophical Papers. Vol. 1. New York: Oxford UP, 1983. 39-46. 2 vols.

-----. "Postscripts to 'Mad Pain and Martian Pain.'" Philosophical Papers. Vol. 1. New York: Oxford UP, 1983. 130-32. 2 vols.

-----. "Postscripts to 'Truth in Fiction.'" Philosophical Papers. Vol. 1. New York: Oxford UP, 1983. 276-80. 2 vols.

-----. "Truth in Fiction." American Philosophical Quarterly 15 (1978): 37-46.

McHale, Brian. Postmodernist Fiction. London: Routledge, 1987.

Parsons, Terence. Nonexistent Objects. New Haven: Yale UP, 1980.

Rescher, Nicholas, and Robert Brandom. The Logic of Inconsistency. Totowa: Rowman, 1979.

Robbe-Grillet, Alain. La maison de rendez-vous. Trans. Richard Howard. New York: Grove, 1966.

-----. Project for a Revolution in New York. Trans. Richard Howard. New York: Grove, 1972.

Ryan, Marie-Laure. Possible Worlds, Artificial Intelligence, and Narrative Theory. Bloomington: Indiana UP, 1991.

-----. "Possible Worlds in Recent Literary Theory." Style 26 (1992): 528-53.

Walton, Kendall. Mimesis as Make-Believe: On the Foundations of the Representational Arts. Cambridge: Harvard UP, 1990.

William L. Ashline recently completed his M.A. in English at Colorado State University. He has published on Julia Kristeva and theories of human sacrifice. His thesis project is on Georges Bataille and transgression.
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