SOURCE: “According to the Eye of the Beholder,” in Unthinking Thinking: Jorge Luis Borges, Mathematics, and the New Physics, Purdue University Press, 1991, pp. 32–42.

[In the following excerpt, Merrell explores Borges's use of paradox.]

I don't like writers who are making sweeping statements all the time. Of course, you might argue that what I'm saying is a sweeping statement, no?

—Jorge Luis Borges

1.

It has been said that paradox is truth standing on its head to attract attention, and that truth is paradox crying out to be transcended. The word comes from the Greek para doxos, meaning beyond belief, which is actually not befitting, for many paradoxes are the source of deep-seated convictions, if not “truth.” More appropriately, then, we might say that paradoxes are trains of thought condensed into a point of time and space. Contemplating a paradox has been compared to meditating on a Zen Koan, gazing at a mandala, entering momentarily into the realm of the infinite. A world free of paradox is the stuff only dreams are made of, yet rationalism, even logic itself, in the final analysis “teaches us to expect some dreaminess in the world, and even contradictions” (Peirce 1960; 4:79). According to Kierkegaard, reason ultimately leads to paradox, and faith is needed to remedy it. But a paradox is not resolved by faith alone, nor can it logically be disposed of in many cases. It remains coiled at the very heart of our reasoning process.

Guillermo Sucre (1970, 469) correctly remarks that Borges's writing is a “fusion of contradictions.” What he fails to note is that such fusion is inescapable, for the knowledge paradox inheres in all viable thinking, whether one be a nominalist, realist, idealist, Vaihingerian “fictionalist,” Meinongian, or whatever. That is, the fusion of one's knowledge (what one believes one knows) with one's “meta-knowledge” (one's knowledge about one's knowledge) breeds paradox, for, like the “preface paradox” that marked the beginning of this book, at the second level one ultimately knows one does not, and cannot, be in possession of absolute “truth”; some of one's knowledge is, unfortunately, always either inconsistent or incomplete, yet at the first level one tends to persist in believing it may well be absolute. Rather than “truth” standing on its head, then, the knowledge paradox is “truth” as an asymmetric object looking at itself in a mirror. It sees its own inverse, its right side becomes its left side: its mirror image is its own falsity, and it can do no more than oscillate between the two poles of the contradiction ad infinitum.

Richard Burgin (1968, 115) observes that Escher's work in visual terms compares favorably with some of Borges's cherished themes. Indeed, some of Borges's stories elicit what Douglas Hofstadter (1979, 94–95; 688–89) calls the “authorship triangle.” There are three authors, A, B, and C. A exists in a novel by B, B in a novel by C, and, strangely, C is to be found in A's novel. This tangled triad is analogous, Hofstadter tells us, to Escher's well-known print of a hand drawing a second hand which is in turn drawing the first hand. How are such puzzles explained? Authors A, B, and C, necessarily unaware of their predicament, will, we must presume, happily tred through life believing they are real people. But another author, say, D, from a “meta-perspective,” knows that they are mere imaginary beings. So assume D writes his own novel about those three unfortunate souls who think they are real people. Fine. But how is he to know that he is not a character in another novel by author E? We can gaze at Escher's hands drawing themselves and with confidence remark on the anomaly from our “superior” vantage point. We know that behind this print lurks Escher's invisible hand drawing the two appendages. But the problem is not resolved thus, for, like the knowledge paradox, from a “meta-perspective” there is still no guarantee that what we know is not false (or fictitious). There is no recourse but to oscillate between the two horns of the dilemma.

On speaking of such dilemmas, we are introduced to one of Borges's finest stories, “The Circular Ruins” (L, 45–50), which I will treat in some detail here in order that its paradoxical force may be effectively highlighted. In an exotic setting, a magician-priest arrives at the charred ruins of an ancient circular temple. The purpose which guided him “was not impossible, though it was supernatural” (L, 46). He wanted to dream a human being and insert him into reality. After failing in his initial attempt to dream a multitude of young boys and select from them the most promising candidate, he embarked on a second effort: to dream an individual, starting with the heart, and creating outward to the skeleton and finally to each of the innumerable hairs. After gradually accustoming this arduously dreamt boy to reality, the magician sent him downstream to the north “to be born.” His son was now, for practical purposes, a part of “reality”: in fact, “all creatures except Fire itself and the dreamer would believe him to be a man of flesh and blood” (L, 48). One night the magician was awakened by two boatmen who told him of another magician to the north who could walk on fire without being burned. As any good father, the dreamer feared for the emotional well-being of his son, for if he meditated on his rare privilege and discovered that he was a mere image it would be humiliating. However, his thoughts were cut short, for a jungle blaze threatened from the south. The old man, cognizant of his imminent death, walked boldly into the “concentric” blaze only to realize “with relief, with humiliation, with terror,” that the flames could not consume him, for “he too was a mere appearance, dreamt by another” (L, 50).

“The Circular Ruins” reveals one of Borges's strategies for creating contradictions, paradoxes, and infinite regresses, which will have a bearing on later sections of this inquiry. The first step entails a set of apparent oppositions. The magician came from the south, where he had dwelled in “one of the infinite villages upstream.” On the other hand, after sufficiently preparing his “unreal” son for integration into “reality,” the magician sent him downstream to the north, where there lay the ruins of “another propitious temple, whose gods were also burned and dead” (L, 47). The conditions of the son's environment are reciprocally identical to those of the magician. Only the infinitely repetitive trees of the jungle separate one temple from another. Hence, the spatial trajectories of father and son compose two symmetrical oppositions, up(stream)/down(south) and down(stream)/up(north), which structurally produce a “cancellation effect.” As a result, the action of the story terminates simultaneously everywhere and nowhere: at the center of the charred ruins of a circular temple where the magician created his dream image. This symmetry of space reveals the fallacy of what Alfred North Whitehead (1925, ch. 4) calls “simple location.” The story alludes not to precise geographic points but to vague notions of circular surfaces, which become almost as haptic as they are visual.

In contrast to these spatial indices, at the outset it appears that time is linear, and it accumulates with increasing torpidity. The magician required fourteen days to perfect the heart of his subject, one year to create the skeleton, a little less than two additional years to complete his project, and two more long years to prepare his son for “birth.” The son's development, then, is first decelerated and finally halted altogether when the magician interpolates him into the world. However, this effort to annihilate the past is ultimately futile. Temporal recurrence is foretold by the magician's impression that “all this had happened before” (L, 45). If the obliteration of “simple location” of space coupled with vague images of spatial circularity implies a denial of linear movement, concomitantly, the attempt to annihilate the past and establish an eternal “now” stems from an implicit attempt to deny temporal irreversibility.

The “invincible purpose” that drives the magician can be explicated on two levels: concrete and abstract. On a concrete level, the magician strives to coordinate his activities with those of his son. He daily prostrates himself at dawn and at twilight “before the stone figure, imagining perhaps that his unreal child was practicing the same rites, in other circular ruins” (L, 49). By means of these ritualistic acts, he gradually becomes “as all men,” and his absent son is nurtured with the progressive diminution of his maker's own soul. When the magician's purpose in life is finally completed, he assumes that his son's immortality is now projected into the physical world, an event that at once symbolically represents the concretion of the “unreal” (dream) and the eternal coexistence of the “real” (physical) world. On an abstract level, the coexistence of “real” father with “unreal” son coheres with the symbolic coexistence of space and time. Spatial and temporal synchronicity portrayed in Borges's story is a condition quite unlike the linear temporal existence of the physical world. In this sense, physical existence, which presupposes human finitude, is opposed to the dream world of spaceless and timeless coexistence. In the material sphere of existence, the contradiction between life and death is presumably irreconcilable. On the other hand, in the nonmaterial order, governed by spatio-temporal synchronicity, this contradiction is nonexistent.

Consider the possibility that in “The Circular Ruins” a projection of spatio-temporal synchronicity into linear existence entails a symbolic abolition of the life/death dichotomy. This assumes an implicit attempt to overcome temporal existence wherein spatial hierarchy and temporal linearity predominate. In more concrete terms, the magician's “purpose” stems from a desire to make his “unreal” son part of tangible “reality” and vicariously to transcend mortality himself, for even though all fathers “are interested in the children they have procreated,” this interest is at the same time self-interest. Therefore, the constraint in the text subjected to potential restructuration is the life/death duality, perhaps the most intransigent of all. For obvious reasons, the protagonist is a “magician” and the story reads like a “myth.”

The relation between father and son (“reality” and dream) can be illustrated by an abstract scheme, in which the sequential and parallel planes intersect where there is potential movement in the narrative toward a more complex level of organization. The desired goal entails actualization of relations of similitude between father-son and “reality”-dream. By inserting dream image into “reality,” the son can become a “man” and the magician can vicariously transcend the finitude of his physical existence. In order to accomplish this goal, the magician must activate a fusion of opposites wherein the son's timelessness predominates over the father's temporality and the father's essence over the son's materialessness. However, the “logical” end prevails: the magician realizes he is an integral part of dream existence, which discounts the son's supposed entry into “reality,” and the “unreal” enjoys synonymity with the “real.” …

According to the reading I have proposed, this impossible intersection of the “unreal” and the “real” becomes manifest at the end of the story. The magician assumes that his monumental task is completed, but when the parallel and sequential axes converge, the paradox underlying his project potentially becomes apparent. His status as the object of yet another dream is obviously a proposition embedded in his mind, since his own maker had instilled in him, as he in his son, complete oblivion of his apprenticeship. Hence, from the very beginning, it may be conjectured, the magician's grand design is doomed to failure. In the first place, he strives to force the dreamt image into his own supposedly tangible form of existence in order to concretize the sequential chain of mental events (dream “reality”) that are the product of unlimited semiotic activity and to establish lines of similarity where ordinarily there would exist only lines of opposition. In other words, he tries to make dream “reality” denote something other than what it would ordinarily denote. In the second place, realization of the magician's desire would be equivalent to a desiring subject's becoming part of the imagined world he has created and at the same time a prisoner of/in his own desires. The fusion cannot be actualized, however, and what the magician presumed to accomplish at one level backfires at another level.

To determine more precisely the nature of the magician's dilemma, let us return to the implicit purpose guiding his action. After the magician's preliminary effort to create a “real” son fails, he realizes that his project will be much more arduous than “weaving a rope of sand or coining the faceless wind” (L, 47). This passage reveals two metaphorical (oxymoronic) images, which on a local level represent the impossible conjunction of distinct classes of things: rope (fibered) out of sand (nonfibered) or coin (malleable-solid) out of wind (nonmalleable-nonsolid). The magician now attempts to construct a solitary dreamt image by means of another approach. The problem is that to integrate the attributes of this image into his own world logically implies a simultaneous rupture of boundaries. In other words, two distinct classes, A and B, are governed by different logical orders, and they cannot be integrated while maintaining intact the logical order of either A or B, but both, on becoming members of the same class, must be subjected to a different order. Hence, the magician cannot conjoin two distinct spheres of existence into his own without altering both. If, on the other hand, the magician had conceived of his dream world as does primitive man, as merely another facet of the same “reality,” his project would nonetheless have been equally futile. For to make a dream coexist with “reality” would be nonsensical, given the fact that in the primitive's animistic conception of things, the two entities could not represent an intractable dualism in the first place.

Fire might have been construed as a potential mediator between the “reality” of the magician and the “nonreality” of the boy, since fire symbolically “converts” essence to nonessence (matter to energy). Following this metaphorical line of reasoning, the magician would be attempting to reverse the process and convert his “unreal” son (nonessence) to “reality” (essence). Moreover, only fire would be able to discern the created being's lack of essence, since it cannot consume that which is the final product of its consummatory process. In fact, fire appears as an earthly god in one of the magician's dreams and offers to give life to his inert dream image. However, the fire deity is helpless against that over which it presumably exercises dominion: its very sanctuary, as in centuries past, is destroyed by fire. This destruction recapitulates the paradox inherent in the magician's project. That is, the god of fire is the “symbolic,” or “archetypal,” expression of fire, and as such it rests at a distinct level of organization. The symbol can be representative of fire but cannot coexist on the same logical level as fire; it cannot be fire itself. When the magician assumes he possesses the ability to annihilate the boundaries between logical categories, all distinctions between symbol and referent, dreamer and dreamt, become nonexistent, and he loses his capacity, as Homo symbolicus, to create an ideal world that rests in contradiction to “real” reference.

“The Circular Ruins” is merely one exemplary instantiation of Borgesian paradoxes. Like the Aleph itself, most of these paradoxes entail an untenable collaboration of the infinite and the finite, time and timelessness, continuity and discontinuity, the One and the Many. These are “hyperfictions” in the extreme; that is, they imply oxymoronic collusion at the deepest level. Weaving a rope of sand or coining the faceless wind serve as microcosmic embellishments of the larger tragedy being played out, which is equally oxymoronic, but, in addition to its poetic qualities, it is also metaphysical—cosmic metaphors, which place Borges's fictions in the same orb with the range of Vaihingerian fictions and scientific models-fictions.

Regarding further the nature of Borges's paradoxes, Bruce Lorich (1973, 53)—and he is certainly not alone here—disparagingly proclaims that most of Borges's fictions are “heretical texts for solipsists.” The Argentine writer, he declares, “has created a complex, labyrinthine puzzle of paradoxes in which pedantic psyche-twisters, related only to themselves and to a philosophical stance, appear more regularly than do ingenious truly fictional artifices. Most of his so-called fictions are intellectual games.”¹ Lorich, I believe, is correct on one point: Borges's fictions are intellectual games. But they are far from trivial. The fact is that all paradoxes potentially bear on “truth,” but in a negative manner, for negation (i.e., Nietzsche's “lie”) is one of the prerequisites for their existence. For example, a variation of the Liar paradox, “This sentence is false,” entails negation, since it says of itself that it is not true. It also entails two other conditions necessary for paradox: self-reference and infinite regress. The sentence self-referentially speaks of its own lack of truthfulness, and hence if it is true, then it is false, and if so, then it is true, and so on, ad infinitum.

These three conditions—negation, self-reference, and infinite regress—should reveal many pseudoparadoxes being passed off as logical paradoxes in Borges criticism and elsewhere. As a case in point, the injunctionplaces the reader in a quandry, but it is not logically paradoxical, since, rather than reflect upon itself, it includes the reader; it constitutes merely a “pragmatic” paradox. That is to say, the reader, having already read the sign, cannot ignore it so as to obey the injunction, hence there is no infinite regress. Nor can self-reference alone create paradox, in spite of the overenthusiastic claims of certain contemporary literary critics of poststructuralist ilk. It might simply create an absurd situation comparable to Lewis Carroll's mythical island whose inhabitants earn a living by taking in each other's washing. With respect to Borges's work, for example, critics have often commented on the “paradox” inherent in History of Eternity, since eternity is atemporal and hence incompatible with the notion of historicity. However contradictory this title may be, it is not paradoxical, for there is no infinite regress.

The essence of Borges's genius lies in his recognition of false dichotomies and his uncanny ability to dramatize paradox within an ethereal, timeless framework. Borges seems to suggest that if the universe operates consistently at all, it operates consistently on paradox, and insofar as it does so, the universe may be rational instead of absurd, a rationalism, nonetheless, edified upon inconsistent premises. Paradox, like infinity, is contingent upon simultaneity. “This sentence is false” must, logically speaking, be construed at once as both true and false. However, the mnemonic function of the brain is linear. It entails sequential expression and analysis, which contradicts the simultaneity essential for Borges's and other paradoxes to emerge. Properly perceiving paradox, then, involves the perceiver's oscillating between the either and the or, an oscillation in time, but, since it goes nowhere so to speak, it is timeless. It has no tenses of past and future, for the oscillations in their composite are static.

Paradox viewed from two perspectives, the temporal and the timeless, can be illustrated by what is called the “prisoner paradox.” It is Sunday. A group of prisoners is told by the warden that they will be executed on one day of that week, but they will not be informed which day it will be until the arrival of that very day, hence it will be a surprise. These prisoners happen to have found a quite astute lawyer. He reasons, after some deliberation, that assuming the warden to have told them the truth, they cannot be executed, for if the fatal day is to be Saturday, then it cannot be a surprise, since it will be the only day remaining. By this mode of reasoning neither can it be Friday, for Saturday now having been eliminated, Friday is no longer a candidate. The same can be said of Thursday, and so on down to Sunday. Therefore they cannot legitimately be executed. Now, there seems to be a flaw somewhere, and there is, but it has nothing to do with logic. The problem is that the lawyer's reasoning is strictly by logical means; he can certainly afford to be logical, for his life is not at stake. In contrast, the prisoners' very existence is in jeopardy. They are rightly concerned over how much time remains of their life, and time is precisely the issue here. The lawyer's logic is timeless, and within this framework the paradox springs forth in full force. But the prisoners, their emotions having understandably taken precedence over their reasoning faculties, exist in time, hence try as their lawyer may to convince them otherwise, they cannot reason away their expectations of an unexpected moment announcing their death. Trapped inside their particular mind-set, they are condemned to temporality.

Existentially the human organism cannot help but project into the future and carry within itself conglomerate memories of the past, for without such memories, there is no future anticipation. Such would be a rudimentary form of animal consciousness, which, as Borges often reiterates in his works, is situated outside time. We humans, in contrast, are caught within a temporality that, for better or for worse, generates quandaries necessary to our very existence. For example, the narrator's obsession with the twenty-centavo coin in “The Zahir” exhibits our unwillingness to let go of the past: he simply cannot forget the coin, yet at times he feels so confident he can forget it that he “deliberately recalled it to mind” (L, 160–61). Here Borges reveals the subtle “forgetfulness paradox.” The narrator gives himself the injunction “Don't think about the Zahir” or “Forget the Zahir.” But if he does not think about it, then he runs the risk of forgetting what it is he is supposed to forget and he might think about it; therefore he must maintain mindfulness of it so as not to forget he must forget it. This pragmatic paradox depends as much on memory as does the “prisoner paradox” on anticipation. And both are existential rather than purely logical, time-bound rather than atemporal.

Interestingly, in Borges's “The Secret Miracle” (L, 88–94) we have another variation on the prisoner paradox. Jaromir Hladik is condemned to die before a firing squad at dawn, the twenty-ninth of March, 1943. He “infinitely anticipated the process of his dying, from the sleepless dawn to the mysterious volley” (L, 89). He imagined himself dying hundreds of deaths “in courtyards whose forms and angles strained geometrical probabilities, machine-gunned by variable soldiers in changing numbers, who at times killed him from a distance, at others from close by” (L, 89). One day he reflects that

reality does not usually coincide with our anticipation of it; with a logic of his own he inferred that to foresee a circumstantial detail is to prevent its happening. Trusting in this weak magic, he invented, so that they would not happen, the most gruesome details. Finally, as was natural, he came to fear that they were prophetic. Miserable in the night, he endeavored to find some way to hold fast to the fleeting substance of time. He knew that it was rushing headlong toward the dawn of the twenty ninth. He remembered aloud: “I am now in the night of the twenty second; while this night lasts (and for six nights more), I am invulnerable, immortal.”

(L, 89–90)

Hladik is a writer who has never been satisfied with the fruits of his craft. Perhaps his most successful book was the one entitled, significantly, Vindication of Eternity. The first volume “gave a history of man's various concepts of eternity, from the immutable being of Parmenides to the modifiable past of Hinton” (L, 90).² The second denied that “all the events of the universe make up a temporal series, arguing that the number of man's possible experiences is not infinite, and that a single ‘repetition’ suffices to prove that time is a fallacy. … Unfortunately, the arguments that demonstrate this fallacy are equally fallacious” (ibid.).³ Indeed, with such remarkable precedents, how could Hladik possibly be overtaken by time?

To “redeem himself” of his past failures, Hladik has been writing a play in verse entitled The Enemies, which remains unfinished. He petitions God that he be granted an extra year to finish it before his execution. It is granted. Then, on the twenty-ninth, before the firing squad and at the moment the command is given to execute him, the “physical universe comes to a halt”: Hladik's “weak magic” had triumphed. For the duration of one year, motionlessly, secretly, he then “wrought in time his lofty, invisible labyrinth. … nothing hurried him. He omitted, he condensed, he amplified. … He concluded his drama” (L, 94). Then he was shot at dawn, on the twenty-ninth.

For the prisoners, existence took precedence over logic. For Hladik, like the prisoners' lawyer, logic took precedence over existence. The lawyer's reasoning was helpless in the face of “reality,” since the prisoners were sure to die on the designated day. Hladik's reasoning powers, in contrast, became “reality” in much the sense of scientific theories, which, purely imaginary mental constructs in the beginning, can subsequently become in the minds of their believers synonymous with the “real” (i.e., the Newtonian-Cartesian machine model of the universe and other such models and metaphors).

Notes

1. It bears mentioning that Lorich does attribute excellence to Borges's “The South” (F, 167–74), since, like Julio Cortázar's short story, “Axolotl,” it does not merely “depend upon convoluted abstractions.”

2. Borges's interest in and allusion to C. Howard Hinton is most appropriate. Hinton held some strange ideas, among them the notion that the ultimate components of our nervous system are of a higher dimension, thus affording us the capacity to imagine four-dimensional space. The fourth dimension will be discussed in conjunction with relativity theory in the second section of Chapter Four.

3. This quote is relevant to Borges's “New Refutation of Time.”

Works Cited

Burgin, Richard. 1968. Conversations with Jorge Luis Borges. New York: Holt, Rinehart & Winston.

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

Lorich, Bruce. 1973. “Borges's Puzzle of Paradoxes.” Southwest Review 58: 53–65.

Peirce, Charles Sanders. 1960. Collected Papers. Ed. C. Hartshorne and P. Weiss. Cambridge, Mass.: Harvard University Press, Belknap Press.

Sucre, Guillermo. 1970. “La biografia del infinito.” Eco, No. 125: 466–502.

Whitehead, Alfred North. 1925. Science and the Modern World. New York: Macmillan