Borges and Mathematics

4. The Short Story as Logical System

4 The Short Story as Logical System1 There are certain elements in the structure of the short story—brevity and rigor, for example—that too easily tempt us into formulating rules for the genre and dreaming up possible classifications and commandments . These efforts usually turn out either too vague and general to be of interest or else, regardless of how many carefully thought-out axioms are presented and precautions taken, they fail to consider some perfectly legitimate example of a short story that mocks the laws.And just as in that old-fashioned book One Hundred Ways to Say NO to a Sexual Proposition, the hundredth answer is YES; in every list of Ten Commandments, the tenth seems condemned to be (as Argentine writer Abelardo Castillo has suggested): Don’t take the previous nine too seriously. This deficiency in all attempts to formalize the genre may produce a sigh of relief and the swift and misleading conclusion that there really are no guidelines to consider when tackling the task of writing a short story. And yet—as anyone who has seriously attempted it knows—it doesn’t take too long for us to realize that the rules we thought we’d thrown out the door come flying back through| 67 | | 68 | BORGES AND MATHEMATICS the window. They’re slippery, intangible rules that can be recognized in specific examples but which don’t lend themselves to generalization and cannot be readily articulated. I’ll mention two that strike me as especially profound. The first is one that Borges suggests (by opposition ) in a paragraph where he tries to contrast the short story with the novel. Borges skips the most obvious and superficial difference —length—and observes that what characterizes the novel, above all, is the evolution of the characters. In short stories the preeminent aspect is the plot; the characters are important only as agents of the plot, and therefore they lose a certain degree of liberty. The second rule is one Ricardo Piglia declares in his “Tesis sobre el cuento,” in an article that appeared in Clarín a few years ago.2 There he maintains that every short story is the interplay of two tales, one told on the surface and another, subterranean and secret, that the writer gradually unfolds throughout the course of the story and reveals in its entirety only at the end. This idea coincides with my own most frequent image of the short story writer: an illusionist who diverts the public’s attention with one hand while he executes his magical act with the other. An added benefit to this approach is that it allows us to see the short story not as a finished product, ready to be dismantled by critics, but rather as a living process, from its inception on. A slight variation of this idea allows us to think of the short story as a logical system. The word “logical,” inserted into an artistic context , shouldn’t necessarily be alarming. Logic—not to be confused with the rigid syllogisms we learned in high school or the binary fragment used by mathematics—has proved to be a very malleable substance. From the historic moment in the early 1800s when the young student Nikolai Lobachevsky denied Euclid’s fifth postulate in the belief that it would lead to an absurd conclusion, and when a new, perfectly strange but perfectly consistent geometric world emerged instead, a silent revolution has erupted in human thinking. Since then, various disciplines and branches of thought have developed their own logic. Thus, the field of law formalizes and attempts THE SHORT STORY AS LOGICAL SYSTEM | 69 | to introduce automatic procedures into its criteria for evidence and validity; mathematics begins to reason with polyvalent logics; psychiatry attempts to formulate models for the logic of schizophrenia; and washing machines incorporate fuzzy logic. What is, in fact, a logical system? It’s a set of initial assumptions and a series of deductive rules—which can be thought of as rules of the game—that allow us to proceed “legitimately” from the initial assumptions to new assertions. The variety and diversity of types of logic basically depend on which rules of deduction are chosen. In intuitionist logic, for example, demonstrations per reductio ad absurdum are not allowed, and in trivalent logic it is possible to affirm and deny the same proposition simultaneously without causing too much of a scandal. On close inspection...