Consider the following sentence:This statement is false.
It is devastatingly simple in its breaking of logic. You cannot believe it. You cannot disbelieve it. It has no truth value that you can settle on. You’re stuck in the middle, thrown on an endless loop from one end of the sentence to the next.
The Liar Paradox was one of the oldest paradoxes of all time, for it violated that central premise of classical logic: the law of the excluded middle. Statements must either be true or false, and nothing in between. Still no one knew how to resolve the paradox. The Greeks and the Indians had been tooling around with the Liar Paradox for centuries; instead of resolving it, they merely came up with a whole family of related paradoxes, one of which involves Socrates, a crocodile, and a stolen child. It posed serious problems for the foundations of logic—indeed, Philitas of Cos agonized so much over the solution that he wasted away and died.
Inscribed in a pentagram, the Liar Paradox could suspend truth and falsity entirely. Magicians did not use it often, for most of the time they needed someone to believe something, not to exist in a state of uncertainty. But Alice didn’t need Elspeth to believe anything in particular about them. She only needed Elspeth off her guard; willing to talk. And she already knew Elspeth liked to talk. The poor girl was desperate for anyone who would listen.
“That’ll never work,” said Peter. “Everyone knows how to ward off the Liar Paradox.”
“Not if she’s not expecting it.”
“She might be. She already doesn’t trust us.”
“She does now.” Alice was absolutely sure of this. “She thinks we’re just like her. Depressed, hopeless souls. She thinks we hate Cambridge, too—she thinks we’re on her side.”
“Jesus, Law.” Peter shifted under his blanket. “What is wrong with you?”
“We have to make it count.” She felt a lump in her throat. “All this, I mean. It has to be worth something. We can’t have done this all for nothing.”
“Hm,” said Peter.
Alice waited, hoping that he might say anything more. Wickedness felt better when you had a coconspirator; otherwise it was just you and your conscience. But he remained silent. Eventually his breathing evened out, and she assumed he’d fallen asleep.
Something tickled her cheek. She opened her eyes to see two vast, blinking green pools, inches from her face. Tiny pupils, narrowed to slits. They seemed quite judgmental.
“Don’tyoutell,” Alice whispered.
Archimedes spun round, flicked his tail against her face, and disappeared into the shadow.
Irked, embarrassed for reasons too petty to name, she turned onto her side and closed her eyes.
“I have a theory about whyyou’re so stuck on academia,” an old boyfriend of Alice’s had once told her, shortly before he became an ex. This was during their senior year of college, when she had been single-mindedly obsessed with graduate school applications to the point of neglect—and perhaps downright rudeness, as shehadstood him up at least half a dozen times by now. This, paired with this boyfriend’s recent enrollment in a psychoanalysis seminar, made him vindictive. “You’re obsessed with gold stars. You never got over the high school thrill of an A+ at the top of your paper and academia will let you chase those little gold stars for the rest of your life.” He flicked her forehead. “Little ivory tower princess, you. You’re a teacher’s pet, Alice. You have a fetish for validation.”
“Is that so?” Alice, whose mind was only on the prospect of fat envelopes from Cambridge, Oxford, Harvard, and Yale arriving in her mailbox, barely registered what he was saying. Indeed it took her months to realize this nasty monologue had been his attempt to get her into bed. “Yes. I suppose that’s right.”
They broke up shortly after. Alice reflected on his words in those following months, but only with a thrilling contempt. “You’re giving up too much,” he had told her. “This can’t be worth it.”
But of course it was worth it. It was the only thing that was worth it. She had been fortunate to find a vocation that made irrelevant everything else, and anything that made you forget to eat, drink, sleep, or maintain basic relationships—anything that made you so inhumanlyexcited—had to be pursued with single-minded devotion.
Academia was decidedly not about the gold stars. If Alice had ever fallen prey to this notion, she was quickly disabused of it during her first year of coursework, wherein she heard every day a million things wrong with the way she thought, and only the occasional, “Not bad.” If you went into the field for gold stars you were in for disappointment.
No, the point was the high of discovery. No one else understood—certainly not the ex, who went on to do something involving mortgages and making poor people poorer. How could she explain to him the way her mind felt as if it were chewing, digesting difficult concepts? That the headache she got after marking up an impenetrable text was like the pain in her gums after masticating on a good steak? The way her whole body thrummed in excitement when she came across the exact algorithm, translation, historical reproduction, she’d spent hours searching for in the library. The way she always forgot she needed rest as she hunched over a pentagram for hours, sometimes days, scribbling frantically away as idea after idea surged through her mind.
How good it felt when she seemed to abandon her body altogether—when she became fully incorporeal, drifting happily in a universe of ideas. She was very proud of the days that she forgot to eat. Not because she had any revulsion for food, but because it was some proof that she had transcended some basic cycle of need. That she was not just an animal after all, held captive by her desires to eat and fuck and shit. That she was above all a mind, and the mind was capable of miraculous things.
Sometimes she would jolt, and feel suddenly that she was standing still on a spinning plane while abstract shapes swirled about her, calling to her, revealing themselves in full. The mundane world faded away and she was alone in a field of black, except for the brilliant spots—revelations, directions, connections—dancing in the corners of her vision. Everything else was so insubstantial! The world of the college; of chairs screeching on classroom floors, spoons clicking in cups, umbrellas trembling under constant rain—it was just a front, she realized; only a flimsy glamour. Blink and it was gone. It was in the hidden world where truth resided and concepts begged to be understood. She only had to reach for them, and they would come to her. Yes. She only had to listen, and she would hear the music.
In her freshman year, Alice had a professor whose lecturing style was defined by deep, spontaneous sighs. You could tell those weren’t preplanned sighs. Some professors sighed as a performance, obnoxiously, to inject profundity where really there was none, but no—this professor was simply so overwhelmed by the moment, by the tangled thoughts waiting to be undone and then articulated, that he would stare off into space and look deeply bothered and tap his fingers together until he figured out in what order to convey it all—and then his spindly shoulders would shake and he would rock back and forth, as if he were a mere vessel, and his body an imperfect tool to convey a message from the gods. Alice’s classmates found it funny. They would imitate Professor Eklund in the cafeteria, the way he sometimes lifted his entire knee onto the table as he rocked back and forth. What a dork, they said. What a poser, who does he think he is, who does he think he’s fooling? But Alice knew it was not a front. Professor Eklund was in that dark, spinning plane, hearing the music. She could see it in his eyes. She wanted to follow him there.
No, prestige wasn’t the point. Elspeth was wrong. Elspeth had invested all her hopes in the wrong symbols. The symbolic order—the paper publications, the applause, the job postings, the grants—was not the point. Even the Oxbridge credentials, which Alice’s ex had assumed were solely what she was after, were not the point. Those were only instrumentally valuable to secure what Alice really wanted, which was unhampered time and access to the necessary resources tothink.
This was why she kept at it for years. This was why every graduate student she knew didn’t mind the low pay, the exhausting teaching assignments, or the nonexistent health care. They were all doing their best to extricate themselves from their bodies because they’d been told this was simply what they had to do. The whole system could be broken, and it wouldn’t matter. They’d put up with anything, only for the promise of access to that abstract plane.
Peter understood. She’d seen the pure, serene bliss on his face as he stood at the blackboard, copying out equations so quickly she feared his wrist would cramp. That mode of concentration so deep you couldn’t snap him out of it if you tried, and nor would you want to. It was too lovely to watch a mind at ferocious work.
Anyhow, it wasn’t just pretentious asceticism. There were the good nights, too. She remembered an end-of-term social her first year, when they’d all congregated at the local pizza shop and ordered a massive sourdough margherita to share. Even Peter had come that night, and everyone, Alice included, was too delighted by his presence to ask why he’d stood them up a dozen times throughout the semester. They’d started arguing about dialects and the reliability of regional studies, and from there moved on to debating what it meant to do close reading versus distance reading, and whether it made any sense to impose a third criterion called middle reading.
Alice had never been so fond of her classmates until that night. It helped that the faculty were not present, and it helped that everyone was a little drunk, and no longer speaking to make the right impressions. They had the freedom to be wrong, which meant the freedom to get silly. And they got very silly. What was the difference between Kant’s noumena and Plato’s forms, they wondered. What was the precise definition of a sandwich, and was it still a sandwich if you ate it vertically? Was the horizontal definition sufficient to exclude tacos? Also, where were the aliens? From aliens they moved to Aristotle’s schema of cosmological physics—earth, water, air, the stars expanding outward from the center like shells, and above it all a celestial body—a “celestial space worm,” Michele called it, because it was more fun to think of this enormous, rotating, writhing being causing all the motion in the lower shells because it was thinking so hard about God, the unmoved first mover.