Page 29 of Katabasis

T wo principles ground the whole of classical logic.

They are the Law of Noncontradiction and the Law of the Excluded Middle.

The Law of Noncontradiction holds, quite simply, that two contradictory propositions cannot both be true at once.

You cannot have both P and not-P. It cannot be true both that it is snowing and that it is not snowing.

It cannot be true that Alice and Peter are friends and not friends.

Schrodinger’s cat is dead, or it is not.

The Law of the Excluded Middle holds that either a proposition is true, or it is false.

There is no hazy middle ground. As Aristotle put it, sentences can be ambiguous in their meaning but not in their truth.

So either the statement that Alice and Peter are friends is true, or it is false.

This statement cannot be some mysterious third thing.

Many problems threaten to break classical logic.

The Sorites Paradox and the Liar Paradox, for instance, are difficult puzzles that force classical logic to reexamine what it means by truth.

classical logic also has yet to come up with an answer to Russell’s Paradox, which is too complicated to explain here but has to do with a contradiction of set theory.

And classical logic especially falls apart as a language applied to human relationships, which are messy and complicated and often situated in that excluded middle; that space where no one is right and no one is wrong and things are neither true nor false.

The upshot here is that classical logic does not know what to do with the statement:

S: Peter and Alice are friends.

Alice would always remember the moment she first laid eyes on Peter Murdoch.

Michaelmas Term, two years prior. Cambridge was gorgeous in golden autumn sun.

The wind was pleasantly cool, the leaves reddening ever so slightly in a way that had always excited Alice, for the end of summer meant the start of a new semester; new classes, new instructors, and new classmates.

A chance to reinvent herself, and become the person she wanted to be.

Six students had been admitted to their cohort but that afternoon only five were present at the tea in the courtyard behind the department, clutching cups and saucers close to their chests as they cautiously made introductions.

There was Belinda Wilcox, an English rose whose red-gold hair and pert nose made Alice hopelessly jealous; a Frenchman and an Italian whose names she could not make out over the clamor of voices; and Calvin Bailey, a fellow American transplant from Michigan, who shared Alice’s ineptitude with all the little spoons, saucers, and tongs that went into constructing a cup of tea.

The small talk was polite and meaningless.

Alice was too focused on keeping her hands from shaking to say much.

She felt badly out of place—American colleges were grand, but they didn’t have history , didn’t have tradition , and her advisor at Cornell had actually invited her to a sit-down dinner in which he taught her how to use cutlery before she flew out to London—and the easy shine and polish of her new cohort-mates made her feel doubly inadequate.

Even the Europeans seemed more fluent in British English than she was; she could barely keep up with what they were saying.

She didn’t know what a tripos was; she was still saying “math” in the singular; she didn’t understand what anyone meant by Mill or Peterhouse.

That morning she’d put on her best summer dress, a frilly yellow thing with a lace collar that normally made her feel sharp, but now, among her sleek, darkly dressed colleagues, she felt like a cheap and gaudy daffodil.

She tried to squash her anxieties and focus on Belinda, though up close Belinda was so dazzling it was hard to get any words out.

The sun kept catching her eyelashes in a manner that was truly unfair, for how could lashes be so dark and shimmering both at once?

Belinda was telling some story about a Chinese undergraduate she’d mentored over the summer—“Her English was fine, and she was very sweet and polite and all that, but my God , she never talked. It was only ever Yes, Belinda , or I’m great, Belinda in these little simpering tones—and I was getting really angry at her for it, that is, the fact that she was so uninteresting, because being boring is a trait I find unforgivable .

And then halfway through the summer she revealed that her father is one of the richest men in Taiwan, one of those real estate millionaires, and he didn’t approve of women in the sciences, and she’d told him she’d come to an art history program and was learning magick on the sly! Can you imagine!”

Something in this story disposed Alice to not like Belinda but she couldn’t immediately articulate why, especially as the punch line to this story indicated that Belinda was not racist, and everyone else was laughing so hard.

Anyhow Belinda had pulled all the attention into her orbit; there was no other conversation to escape to.

“Did you do your undergraduate studies here as well?” Alice managed.

“Oh no, I was at Oxford.” Belinda squinted at Alice. “And you’re from—somewhere stateside?”

“The hotel school,” Alice joked, then regretted it. No one here understood the reference; truly, no one back in America understood the reference. “That is, um, Cornell.”

“I’ve heard good things about that program! Did you work with Zohar?”

“No, he went emeritus a few years ago. His wife had a stroke, and he stays home to take care of her—”

“That’s just awful. I was wondering why he’d pulled out of that edited volume. How’s she doing?”

“Much better now, I’m told. They got a dog, which helps—um, with the depression—”

“Oh, very good—my own advisor had a bout of cancer a while back, and they got a cat. Supposedly an animal companion really helps—”

She and Belinda carried on like this for a little bit.

Alice thought she was doing quite well. She recognized all the names Belinda dropped, she’d mentioned the right connections for Belinda to take her seriously, and she hadn’t managed to make a mess of her tea or her biscuit.

Except Belinda’s eyes kept trailing to a spot over Alice’s shoulder, as if seeking someone to rescue her from this conversation.

The third time she did this, Alice wilted.

“Sorry,” said Belinda. “I don’t mean to be rude—I’m just wondering where Peter is.”

“Who’s Peter?”

“He’s the sixth,” said Belinda. “In the cohort. We were undergraduates together.”

“Are you talking about Peter Murdoch?” the Frenchman piped up. Felix? Philip? “That’s the Oxford prodigy?”

“I heard he’s the only advisee Jacob Grimes’s taken on in years,” said the Italian, whose name Alice thought was either Paolo or Lorenzo.

“That’s right,” Belinda said proudly.

“I’m working with Jacob Grimes,” Alice said, but no one heard her.

The conversation drifted on to Professor Grimes’s reputation, Peter’s reputation, and the way Peter had supposedly impressed Professor Grimes by inventing a new pentagram, a twist on the Liar Paradox, on the spot during his entrance interview.

Did they know that Peter Murdoch was the youngest person ever to publish in Arcana ?

Did they know Harvard had written to Peter Murdoch with a job offer after his Arcana paper came out, and that Peter had responded politely that he needed to finish his A-levels first?

“Does he have scholars for parents?” asked the Frenchman. “He must have.”

“I think his mother does biology,” said the Italian. “And the father—mathematics, isn’t that right?”

“I wish I had academic parents,” said the Frenchman.

“It’s a terrible advantage,” said the Italian. “He’s a magician made in a bottle.”

“ There you are.” Belinda shouted toward the garden gate, where stood a lanky young man who’d either forgotten or decided against wearing the requisite black gown. “Late as usual. Peter Murdoch, everyone.”

The famous Peter Murdoch had overlong arms, overlong legs, and a wild bird’s nest of light brown hair under which sat a massive pair of wire spectacles.

The lenses were very thick, which had the effect of making his brown eyes appear owlishly huge against his face.

When he smiled his whole face split apart, revealing slightly uneven teeth.

He looked like someone who wore a retainer.

The overall effect was not unpleasant. He was decidedly no Greek god, and yet Alice could not stop staring at him.

She kept looking him up and down, trying to determine if he was a real person.

They all made their introductions. Peter was a cheerful, easy interlocutor.

You got the sense, watching him nod and smile, that everything in the world was interesting to him.

He kept asking everyone about their research, then asking follow-up questions about particular methods, but because everybody wanted to impress him and because the Italian (his name was Michele, Alice finally learned) went on and on so long about his work on rational choice theory, it was an eternity before Peter’s eyes alighted finally on Alice.

“Hello,” said Alice. “We’re advisee siblings.”

“Oh, we are?” Peter enthusiastically shook her hand. “I didn’t know he took on another one.”

She chose not to take this as a slight. “Right, well, that’s me.”

“I suppose we’ll be working together a lot. I do logic, by the way.”

“Linguistics and wordplay. And, um, some archival work.”

“A wordsmith!”

Alice’s cheeks felt very hot; she wondered if anyone could see. “Well, you know, Americans are only good for the weird, experimental stuff.”

“I love it,” he said. “I love Americans. So unconventional.”

Emboldened, she took a chance. “Say, do you want to get drinks sometime? Talk about our projects?”

“Yes! Tomorrow, the Pick? I’ve got a meeting before—so, five?”