The Paradox of the Ravens
Just as Twilight Sparkle shelved the last book, a shower of shattered glass cascaded onto her head. A ball of cyan fur and feathers barrelled across the library floor, colliding with the shelf on the opposite wall before coming to a standstill as half the books on the shelf fell upon it.
Twilight carefully stepped through the broken glass and started picking up the books. “Rainbow, I don’t see why you can’t just use the front door like every pony else.”
“Doors aren’t my style, nerd,” Rainbow Dash explained, standing up, folding her wings carefully, and rubbing the back of her head, where a particularly voluminous book by Colt Gustav Amble had landed.
Twilight’s horn lit, and the shattered glass reassembled into a window, slotting itself perfectly into the pegasus-shaped hole that her friend had left in her wake. “So annoying,” she muttered to herself.
Rainbow looked at Twilight, kicking the floorboards with a hoof. After some time, she said, “wellllll…”
“What?” Twilight asked.
“Aren’t you going to ask me about my trip to Las Pegasus?”
Twilight sat down at her writing desk. “Oh yes… with Fluttershy. How did it go?”
“Totally awesome!”
“Of course. Anything else to say on the matter?”
Rainbow was confused. What else did Twilight want to know? “Errr…”
“Like weren’t you supposed to be studying bird migration patterns or something?”
Rainbow’s eyes lit up. Something else awesome that she could talk about! “Oh yes… Fluttershy had me following a flock of ravens around, trailing them to see where they go. Ravens are super fast, but not as fast as Rainbow Dash!”
“Oh,” Twilight said, “I’ve never actually seen a raven. Read about them in Edgar Allen Pony books, but never seen one.”
“Meh, they’re just black birds, Twilight. Nothing special.”
“Are they all black?” Twilight asked.
Rainbow shrugged. “Head to toe.”
Twilight shook her head. “No, no… you misunderstand me… is each individual raven black?”
“Yeah, sure,” Rainbow replied.
“But how can you be sure?”
Rainbow sensed another one of Twilight’s talks coming on and didn’t like it. “I don’t know… they just are. Every raven I’ve seen is black.”
Twilight stood up and emerged from behind her writing desk and began pacing the floor. “Let us examine the proposition, all ravens are black.”
Rainbow groaned.
Twilight continued. “Now, you see a raven, and it is black. This doesn’t prove our proposition—”
“Your proposition,” Rainbow interrupted.
“Our proposition. It doesn’t prove our proposition, but it is evidence in support of it. Right?”
“I guess,” Rainbow said. “Until I see a white raven anyway.”
“Well, yes.” Twilight smiled. “Exactly. That would entirely disprove our proposition. Very good. You’re learning.” Rainbow rolled her eyes and Twilight continued. “But you haven’t seen a white raven. Every raven you’ve seen has been black. Each time you’ve seen a black raven, it has added evidence to support our proposition. No matter how many black ravens you see, you’ll never prove our proposition, but we can gain confidence in it.”
“Okay,” Rainbow said a little hesitantly.
“But…”
“I knew there’d be a but.”
Twilight smiled. “There’s always a but.”
“You’re always a butt,” Rainbow muttered under her breath.
“But our proposition, all ravens are black can be restated another way. All non-black things are non-ravens.”
“What?” Rainbow asked.
“Think about it. It’s saying the same thing. If all ravens are black, then logically anything which isn’t black cannot be a raven, right?”
Rainbow scratched her head. “I guess.”
“And if anything which is white, or red, or blue, or green, or yellow, or whatever isn’t a raven, then it means all ravens must be black, right?”
“Aha.”
Twilight looked triumphant. “Exactly! So our two propositions are equivalent. All ravens are black. All non-black things are non-ravens.”
“So what?” Rainbow asked.
“But you see, this is how we can add more evidence in favour of our original proposition!”
Rainbow shook her head. “I don’t get it.”
“Look at my writing desk” Twilight pointed. “What colour is it?”
“Brown,” Rainbow answered.
“So it’s non-black.”
“Sure.”
Twilight smiled. “And is it a raven?”
“Of course not.”
“Precisely,” Twilight argued. “It’s a non-black thing and it’s a non-raven.”
“So what?” Rainbow asked, clearly confused.
“Well, it supports our proposition, all non-black things are non-ravens.”
Rainbow thought she’d spotted an early flaw in Twilight’s argument. “It doesn’t prove it though!”
Twilight nodded. “No, it doesn’t prove it. Just like seeing one raven doesn’t prove all ravens are black. But it’s evidence in favour of the proposition.” Twilight walked around the room pointing at things. “Look at my red coffee cup. This yellow book. This green carpet. The blue sky out there. All of that is evidence in favour of our proposition that all non-black things are non-ravens.”
“But this bookmark is black, and it isn’t a raven,” Rainbow pointed out.
“Yes, the bookmark is black, but our second proposition doesn’t talk about black things. It talks about non-black things. All non-black things are non-ravens. So a black bookmark doesn’t add any evidence for or against that proposition.”
Rainbow admitted defeat on this small matter. “Yeah.”
“So by walking around this room, we’ve found quite a lot of evidence that all non-black things are non-ravens, right?”
“So what?” Rainbow asked.
“Well, like I said earlier. Our two propositions are exactly equivalent. If all non-black things are non-ravens, then all ravens are black.”
“And?”
“Which means, by looking around this room, without observing any ravens, we’ve added evidence in favour of our original proposition that all ravens are black!”
“What?” Rainbow asked, suddenly shocked.
“My writing desk, my coffee cup, that book, the sky… all of it is evidence that all ravens are black.”
“That makes no sense whatsoever,” Rainbow said.
“Prove it.”
Rainbow started to cry.
