Chương 20: Chapter 1.20: Proper Philosophy

If that's the level of challenge I'm going to be facing… But he maintained a carefully neutral expression. Instead of showing his amusement, he gave Cassian a thoughtful smile.

"May I involve my sister in this? She has quite a talent for numbers." Cassian nodded generously.

"Why not?" The two of them focused on Urania, who flinched slightly under the attention before scrambling to answer.

"It—um…" She swallowed and looked at Favius.

"You told me how you can split the distance between any two numbers again and again. So if you count every half step between one and two, you can never reach two." Favius hummed and found himself sharing a smile with Cassian. He prodded his sister, "But you get ever closer, and—" She looked at the stone in Favius's hand, took it, and dropped it onto the table.

"The stone clearly hits the table, so—" She drew out the last word. After a brief silence, Favius gave her a tip.

"The framing of a problem can be helpful, but often it will hinder you." Cassian hummed and stroked his chin in appreciation.

"Indeed, asking the right questions is a fundamental skill of any philosopher." Urania's eyes narrowed.

"So you are saying there's something wrong about the question…" While she thought, Favius considered the situation. The very same paradox had existed on Earth. Zeno's paradox. It was mostly a joke, a simple trap that anyone should be able to escape. Let's see if she can figure it out. Urania snapped her fingers.

"Ah! The question is suggesting that you should count the half steps, but the world doesn't run on half steps, it runs on time." Favius nodded, urging her on.

"And what's the relationship between steps and time?"

"Each step is shorter," she replied, then nodded to herself.

"So while there are steps beyond counting, at some point, the steps stop taking up time." Favius nodded and squeezed her forearm. Smiling, both of them turned to Cassian, who nodded.

"I was all but certain that you wouldn't stumble on this. But it is tradition. A jest to challenge young philosophers." He gave a genuine smile, his white teeth flashing.

"Now, onto the real problems." Favius exhaled as Cassian continued in a more serious tone.

"You referenced emptiness with a symbol. I believe I might have made a mistake calling what you did heresy without ensuring you understood the error of what you did."

"Take nothing." He held out an empty hand in the air.

"And now try to take away from nothing." He nodded and tried to grasp the empty air above his palm, holding it open and empty as well.

"You see, absence doesn't behave when interacting with other numbers. Try to subtract from it, and you shall still have nothing. Try to use it in division or multiplication…" He shook his head.

"It is either unchanged or results in nonsensical outcomes. Thus, it is obvious to anyone who can see the heavens that emptiness is not to be used in mathematics." Cassian studied him expectantly. Well, this is a more interesting problem. He's patently false about subtracting from zero, but zero is weird. Even on Earth, division by zero was undefined. So I can see where they are coming from. He nodded to himself and studied the man in front of him.

The intellectually honest approach would be to admit he has a point about division by zero and convince him that multiplication and subtraction are legitimate. But if I understand how they do philosophy here correctly, this is a contest, so—"If I have zero coins and borrow five from you, doesn't that mean I'm in your debt?" Cassian tilted his head to the side, then nodded.

"True. But what point are you trying to make?"

"Well, if I spent the coins you gave me, I wouldn't just have zero coins. I would have negative five coins, as I would still have to pay you back. My debt is now calculated as a number lesser than zero. I own minus five coins." Urania nodded along, but Cassian shook his head.

"That's not how it works. Subtraction is merely an operation, but debt is a quantity, and all quantities are positive by their nature." Urania narrowed her eyes and looked between her brother and the tutor.

"But Favius, you said that numbers extend infinitely towards positive and negative." This story originates from a different website. Ensure the author gets the support they deserve by reading it there. Before Favius could reply, Cassian shook his head.

"Negative numbers are an erroneous idea, stemming from the conflation of operation and quantity. Those things ought to be kept separate." Favius narrowed his eyes. Well, it's wrong, but numbers are ultimately abstractions. And—I could see a system of mathematics where you deny negative numbers and view them as a mere convenience of notation. They continued discussing it, Favius insisting on debt, trade, and reduction, but Cassian didn't budge. Urania studied both of them.

Ultimately, Cassian made a cutting gesture and nodded.

"You argue your position well, even though it is not the commonly accepted one." Favius opened his mouth, ready to say something scathing about the disconnect between public opinion and truth, but Cassian held up a finger.

"Conviction is a virtue for a philosopher. Those who merely follow what is popular shall never achieve anything great." Brutus chuckled in the background. Cassian looked up, and everyone in the room turned to the man.

"Something you would like to contribute to our discourse, Ovinius Kestrelo?" Brutus gave an ugly sneer, blood again running from his nose, then shook his head and returned his focus. What's up with him? Favius shrugged and looked back at Cassian.

"So what's your third challenge?" Cassian nodded gravely.

"Your use of malformed division." He took out a stick, and Brutus shifted, making the tutor flinch. But the man rallied quickly and held it up.

"Behold, one whole stick. Are we in agreement about this?" Favius nodded, but Urania narrowed her eyes before venturing an answer.

"Yes?" Cassian smiled, then broke it apart, holding one stick in each hand.

"What do I have now, Urania?" She responded confidently, "Two halves of a stick." The tutor shook his head.

"No. I have two whole sticks. The separation of a whole creates two new wholes. There exists no such thing as a half." He tried to press the sticks together, but they fell apart.

"You see, all things are divisible, until they are broken into the atomi. Yet even at the level of the atomi, which can no longer be split, you are dealing with wholes and not parts." Favius smirked briefly. Well, technically I know how to split an atom, but that is not going to be a useful point of discussion. Still smiling, he spoke to the tutor.

"But if everything is made from atomi, how can you argue that the stick is a whole? You know it could be broken down, which suggests it is made of parts." Cassian shrugged.

"This is one of the greater mysteries of the universe. Philosophers have not yet found a satisfying answer, though I personally believe that the atomi do not exist until you break a whole again and again and again." Favius narrowed his eyes. That's not how physics works. But if you don't have any way to analyze the structure of matter… I can see how you might arrive at such a conclusion. No matter. He shook his head and turned to Urania.

"What are your thoughts on this?" His sister scrunched up her nose and massaged its bridge in thought.

"Well, he has a point…" She studied the broken stick.

"You talked about the difference between description and reality. So what if you're both right?" Cassian gestured at her.

"Please elaborate, girl." She straightened and nodded to herself.

"If you had the stick you began with and you wanted to make a fire, you need two whole sticks to rub them against each other. For that, you break it apart and make two sticks from one. That is your description of what is happening to the stick."

"Yes?" Cassian considered, then nodded, and Urania turned to Favius.

"But if the stick was all the firewood you had to feed a fire for the night, and you burned up half of it, then you would be left with half of your firewood." She looked between the two men.

"Maybe what matters is the context in which the stick is broken and how it can be most usefully described." Cassian stroked his chin, then nodded.

"An interesting perspective indeed." A slow clapping erupted from behind them, and Brutus sat there with a mocking smile.

"Well done, Urania. If you continue like this, we might actually end up having one real philosopher in this room." Cassian's upper lip curled, and he glared across the room. As did Favius. He met the man's eye and mouthed silent words. What are you doing? Brutus met his eyes, then slightly shook his head before deliberately turning back to studying the wax tablets. Cassian's fists clenched, and Favius considered. Why is Brutus antagonizing him? It doesn't make sense. But—ah, shit. Probably no use in dwelling on it.

He gestured at Urania before addressing Cassian.

"I think what she is addressing is the difference between reality and existence. You point to the stick turning into two smaller sticks, and that is what objectively exists. However, mere existence is the realm of animals. We as thinking men concern ourselves with the reality of ideas and apply them wherever they are useful." Cassian's frown shifted from anger to thoughtfulness, but Brutus spoke up again behind him.

"There is wisdom in that. There exists a tutor and a student in this room, yet the reality of it is that only one of them is actually useful." Favius turned, hot anger churning in his stomach. What the fuck does he think he's doing? Before he could say anything, Cassian hissed, "I will not suffer more of those indignities from a Rhexioni wildlander. Leave."

"Or what?" Brutus stood up and picked up his axe.

"What are you going to do, little man?" Favius stood up and hissed at the cultivator, "Brutus, what—" But the man made a sharp gesture.

"Don't think that by acting nice your insults will be forgiven, Cassian." The tutor tightened his grip on the sticks in his hands and puffed himself up, his face red with anger. Favius's eyes widened slightly. Is he really going to—? Then Cassian let out a breath and let the sticks clatter to the floor. The tutor stormed out of the room, but at the door he glared at Brutus, then at Favius.

"Don't think there won't be consequences for this, boy. If you think you can sic your dog on me, even if I show goodwill, your father will hear of this." With those words, he was gone. Favius briefly took in the room—his sisters. Urania looked confused, while Caliga grinned like a cat playing with a mouse. He turned to Brutus.

"What the fuck do you think you're doing?" he hissed at the cultivator. A condescending smile was his only answer, and it made Favius' blood boil.