"A paradox is something that seems like it should make sense, but doesn't."
Oz could see the scrunched up, concentrated look on Echo's face as she quickly wrote the statement down. He watched with interest as her brows furrowed once she'd finished writing, and looked over the statement. She spent a long time looking at it spread on paper, in her even handwriting, turning her head to the left, then to the right, as if it would suddenly make sense to her if she looked at it from a different angle. It almost seemed like it had been five minutes, when she finally looked back up at him, but Oz found he didn't mind at all. Echo was so very pretty and cute; he didn't mind watching her even the slightest bit. He was over the moon that they'd ended up taking the same philosophy class.
When she did look up at him, her confusion had not dissipated, but her face was none the less, earnest. "The first example." She requested.
He smiled, and did as she had instructed. "Hempel's Ravens, which states that looking at a green apple increases the likely hood that all ravens will be black." She hurried to write that down again, but spent even more time looking at it than she had before. She kept looking at the first thing she'd written, then the other. It was really cute. He wondered if Sharon felt the same way about confusing cute boys, because she seemed to intentionally confuse as many as she could. He was definitely starting to see why. Not that he was intentionally trying to confuse Echo, and not that he ever would, but it was an observation to be made.
Finally, he shook her head, as if to dispel unwanted thoughts, and looked up at him again. "Next."
"Horse Paradox." He said. "This states that all horses are the same color."
This time, she scrolled out what he'd said, but looked almost a little skeptical. He'd never really seen Echo look skeptical before, but he could see it more easily at that exact moment. She seemed to be struggling between saying something, and keeping her mouth shut. Since Oz liked listening to her voice he hoped she would say what was on her mind, but he knew better than to prompt her. He waited patiently, as she clicked her pen evenly, looking between the three things she'd written.
"Are they all about animals, or colors?" She eventually asked. Oz had a pretty good poker face, but he was hard pressed not to smile and giggle at how cute she was. And he was tutoring her, what absolute luck!
He thanked his photographic memory, and spoke. "No, not all of them. There are many that don't. The only real requirement is that something that may seem logical, is not." He went over the list he'd memorized for the test and cocked his head. "These might be bad examples to start with. How about the Unexpected Hanging Paradox. This one states that a hanging will happen, but that the day of the hanging will be a surprise. So the hanging will never happen."
She looked at him in confusion, before realizing she was suppose to write the statement down, and hurried to do so. Once it was down, she clicked her pen a few times, and looked at him. "This seems like a bad conclusion to come to. Especially for the hangman..."
Oz's smile widened, and his eyes glittered. "You're right, it is, but that's the point. The idea behind this one is that if the hanging happens, it won't be a surprise anymore. So, for it to stay a surprise, it must never happen."
Echo shook her head in disbelief. "But if it never happens, why was the hanging brought up in the first place?"
"Because it will happen."
She glowered down at the statement for a few seconds. "Because it doesn't actually make sense?"
Oz chuckled. "That is the nature of a paradox. You're getting it! Now onto the next one-"
"Wait." Echo said suddenly, looking over at him with all seriousness. "I got that one, but what do apples and ravens have anything to do with one another?"
The statement on his lip died, and smiled sheepishly. "Uh..." He scratched the back of his neck nervously. "I, uh, never really thought about it. I just memorized that one, since the study guide said it would be on the test..."
Echo gave him a long, searching gaze, before nodding her head once, and looking back down at her notes. "The next one." She stated, after a short silence.
Oz looked away sheepishly. "I'm sorry."
Echo shook her head, and angled him with a strong gaze. The kind of gaze that Echo often gave, likely without even knowing it. "It's okay. I'll tell you when I find the answer."
He smiled back at her sheepishly. "Echo, did you know you're the cutest girl in class?"
She blushed for five seconds, before scowling at him. "The next one, Oz."