A dialogue on rigorous thought

Sep 16 2011 Published by under Uncategorized

"My dear mathematician friend, you must never tell anyone what you saw me do to evil dean Sharkhorn's office chair."

"Okay."

"Great! You're a true friend and a hero of the faculty, not afraid to excuse action against the evil dean Sharkhorn and his foul throne!"

"A question arises."

"Uh, sure."

"Is it okay for me to admit I've promised to never tell a certain undefined thing?"

"No!"

"So if the chair affair is denoted by X, I am to not speak of X, and to not speak of not speaking of X."

"Er, yes."

"And if someone was to inquire, say, do I have ever promised to never speak of a promise?"

"What--- who would ask something like that?"

"Little you know of mathematicians. Logicians especially; they are conversation fiends."

"Wait, look, just promise to never speak of this event, recursive."

"Okay. That's much better; we could be here for a long time otherwise. But... if I'm to not speak of the incident, or of this conversation relating to it, or of me later thinking of that or this, or of any incident relating to these earlier incidents... do you think that could become a dense subset of my future actions? If so, I couldn't speak, within the limits of easy conversational error of epsilon arbitrarily small, of anything! I would have to deny having any experiences or thought processes at all!"

"You don't have--- I--- I don't know what that means, but don't worry, won't happen. Nothing with epsilons ever happens in real life."

"Oh. Well, it's a practical matter; I trust your judgment."

"Great."

"Wait. If someone asks, 'where were you at the exact moment five minutes ago?', I would have nothing to say."

"That's the purpose."

"If they asked, was I in the loo, what should I say?"

"I... what?"

"I mean, if I'm allowed to comment on anything except the actual tacky truth, there's the possibility of excluding all other alternatives---"

"That'd take centuries! And a Sherlock Holmes!"

"No no no. 'Did you see anything unusual? Oh, no answer. Did you see anything unusual involving two or more humans? No, you say? Involving one human? No answer, eh? Ehhh? Who was it?'"

"...you don't need to be that obliging."

"But I don't like lying. And I don't like to get started; I don't know where to stop. Remember my cousin Jeremy?"

"Sure."

"I don't have no cousin Jeremy. He's a little white lie that got out of hand."

"But I've met... look, just say you were on the toilet. If they ask any details, say that's disgusting and shut up."

"Oh."

"Finished?"

"I guess that covers most... what if someone says they know I'm lying?"

"Then say you aren't!"

"What if they provide evidence to the contrary? Witness testimony or video or---"

"WHAT?"

"I mean, do I call that a lie? A fabricated, slanderous, untrue thing? Because I'd be arguing against the coherency of their memory, or the veracity of video imagery showing me in the dean's office's doorway talking to you. Even with the admittedly powerful position of arguing assuming a reality-contradicting premise---"

"What do you mean, video?"

"You know, from that surveillance camera in the corner of the office --- oh, and now he runs away, leaving this business unfinished. What an inconsiderate person!"

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