"Today is opposite day," said the Bully, "yes means no and no means yes. Now, do you want me to hit you?"
Clyde scratched his head. He could see that this was going to be a very delicate negotiation, but he was fairly sure that he would be able to maneuver his way out of it.
"That statement is inherently contradictory," Clyde said, adjusting his glasses, "as Im sure you are aware. If today is, in fact, opposite day, then your statement to that effect would be false, and today would, consequently, not be opposite day at all. On the other hand, if today is then not opposite day, then your statement is true, and if your statement is true, then it is false. So by making that statement, you trap yourself in a logical loop, in that the statement, in and of itself, cannot be true if it is true, and is not false if it is false." Clyde smiled. The Bully, at this point, would be reeling with the implications of his own contradiction, and would be unable to pursue the matter further.
"Its an interesting point you make, Clyde," said the Bully, "but, unfortunately, not applicable. You are, Im sure, thinking of the conundrum regarding the people who always lie, and the people who always tell the truth, and applying that logic to this set of circumstances. But in this particular case, the situation is not quite as absolute. In point of fact, opposite day does not officially begin until after I make the statement to the effect that it is opposite day, and therefore the statement is not contradictory, but rather introductory. Your mistake was assuming that opposite day exists prior to my assertion that today is that day, when, in fact, opposite day is only created by that assertion."
Clyde was impressed. It was clear that this Bully had done his research. He was presenting the classic Big Mayan rebuttal to Clydes opposite day opening argument. But Clyde wasnt licked yet. "Interesting," he said, "but it seems to me that youre ignoring the fact that once you have declared that it IS opposite day, then the statement becomes true of the whole day, even the time preceding your statement. So that while the statement is, by your reasoning, not contradictory when you say it, once you have finished saying it, it becomes retroactively contradictory. So, yes, I grant you, it is true during the actual time of speaking, but immediately after it begins to not have been true as you said it. Do you see?"
"Again, theres an error in your logic, Clyde." The Bully smiled, "you seem to be of the impression that opposite day is a calendar day, such as Memorial Day or Presidents Day. In fact, opposite day is simply a twenty-four hour period which begins immediately following the declaration that it is. I think youll agree that I can describe any twenty-four hour period as a "day" even if it is not a day as defined by the roman calendar. Indeed, in any given twenty-four hours, the earth does rotate once fully around its axis, which is certainly a more accurate measure of a "day" than the flawed calendar of the Romans."
Clyde adjusted his glasses. Astronomy, he was sorry to say, was not exactly his strong suit. He decided to attack the problem from a different angle. "All right then, given that thats the case, then the statement you make after today is opposite day becomes suspect. You stated, if I am remembering correctly, that no means yes and yes means no."
"I think I said it the other way around, but go on."
"Well, that statement then becomes the contradiction. You say that yes means no, but, since it is opposite day by the time you make that statement, what you are actually saying is that yes means yes, which, given the fact that it is opposite day and yes in actuality means no, is---"
"I see where youre going with this, but Im afraid youre in error. You see, the statement yes means no and no means yes, is simply a clarification of the previous statement. It is, in fact, an adjunct to the statement today is opposite day. Therefore, since yes means no and no means yes is a part of the declaration of opposite day, it is subject to the same exemption from oppositing, if you will, as the original statement."
Clydes glasses were beginning to fog. He took them off, wiped them on his shirt, replaced them, and looked at the Bully. "So, then, as I understand it, you claim that the full statement of opposite day runs Today is opposite day. Yes means no and no means yes, after which the twenty-four hour period which you have declared as opposite day begins."
"Yes," said the Bully.
"By that reasoning, then, the question do you want me to hit you? does fall in the time period you have described as opposite day."
"Yes," said the Bully, "but, being a question, Im not sure that it is subject to the same process of oppositing that an empirical statement is."
"I disagree," Clyde scratched his nose, "because if I, to use your terminology, opposite the question, it becomes do you want me NOT to hit you? Let us say, for the sake of argument, that I answered yes to the question, because I take your question at face value and assume I am answering no, I do not want you to hit me. However, you could then hit me with impunity, because you can claim that my answer yes meant no in response to your question do you want me to hit you? which meant do you want me NOT to hit you? (or, indeed, do you NOT want me to hit you?) so that my response could then be interpreted as I do not want you not to hit me, which, because of the double negative, would have become I want you to hit me."
The Bully shook his head. "But can you really say that the question do you want me NOT to hit you? is the opposite of the question do you want me to hit you? Its true that one query in the negative and the other is in the positive, but it seems to me that they ultimately ask the same question. In fact, I could combine the two to form the resulting uber-question do you want me to hit you or not? which removes the issue altogether. In fact, that restatement of the question eliminates your ability to provide a simple yes or no response, since neither would adequately address the question as stated. No, instead your answer would have to be more specific. In fact, it would be in your best interests for it to be so, because that specificity would eliminate the ambiguity of a yes or no response and circumvent the problem you just brought up."
The Bully smiled. Clyde thought for a moment. The Bully had presented his case clearly and intelligently, and without room for interpretation. He was sure he understood the Bullys logic, as stated, and would be able to address the query in a manner that would concisely convey his preferences regarding being hit by the Bully. "Okay," said Clyde, "just for the record, would you mind restating your question?"
"Not at all," the Bully said. "It is simply this; do you want me to hit you?"
Clyde took a deep breath, adjusted his glasses, wiped the sweat off of his forehead, gave the Bully a good hard kick in the shin, and ran like hell away.