James was the tallest child at Wayside Homeschool. He had always been the tallest, because he had always been the oldest. He would have been glad to let Owen or Felix take a turn at being the tallest or the oldest, but every time that they got a little taller or a little older, James had become even taller and older still. He felt that it was an unfair advantage.
James was learning Logic in school this year, which is the art of critical thinking. His Father read him the Logic assignment.
"My dog doesn't like cats, and no mouse likes cats. So my dog is a mouse. Represent this argument in logical notation."
James scratched his head.
Father explained it to him. James scratched his head again.
Father tried to have James put the argument into a system of letters where each letter represented a proposition. A proposition was a single statement. Then Father would have him falsify each statement by writing a squiggle in front of it. Then Father would have him convert the statement by switching the orders of terms, and invert the statement switching the quality of the terms, and then find the contrapositive by converting and inverting at the same time.
James scratched his head.
"Come on, James," said Father "if you don't learn how to use logic then you'll never be able to communicate clearly."
James thought that maybe if he wanted to communicate ideas clearly that he should probably steer clear of logic. That was a conversion of Father's proposition.
"Let's review necessary and sufficient conditions," said Father, "and we'll see how much you remember. Is rain a necessary or a sufficient condition for clouds?"
"Well," explained James, "you have to have clouds in order to have rain. But you don't need to have rain if you have clouds."
"Right," said Father, "so what kind of condition is rain for clouds?"
James thought for a minute.
"Sounds like wet conditions to me."
Father scratched his head.
"In any 'if-then' statement where if you have P, then Q follows, what sort of a condition is P for Q?"
James scratched his head.
"A conditional condition?"
"Not a conditional condition."
James wrote down a squiggle in front of the proposition, "if p then q," and put brackets around it.
"I didn't mean that you should invert that proposition. What kind of a condition is P for Q in the proposition?"
James said it that P was an invalid condition for Q, since the proposition (which he had bracketed) was negated by the squiggly sign.
"No, no, no!" said Father.
James counted each "no" and wrote three more squiggly signs in front of the proposition. He looked at it for a moment.
"So it is not true that it's false that it's incorrect that the proposition that if it rains then there are clouds is untrue?"
Father rolled his eyes rudely, and Mother, who happened to be walking by, told him to mind his ps and qs.
"Let's practice spotting a fallacy. If I tell you that you can have ice cream only if you do all of your logic homework perfectly, and you do your logic homework perfectly, but then I don't give you ice cream after it's completed, did I lie to you?"
James asked what kind of ice cream was being offered.
"I would not have lied to you," said Father, "because you would have substituted the conversion of the original proposition for the proposition I made."
James said he wouldn't have lied because he didn't want to do his logic homework anyway.
Father didn't want to teach the logic homework either.
They had some ice cream.
