## Archive for October 8, 2010

### There Must Be Some Misunderstanding

The WordPress blogging system comes with administrative controls, and it allows me to see what folks are searching for when they reach my blog. One of the search phrases that showed in the admin area today:

“math jokes – if you get them, you don’t have friends”

That’s not true. And I can prove it’s not true, by showing that its contrapositive is untrue.

P = You get math jokes.

Q = You have friends.

Then this argument is

If P, then -Q.

The contrapositive is, “If you have friends, then you don’t get math jokes.” Symbolically,

If Q, then -P.

I have friends. Or, I have at least one friend, which is all I need to prove the truth of Q. And given that I’m the author of this blog, then clearly I get math jokes. Consequently, the contrapositive is untrue; and by the Law of Contrapositives, then the original statement is untrue. Q.E.D.

Sticking to formal logic, Brent Yorgey recently reviewed Math Jokes 4 Mathy Folks on his blog The Math Less Traveled. In his review, he stated that this was one of his favorite jokes in the book:

A logician said to his son, “If you don’t eat your vegetables, you can’t have any ice cream.” Upon hearing this, the son choked down a plate of broccoli, and his father, duly impressed, sent him to bed without any ice cream.

Upon reading this review, my publisher said, “What a terrible joke he chose to highlight! I don’t understand why it’s funny. The logician just sounds cruel!”

I then had to explain that the humor derives from the logical error known as denying the antecedent. The logician said, “If you don’t eat your vegetables, then you can’t have any ice cream.” It is a common mistake for folks to assume that the logician’s statement is equivalent to, “If you eat your vegetables, then you can have ice cream.” But it’s not. The second statement is the inverse of the original statement, and a statement and its inverse are not logically equivalent. The logician asserted that if the son didn’t eat the vegetables, then he would not get ice cream; however, he did not guarantee that his son would get ice cream for eating his vegetables.

Yeah, you’re right. Even if you understand it, it’s still not very funny.