Paradoxes 101

In many parts of the U.S. it is back to school time and with that in mind I take time out from prepping for my teaching duties at Thunderwood College to offer our loyal Skeptoid readers a free peek at the class, Paradoxes 101.

A paradox is a seemingly true statement that leads to a contradiction or a situation that seems to defy logic. Usually, most paradoxical statements do not imply a true contradiction and can be solved by demonstrating that one or more of the premises are false. The premise could also be a play on words, a product of faulty logic or a half-truth and the resulting biased assumptions.

For example: Suppose that a father and son are driving down the road. The car swerves off the road, hits a tree, and the father is killed. The boy is rushed by ambulance to a local hospital where he is prepared for surgery. The surgeon upon seeing him says, "I can't operate on this boy, he's my son!" How can this be?

This apparent paradox is caused by the reader making a hasty generalization. If the surgeon was the boy's father, then the statement can't be true. The paradox is resolved when it is revealed that the surgeon is a woman. The boy's mother.

It is somewhat common for a no-win situation today to be referred to as a "Catch-22". This is from Joseph Heller’s 1961 classic novel of the same name. Within the book, "Catch-22" is a military rule, the self-contradictory circular logic that, for example, prevents anyone from avoiding combat missions. The paradox is best explained in Heller's own words:

There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he were sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.

Sometimes when paradoxes are described you end up reading about ancient Greeks and mathematics. Nothing wrong with that. Today I’m focusing on, if you will, the lighter side of the topic. That brings us to what is known as the “Proof I am Dracula” paradox. It relies on two assumptions:

1. Everyone is afraid of Dracula.

2. Dracula is afraid of only me.

Therefore, I am Dracula

It sounds rather child-like and goofy, but the logic is valid. Of course any name can be inserted where it says Dracula.

Since everyone is afraid of Dracula, Dracula is afraid of Dracula. So Dracula is afraid of Dracula, but also is afraid of no one but me. Therefore I must be Dracula!

What if someone were to ask you, “Which is better, eternal happiness or a ham sandwich?” Personally, it would depend on how hungry I am. It would appear to most people that eternal happiness would be the more desirable of the two. Not so fast. After all, nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing. Therefore a ham sandwich is better than eternal happiness. Again, somewhat silly, but it makes a point.

Finally, there is what I like to call the Doctor House paradox. It is a version of the liar’s paradox and is the shortest example of the genre I could find. My favorite fictional character is well known for his catchphrase “Everybody lies”.

Discuss.