There’s an old Greek story about a law teacher who guaranteed to refund a student’s tuition if he didn’t win his first case. After graduating, one student refused to pay. So the teacher sued him. The student didn’t mind, though. If he lost this, his first case, he wouldn’t have to pay his tuition. If he won he wouldn’t have to pay either.

The story tickled me when I first heard it in a high school logic class, as did this, the “seducer’s” paradox:

1. Hey sweetheart, will you answer this question the way you’ll answer my next question?
2. Will you go to bed with me?

Paradoxes like these are wormholes in the fabric of reality, as irresistible, at least to me, as a hole in a sweater–I can’t keep from teasing and twisting at the wool hole or the wormhole.

Mind Readers Dictionary: The Podfast : Play in Popup

Mind Readers Dictionary : Play in Popup

 Paradoxes are relationships without resolution, infinite loops, circular interactions, togglers that keep cycling us back to our starting point. Since no one has the patience to cycle indefinitely, paradoxes eventually pop us out of the loop. Their interminability ejects us. We’re on the merry-go-round going in circles and then pop, we’re off the merry-go-round observing the circles from outside them. It’s this popping off that makes paradoxes the source of humor. (See Multi-level headed)

Paradoxes come in many shapes and sizes. The liar’s paradox (the statement “I am lying”). Shaggy dog stories that eat their own tails, optical illusions, ironic humor–I love this stuff. I collect it all and build some of my own:

• I’ve wasted my whole life learning things I now already know.
• No matter how hard I pursue the truth, it will never catch me.
• I wasn’t born yesterday for nothing. (My father’s, actually. He called such paradoxes “Escherisms.”)
• If you only live once, then life is short and you might as well believe in comforting notions like reincarnation, but if you therefore believe in reincarnation and are therefore coming back over and over, you’ll need to be more realistic, in which case you shouldn’t believe in reincarnation.

Paradoxes are popular not just with me but with all of us. Take the ever-popular conversational packing peanut “really” and its variants:

No, really.
Really, I’m not joking.
Take my word for it.
I’m not even kidding. (Which young people say these days most perplexingly.)

These amounts to saying “you don’t believe me, but believe me, you should believe me.” Now in a way it sounds no more paradoxical than “you don’t love me but you should.” What’s paradoxical about wanting persuade someone to regard you differently? But because what’s at stake is one’s credibility, there is a self-referential quality to this attempt to persuade someone to find you credible.

Really, “No, really” is just a variant of the liar’s paradox.

Paradoxes can be thought of as either stand-alone irresolvable declarative statements (declarations such as “I’m hungry”) or as imperative statements (commands such as “Give me something to eat”) addressed to a problem-solver who wants resolution–the law professor trying to figure out how to win the student’s tuition, the seducee who wants to avoid going to bed with the seducer.

Would-be resolvers of the liar’s paradox are people who need to know whether the statement is true or false, which means they aren’t sure. As an imperative then, the statement “I am lying” has an implied commanding first clause.
Clause 1. Believe me when I say
Clause 2. I’m lying.

Its effect on the resolver’s mind is oscillation without resolution:

1. Clause one is true, therefore clause two will be true. (I thought he was maybe lying but he says he’s telling the truth. OK, the solution is to trust him on what he says next.)
2. Clause two is true, therefore clause one isn’t true. (What he said next is to not trust him, which makes me realize he was lying when he said to trust him.)
3. Clause one isn’t true, therefore clause two isn’t be true. (Therefore I shouldn’t trust him about what he says next.)
4. Clause two isn’t true, therefore clause one will be true. (He’s lying when he says he’s lying so I can trust him when he says I should believe him.)
1. [again] Part one is true therefore . . .

Notice that part one, “Believe me when I say,” is the equivalent of “No, really.” Given the self referential quality of this pair of statements, either one alone can imply the pairing and the paradox. The liar’s paradox is evoked with either the utterance “I am lying” or “believe me when I say” in other words “no really.”

Today, joking with someone, I said, “You’re terrible.” Then realizing he might take me seriously, I found myself saying “Really,” to indicate I was joking. I said, “Really” to mean “not really.” At face value this is absurd. It works because by saying “no, really” in the exaggerated self-parodying voice I said it, I called attention to the paradox itself.

Biologist Gregory Bateson noted that animal play-fighting has to have an undecidable or paradoxical quality. It has to be serious enough that it’s good practice for real fighting but not so serious that it becomes dangerous. Animals have no way to say “not,” but they can exaggerate contradictory signals for both seriousness and non-seriousness. A dog play-fighting will in effect parody itself, sending exaggeratedly aggressive and non-aggressive signals simultaneously, for example tugging to and fro on a rope in your hand while also wagging its tail.

We do something similar when we invite greater warmth in a friendship by calling the other person an unusually formal name. A former officemate used to flirt with me by saying, “Hello Mr.” when we passed in the halls. We were past Mr., so it signaled the opposite of formality.

This morning, my “You’re terrible…really,” took the seriousness further than I could possibly have meant, which indicated I wasn’t serious at all. Dizzying, but fun.