James Baquet

    Ming is chatting with his classmate Mark in the common room of their dorm.

    Ming: Hey, Mark. I’ve got a good one for you. Ready?

    Mark: Ready as I’ll ever be!

    Ming: Okay, here it is: What’s the difference between a contradiction and a paradox?

    Mark: Oh, man! That’s a tough one! Let’s start with “contradiction,” since it’s more concrete.

    Ming: Okay…

    Mark: A contradiction is anything which states that something both is and is not.

    Ming: What?! That’s concrete?

    Mark: Well, in terms of logic, we say that something is “both A and not A,” where “A” describes some characteristic.

    Ming: Maybe an example would help.

    Mark: Here’s one: dry water.

    Ming: I see! Water is by nature wet. To say that something is “both wet and not wet,” or “dry,” is a contradiction.

    Mark: Bingo! But they’re usually trickier to spot.

    Ming: How so?

    Mark: Let’s say that your friend told you, “It never rains here in August.” And then it rains in August.

    Ming: I see. The rain contradicts his statement.

    Mark: Exactly.

    Ming: Okay, so what about “paradox?”

    Mark: That one’s a little more slippery. A paradox might seem like a contradiction, but turns out to be true.

    Ming: For example?

    Mark: Well, there’s this idea that if you work harder, you’ll make more money.

    Ming: Isn’t that true?

    Mark: It can be. But at some point, the amount of work one does might fail to bring rewards. Think, for example, of someone who works so hard he gets sick, and starts missing work.

    Ming: Okay, so where’s the paradox?

    Mark: In this statement, something looks like it will be true, based on the assumptions and the logic, and then it isn’t. That’s a paradox.

    Ming: I get it! The effect is the opposite of what we would expect. So what’s another kind of paradox?

    Mark: Just the opposite, where something seems like it won’t be true, and it is.

    Ming: Again, an example?

    Mark: It’s right there in the example I already gave you. Like this: “Work less, and you’ll make more money.”

    Ming: Got it. But aren’t these really just contradictions?

    Mark: You might say that some paradoxes are just special kinds of contradictions: Looks like it’s true but it’s not; or looks like it’s not true, but it is. But there’s a third kind.

    Ming: What’s that?

    Mark: The self-contradictory statement, like “I always lie.”

    Ming: Why is that a paradox?

    Mark: Because if I always lie, then that statement is a lie.