The two-move checkmate in logic

The two-move checkmate in logic. So elegant yet so powerful. So logical yet so amusing. So sneaky, it’s scary. It’s the “gotcha!” trick that makes you wonder how anyone could have missed it.

The tactic not only disproves one statement, it proves another at the same time, yet this combination move is nothing new or astounding in itself. The beauty is in the variety of ways it can be applied.

And I’m going to give it to you right now.

In Latin, it’s called Reductio ad absurdum (reduction to the absurd). In other circles, it’s called proof by contradiction. I like to call it the ‘gotcha!’ trick. Ladies and gentlemen, now introducing…

The Two-Move Checkmate in Logic

I’ve written a little ditty to help you remember the two moves:

1) Assume the claim itself is true
2) Then with the claim, thrust it through

That’s the somewhat poetic, highly corny version. Here’s how it actually works.

Assume the claim itself is true

This one’s easy. Simply assume that whatever the claim states is true. This doesn’t mean it is, but we’ll assume it is for now.

Then with the claim, thrust it through

This second move requires us to use something from logic called the Law of Noncontrediction (or LoNC for short).

The Law of Noncontradiction says, “a statement cannot be both true and false at the same time.”

For example, I couldn’t say the statement “I like carrot juice” is both true and false (some of you no doubt are wondering how I could ever say the statement “I like carrot juice” is true, but that’s beside the issue).

Now, why is this important? Well, the carrot juice isn’t, but the “both true and false” part is.

The LoNC becomes important when discussing beliefs that are self-contradictory or self-refuting. Beliefs like these rely on statements that, while they might seem to be true, cannot be applied to themselves.

Let me give you an example…

Suppose I were trying to argue that knowledge is impossible. The statement, “Knowledge is impossible” then is either true or false. Let’s consider this.

First, we assume that the statement “Knowledge is impossible” is true. If the statement “Knowledge is impossible” is true, then we wouldn’t be able to know anything. Applying the second move then if we can’t know anything, how can we know that knowledge is impossible?

It’s self-defeating. Therefore, and here’s the nifty part, the statement “Knowledge is impossible” has to be false. If the statement, “Knowledge is impossible” is false, then at least some knowledge IS possible.

Whew. If that last bit left you confused, don’t worry.

The important thing to understand regarding these claims is that if you apply the claims of the statement on the statement itself, the statement cannot be true. And a statement that is not true is false. Thrust home.

Elegant. The LoNC disproves one belief (that knowledge is impossible in this example) while at the same time proving another belief (that knowledge is possible). That’s why it’s the two-move checkmate: it kills the king and wins the game all in one motion.

This same reasoning can be applied to hundreds of arguments, particularly those that involve discovering truth or knowledge. Among others, this reasoning dispels each of the following notions:

~ “There is no absolute truth.” (Then how is that claim an absolute truth?)
~ “There is no way to know absolute truth.” (Then how is that claim known to be an absolute truth?)
~ “Science is the only way to prove that something is true.” (Then how is that claim proved by science?)

Serving Suggestions

(1) Remember the rhyme: “Assume the claim itself is true… then with the claim, thrust it through.”

(2) This simple tactic is one of the best ways to establish a common truth with someone who does not believe the Bible.

(3) If you have any questions about this, feel free to ask. I’d be happy to try to answer anything I can. Alternatively, if you have any favorite examples of how to use this tactic, feel free to share. I’d enjoy learning more.