Reductio ad absurdum facts for kids

Reductio ad absurdum is a Latin phrase that means "reduction to the absurd." It's a clever way to prove something is true by showing that if it weren't true, something silly, impossible, or contradictory would happen.

Imagine you want to prove a statement is true. With reductio ad absurdum, you start by pretending the statement is false. Then, you follow the logic of that false idea until you reach a conclusion that is clearly wrong or doesn't make sense. Because the false idea led to something absurd, it means your original statement must be true!

This method has been used for a very long time in mathematics and philosophy.

Here are some examples of how it works:

• Rocks have weight. If they didn't, they would float in the air, which we know doesn't happen. So, rocks must have weight.
• Society needs laws. If there were no laws, there would be total chaos, which nobody wants. So, laws are necessary for society.
• There is no smallest positive rational number (a number that can be written as a fraction). If there were a smallest one, you could always divide it by two to get an even smaller one. This shows there can't be a smallest one.

History of this Idea

The idea behind reductio ad absurdum comes from the Greek language. The ancient Greeks called it hê eis átopon apagogê, which means "reduction to the impossible."

The famous Greek thinker Aristotle often used this method. You can also find it used many times in Euclid's Elements, an ancient book about geometry.

How the Method Works

Reductio ad absurdum is a powerful tool for finding out what's true. It helps you discover facts by testing what happens if something isn't true.

Here's how you can use this method to prove something:

• To prove that a statement (let's call it A) is true:
  • First, pretend the opposite of A is true. (So, you assume "not-A" is true.)
  • Next, think about what would happen if "not-A" were true. What other things would have to be true because of it?
  • Keep following this logic until you reach a conclusion that is clearly false, impossible, or just doesn't make sense.
• Because assuming "not-A" led to something absurd, it means your first assumption ("not-A" is true) must be wrong.
• Therefore, the original statement A must be true after all!

Related Ideas

• Mathematical proof
• Proof by induction
• Straw man

Images for kids

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  Reductio ad absurdum, a painting by John Pettie from 1884.

See also

In Spanish: Reductio ad absurdum para niños