One penguin is enough

About this video

Someone says "All birds can fly." You could argue for an hour, or you could show them one penguin. A penguin is a bird: it has feathers, lays eggs and has a beak, and it can't fly. So "all birds can fly" is false, and one penguin is enough to show it. A case like this is called a counterexample, an example that goes against a claim.

This short animation counts up a thousand flying birds first. They don't prove that every bird can fly, because the next one might be a penguin. That is the lopsided thing about "all" claims: they are much easier to show false than to show true.

Counterexamples have a second job. They show that a conclusion doesn't follow. A counterexample to an argument is a case where the reasons are true and the conclusion is false. "All cats have four legs. Tom has four legs. So Tom is a cat." Imagine Tom is a dog: both reasons are true, and the conclusion is false. The case doesn't even have to be real, only possible to imagine. This video goes with the Can You Imagine It Wrong? lesson of Logic Level 1 on Knaph.

Transcript

1. 0:00All birds can fly. How do you prove that wrong?
2. 0:04A thousand flying birds don't prove it right.
3. 0:10But one bird that can't fly proves it wrong.
4. 0:16That one case is called a counterexample.
5. 0:22On arguments too. If Tom is a dog - true reasons, false conclusion.
6. 0:27One case where it goes wrong is enough.