Four kinds of day

About this video

"If it rains, the ground gets wet" is an if-then claim, which logicians call a conditional. It has an if part (it rains) and a then part (the ground gets wet), and it says something about the link between them: whenever the if part happens, the then part happens too. It doesn't say that it is raining.

This short animation shows four kinds of day. Rain and wet ground fits the claim. No rain and dry ground fits too. No rain but wet ground, because someone watered the garden, doesn't break it either: the claim says nothing about days without rain. Only one day breaks it: rain, and the ground stays dry. So an if-then claim is false only when the if part is true and the then part is false.

Then comes a common trap. You see a wet street and conclude it must have rained. That is going backwards, from the then part to the if part, and it doesn't follow: a street-cleaning truck, a sprinkler or a burst pipe could have wet it. But the other direction works. If the street is dry, it didn't rain, because rain would have made it wet. This video goes with the If It Rains... and The Wet Street lessons of Logic Level 1 on Knaph.

Transcript

1. 0:00If it rains, the ground gets wet. When would that be false?
2. 0:04Rain and wet. No rain and dry. No rain, but wet from a hose. None breaks it. Only rain on dry ground does.
3. 0:14Wet street, so it rained? Not for sure. A truck, a sprinkler, a pipe.
4. 0:20But a dry street does prove it didn't rain.
5. 0:26An if-then claim is false only when the if part happens and the then part doesn't.