Depth 2 · 36 s
The four moves
With one if-then claim you can make four moves. Two always follow, two are traps, and one lit shop at night shows why. The shape is what decides.
About this video
Leo walks past a corner shop every evening and notices: if the shop is open, its lights are on. With an if-then claim like this there are four moves you can make. The shop is open, so its lights are on: this follows, and its old Latin name is modus ponens. The lights are off, so the shop is closed: this follows too, and it is called modus tollens. The lights are on, so the shop is open: this doesn't follow, and it is called affirming the consequent. The shop is closed, so its lights are off: this doesn't follow either, and it is called denying the antecedent.
One night Leo passes the shop. It is closed, with the sign on the door, and the lights are on: a cleaner is mopping the floor. That one scene is a counterexample to both trap moves, and the claim "if the shop is open, its lights are on" is still true. It never said the lights are on only when the shop is open.
This is validity at its second depth: recognising valid and invalid argument forms by their shape. Swap in any if-then claim you like, and the first two moves always follow while the last two never follow by shape alone. This video goes with The Four Moves lesson of Logic Level 2 on Knaph.
This video shows depth 2 of Validity.
Learn ValidityTranscript
- 0:00If the shop is open, its lights are on. One claim, four moves.
- 0:05Open, so the lights are on. Follows. Lights off, so it's closed. Follows too.
- 0:11Lights on, so it's open? Closed, so lights off? Neither follows.
- 0:17One night the shop is closed, and the lights are on. A cleaner. Both traps broken.
- 0:25Swap in any if-then claim. The shape decides.
- 0:31Two moves always work. Two never work by shape alone.