If-Then and Its Two Safe Moves

An if-then sentence has two parts. The “if” part is the condition, and the “then” part is what follows. “If the bridge is closed, the bus takes the long road.” It promises that whenever the first part holds, the second holds too.

Two moves from it are safe. The first affirms the condition: the bridge is closed, so the bus takes the long road. Logicians call this modus ponens, Latin for the affirming way. The second denies what follows: the bus did not take the long road, so the bridge was not closed. That is modus tollens, the denying way.

Both moves are valid: if the if-then sentence and the other premise are true, the conclusion cannot be false. Valid is not the same as true. If the bridge sentence is wrong, the moves carry you faithfully to a wrong place. Check the if-then first, then move.

The kettle warranty

Ines reads the card in her new kettle: “If the seal is broken, the warranty is void.” Her seal is torn, so she knows the shop will refuse a claim, and it does. That is the affirming move.

Her neighbor Tomas took the same kettle back, and the shop honored the warranty. Ines reasons the other way: his warranty was not void, so his seal cannot have been broken. That is the denying move. Each step starts from the same if-then and goes only where it already points.

Try this today Find one if-then sentence today, in a rule or a forecast, and write out which of its two safe moves you are using.