Either-Or and the Reductio

An either-or sentence gives a list. “The key is in my coat or on the hook.” Check the coat, find nothing, and it is on the hook. Ruling out is safe on one condition: the list has to be complete. If the key could also be in the car, ruling out the coat proves little. The False Dilemma in week three was one with a missing option.

The second move is older still. To test a claim, assume it and follow it. If it leads to a contradiction, a statement and its denial both holding, the claim is false. This is the reductio, short for reductio ad absurdum, reduction to absurdity. Euclid used it to show the primes never run out.

Both moves need honesty about the list and about what counts as a contradiction. “That would be awkward” is not one. Nor is “I would not like it.”

The missing invoice

Dario’s bookkeeper says the invoice was either emailed or posted. Dario searches the sent folder, finds nothing, and starts to ring the client about the post. Then he stops. Could it have been handed over at the meeting? The list was not complete, so ruling out email settled little.

Later the client claims the invoice was never issued at all. Dario assumes so and follows it: then the signed delivery note, which quotes the invoice number, could not exist. It does exist. The claim collapses.

Try this today Pick a claim you doubt, assume it is true for two minutes, and follow it until it collides with something you know; write down what collided.