Reductio

Part of speech: noun

Definitions

1. A method of argument that demonstrates a statement's absurdity by reducing it to an extreme or absurd conclusion
2. A technique in logic wherein an argument is disproven by showing that it leads to an unreasonable outcome
3. A strategy in reasoning that refutes a claim by extending it to an illogical or nonsensical result

Etymology: "Reductio" is a Latin word from "reducere," meaning "to lead back," built from "re-" (back) and "ducere" (to lead). The logical sense fits: you follow a claim back along its consequences until it reaches something absurd, and that absurd result is the refutation. The full phrase, "reductio ad absurdum" ("reduction to the absurd"), names a method far older than its Latin label. Aristotle described a related technique as "apagoge," a leading away from a claim toward something impossible. Euclid used this kind of indirect proof throughout his geometry, showing that a false assumption must produce a contradiction.

Synonyms: reduction, refutation, disproof, contradiction, rebuttal