Reductio ad Absurdum

lit. “reduction to absurdity”

An argument that disproves a claim by showing it leads logically to an absurd or contradictory conclusion.

Origin

A standard technique in classical logic and Greek geometry. Euclid uses it constantly: assume the opposite of what you want to prove, derive a contradiction, conclude the original. The Latin name is medieval. Not itself a fallacy, but sometimes confused with the strawman move of caricaturing a position to absurdity.

Modern usage

Standard in philosophy, mathematics, and rigorous argument. Often invoked loosely — 'that's a reductio' — to point out that an opponent's position leads somewhere they won't accept. Stripped of the rigor it's basically 'if we follow your logic, here's the dumb place we end up.'

Q.E.D. (quod erat demonstrandum)

The traditional 'mic-drop' at the end of a mathematical proof — 'this is what we set out to prove, and now we've proved it.'

concept

Mathematics

Gödel's Incompleteness Theorems

Kurt Gödel's 1931 proof that any sufficiently expressive mathematical system contains true statements it cannot prove — math has a built-in limit.

phrase

Latin Phrases

Non Sequitur

A statement, conclusion, or response that doesn't follow logically from what came before.

concept

Logical Fallacies

Strawman

Misrepresenting someone's argument as a weaker, easier-to-attack version of itself, then defeating that version instead of the actual claim.

kiso.to