>[!abstract] >**Reductio ad absurdum** (Latin for "reduction to absurdity"), also called **apagogical argument** in law or **refutation (or proof) by contradiction** in mathematics, is a type of indirect proof that follows a claim (or counterclaim) to show that it leads to an absurd, contradictory, or ridiculously impractical conclusion. Whether it is a *refutation by contradiction* or *proof by contradiction* depends on whether a claim or its counterclaim is used as a starting point. >[!related] >- **North** (upstream): — >- **West** (similar): — >- **East** (different): — >- **South** (downstream): —