Reductio ad Absurdum

An argument that derives a contradiction or an incompatible consequence from an assumption together with accepted premises, thereby showing that the set cannot all be retained.

A reductio tests an assumption by deriving a contradiction or a consequence incompatible with other accepted premises. In a formal proof, each inferential step must be valid and the conflicting statements explicit. A conclusion that merely feels strange, unpopular, or undesirable is not necessarily a logical contradiction.

In practical arguments, the exercise often shows that a collection of requirements cannot all hold together. It may not identify which one should change. Check whether the extreme case is actually allowed by the original claim, whether empirical premises are true, and whether a hidden exception has been added. Logical analysis cannot eliminate the need for evidence about the world.

When to use it

When testing logical consistency or examining whether an assumption entails a contradiction under stated premises.

How it can help

Can reveal an inconsistent specification, an overbroad claim, or a route to a formal proof when the inferential steps are explicit.