# Definition:Circular Proof

## Definition

A circular proof is a proof $A$ in terms of another proof $B$ such that the truth value of $B$ depends (either directly or indirectly) on the truth value of $A$.

A circular proof is valid, as every statement implies itself.

The problem of a circular proof is that if the truth of a conclusion is dubious, premises that are equally dubious provide no reason to support the conclusion.

## Also known as

A circular proof is sometimes known as a vicious circle in the proof.