# Definition:Circular Proof

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## 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**.

## Also see

## Sources

- 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S \text{II}.11$: The formulation of definitions - 1995: Merrilee H. Salmon:
*Introduction to Logic and Critical Thinking*: Appendix $2$,*Circular Reasoning*