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