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The term "vicious circle," circulus vitiosus, and the related term "question begging," petitio principii, are originally technical terms in Aristotle's Analytica posteriora. It was used as a technical term for a certain mistake in proofs. Another derived application can be found in the traditional theory of definition. But in traditional as well as in modern logic, there are several cases in which it is tempting to use the term "vicious circularity" or "question begging" as a metaphor in the description of other logical structures. These also have to be considered because it will soon be obvious that hermeneutical circularity cannot be characterized as an explicit logical circularity. There is an explicit vicious circularity in a proof if the conclusion is listed explicitly among the premises. Such a derivation is, of course, logically valid, and seen from a formal point of view, it is also sound. There is no formal contradiction in the premises, and the conclusion is not a tautology. A vicious circularity in a deduction is therefore not a formal logical fallacy. It is also not an informal fallacy in the narrower sense. A vicious circularity is pointless and useless as a proof because all the other premises are a useless ornament added to the tautology "If p then p." Vicious circularity is therefore not a question of formal logic in the narrower sense. It is a question of applied logic.

DOI: 10.1007/978-1-4020-2618-8_7

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