Going Around in Circles

This paper tries to reconcile the clash between argumentation theory and formal logic regarding circular arguments, which are regarded as the fallacy of begging the question by the former, and a benign and useful inference pattern by the latter. This paper provides a formal system which can represent circular arguments found in the literature. The formal system makes it possible to distinguish two ways in which arguments can be circular. The first type of circularity, which is vicious, is when an argument is based on an inference step which is (indirectly) supported by that inference step itself. The second kind of circularity, which is benign, occurs when one of the premises is the same proposition as the conclusion. The first type of circularity implies the second type of circularity, but not the other way round. This distinction is in line with other approaches to circular arguments. Analyzing selected examples from the literature shows the value of the formal system.