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vicious circle


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


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L ogic, philosophy of mathematics Circular reasoning, also called begging the question or petitio principii , makes use of the conclusion to be proved as a premise, and hence renders the argument invalid. A circular definition explains the definiens in terms of the definiedum and renders the definition empty. Circularity in these cases is vicious. According to Russell, paradoxes in the foundations of mathematics are due to vicious circularity, for they violate the vicious circle principle that “whatever involves all of a collection must not be one of the collection.” His theory of types is established on the basis of this principle and attempts to avoid all paradoxes of this sort. Not all circularities in argument or definition, however, are vicious. All deductions mean to derive the conclusion from the premises and hence the conclusion must have been implied in the premises. If the circle is large enough, and the argument or definition can still provide new knowledge , it is considered to be a virtuous circle. “The vicious circles in question all arise from supposing that a collection of objects may contain members which can only be defined by means of the collection as a whole.” Russell, Collected Papers of Bertrand Russell , vol. VI ... log in or subscribe to read full text

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