circle, vicious

A definition is viciously circular when the term to be defined reappears in the definition, or where the notion that is being defined is implicitly contained in the definition. The definition that ‘“ x is good” means that we think that x is good’ is an example of the former. The definition that ‘“ x is good” means that ideal people like x ’ is an example of the latter, since although the word ‘good’ does not recur, it seems hidden in the notion of an ideal (= maximally good) person. Reasoning is condemned as viciously circular when the conclusion is improperly concealed in the premises, or is improperly needed to get the conclusion itself from the premises (see also begging the question ). It is extremely hard to say when such concealment is vicious, since there is one sense in which in any valid argument the conclusion is concealed in the premises. Controversial cases of circular reasoning in philosophy include Descartes's alleged appeal to God to certify that the clear and distinct ideas that enabled him to prove the existence of God did not deceive him, and the use of the fact that induction has worked well in the past as an argument for supposing that it will work well in the future. For Russell's particular use of the concept, see vicious circle principle.