Circular Argument

circular argument [¦sər·kyə·lər ′är·gyə·mənt]

(mathematics)

An argument that is not valid because it uses the theorem to be proved or a consequence of that theorem that is not proven.

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Circular Argument 

(Latin, circulus in demonstrando or petitio principi ) a logical fallacy in which a consequent of the hypothesis of an argument is used as one of its premises, that is, a proposition is used for whose proof the same hypothesis must be used as a premise. Besides those trivial cases where the premise coincides with the hypothesis or is a reformulation of it, “masked” circularities are possible, in which a premise is equivalent to the hypothesis but does not resemble it in formulation. A circular “proof” is not a proof of its hypothesis; however, as a derivation of the hypothesis from an equivalent premise, it may play an important methodological role, namely, in revealing the equivalence. Examples of this are the attempts to prove Euclid’s fifth, or parallel, postulate using the theorem that the sum of the angles of any triangle equals 180°; the theorem, in turn, is proved by means of the fifth postulate.

IU. A. GASTEV