 Frege’s genius revealed itself in the solution he devised to this circularity problem. He had already covered the necessary logical and conceptual ground in his Begriffsschrift of 1879. For any two-place relation R, Frege had defined what it was for x to be an R-ancestor of y (abbreviated here as R∗xy). For this definition, he had employed two ancillary notions. The first was that of a concept F being R-hereditary: 