  Note that the concept being an author of Principia Mathematica satisfies this condition, since there are distinct objects \(x\) and \(y\), namely, Bertrand Russell and Alfred North Whitehead, who authored Principia Mathematica and who are such that anything else authoring Principia Mathematica is identical to one of them. In this way, Frege analyzed a statement of number (‘there are two authors of Principia Mathematica’) as higher-order logical statements about concepts.