 Russell wrote to Frege with news of his paradox on June 16, 1902. (For the relevant correspondence, see Russell (1902) and Frege (1902) in van Heijenoort (1967).) The paradox was of significance to Frege’s logical work since, in effect, it showed that the axioms Frege was using to formalize his logic were inconsistent. Specifically, Frege’s Axiom V requires that an expression such as \(\phi(x)\) be considered both a function of the argument \(x\) and a function of the argument \(\phi\). (More precisely, Frege’s Law states that the course-of-values of a concept \(f\) is identical to the course-of-values of a concept \(g\) if and only if \(f\) and \(g\) agree on the value of every argument, i.e., if and only if for every object \(x, f(x) = g(x)\). See section 2.4.1 of the entry on  Gottlob Frege  in this encyclopedia for more discussion.) In effect, it was this ambiguity that allowed Russell to construct \(R\) in such a way that it could both be and not be a member of itself.