 The most immediately calamitous challenge to Logicism was, however, the famous paradox Russell raised for one of Frege’s crucial axioms, his prima facie plausible “Basic Law V” (sometimes called “the unrestricted Comprehension Axiom”), which had committed him to the existence of a set for every predicate. But what, asked Russell, of the predicate x is not a member of itself? If there were a set for that predicate, that set itself would be a member of itself if and only if it wasn’t; consequently, there could be no such set. Therefore Frege’s Basic Law V couldn’t be true (but see Frege’s Theorem and Foundations for Arithmetic for ways to rescue something close to logicism, discussed in §5 below).