 Philosophers have attempted to rescue some ideas of Fregean logicism by using axioms weaker than (V). One of the most important such attempts is Bob Hale and Crispin Wright’s neo-logicism, which gives up Frege’s theory of extensions but holds on to the central idea of his definition of cardinal numbers, namely that the number of \(F\)s is identical to the number of \(G\)s just in case the \(F\)s and the \(G\)s can be one-to-one correlated. This has become known as Hume’s Principle, and can be formalized as