http://plato.stanford.edu/entries/philosophy-mathematics/
And there matters stood for more than fifty years. In 1983, Crispin Wright's book on Frege's theory of the natural numbers appeared (Wright 1983). In it, Wright breathes new life into the logicist project. He observes that Frege's derivation of second-order Peano Arithmetic can be broken down in two stages. In a first stage, Frege uses the inconsistent Basic Law V to derive what has come to be known as Hume's Principle:
The number of the Fs = the number of the Gs FG,
where FG means that the Fs and the Gs stand in one-to-one correspondence with each other. (This relation of one-to-one correspondence can be expressed in second-order logic.) Then, in a second stage, the principles of second-order Peano Arithmetic are derived from Hume's Principle and the accepted principles of second-order logic. In particular, Basic Law V is not needed in the second part of the derivation. Moreover, Wright conjectured that in contrast to Frege's Basic Law V, Hume's Principle is consistent. George Boolos and others observed that Hume's Principle is indeed consistent (Boolos 1987). Wright went on to claim that Hume's Principle can be regarded as a truth of logic. If that is so, then at least second-order Peano arithmetic is reducible to logic alone. Thus a new form of logicism was born; today this view is known as neo-logicism (Hale & Wright 2001).
Most philosophers of mathematics today doubt that Hume's Principle is a principle of logic. Indeed, even Wright has in recent years sought to qualify this claim: he now argues that Hume's Principle is analytic of our concept of number, and therefore at least a law of reason.