 where \(F \approx G\) 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).