 Wright’s work has drawn the attention of philosophers of mathematics to the kind of principles of which Basic Law V and Hume’s Principle are examples. These principles are called abstraction principles. At present, philosophers of mathematics attempt to construct general theories of abstraction principles that explain which abstraction principles are acceptable and which are not, and why (Weir 2003; Fine 2002). Also, it has emerged that in the context of weakened versions of second-order logic, Frege’s Basic Law V is consistent. But these weak background theories only allow very weak arithmetical theories to be derived from Basic Law V (Burgess 2005).