Murray N. Rothbard and Hans-Hermann Hoppe build their libertarian theory of justice on two axioms concerning self-ownership and homesteading, which are bolstered by two key arguments: reductio ad absurdum and performative contradiction. Each of these arguments is designed to demonstrate that libertarianism is the only theory of justice that can be justified. If either of these arguments were valid, it would prove the libertarian claim that the state is an unjust political arrangement. Giving due weight to the importance of the libertarian anarchist claim, this article exposes and criticizes the arguments that substantiate it.