In World Poverty and Human Rights, Thomas Pogge argues that the global rich have a duty to eradicate severe poverty in the world. The novelty of Pogges approach is to present this demand as stemming from basic commands which are negative rather than positive in nature: the global rich have an obligation to eradicate the radical poverty of the global poor not because of a norm of beneficence asking them to help those in need when they can at little cost to themselves, but because of their having violated a principle of justice not to unduly harm others by imposing on them a coercive global order that makes their access to the objects of their human right to subsistence insecure. In this paper, I claim that although Pogge is right in arguing that negative duties are crucial in an account of global justice, he is wrong in saying that they are the only ones that are crucial. Harming the global poor by causing their poverty provides a sufficient but not a necessary condition for the global rich to have a duty of justice to assist them. After engaging in a critical analysis of Pogges argument, I conclude by suggesting the need for a robust conception of cosmopolitan solidarity that includes positive duties of assistance which are not mere duties of charity, but enforceable ones of justice.