Latin American decolonial theory is built around the thesis of the coloniality of knowledge, which claims that the socio-political domination of Latin America and other regions of the global periphery by European countries and the United States is directly related to the initial colonial imposition and subsequent cultural reproduction of so-called Western epistemology and science. I argue that the epistemological claims of four decolonial thinkers (Aníbal Quijano, Walter Mignolo, Enrique Dussel, Santiago Castro-Gómez) that make up the coloniality of knowledge thesis are problematic for several reasons: they are based on distorted and simplistic readings of Descartes, Hume and other Enlightenment figures; they make contentious generalizations about so-called Western epistemology; and they ultimately lead to epistemic relativism, which is a problematic basis for the social sciences and, contrary to decolonial aspirations, renders the subaltern unable to speak.