ABSTRACT: Two major objections have been raised to Boghossian’s discrimination argument for the incompatibility of externalism and self-knowledge. Proponents of the first objection claim that thoughts about “twin water” are not relevant alternatives to thoughts about water. Advocates of the second objection argue that the ability to rule out relevant alternatives is not required for knowledge. Even though it has been shown that these two objections to Boghossian’s argument are misguided, it will be argued in this essay that Boghossian’s discrimination argument is nevertheless untenable. Whereas the two unsuccessful objections mentioned above each focus on one of the discrimination argument’s premises in isolation, the target of my criticism of Boghossian’s argument is the conjunction of its third premise and the standard incompatibilist defense of its second premise.