This paper addresses the question whetherintrospection plus externalism about mental contentwarrant an a priori refutation of external-worldskepticism and ontological solipsism. The suggestionis that if thought content is partly determined byaffairs in the environment and if we can havenon-empirical knowledge of our current thoughtcontents, we can, just by reflection, know about theworld around us – we can know that our environment ispopulated with content-determining entities. Afterexamining this type of transcendental argument anddiscussing various objections found in the literature,I argue that the notion of privileged self-knowledgeunderlying this argument presupposes that we canlearn, via introspection, that our so-called thoughtsare propositional attitudes rather than contentlessstates. If, however, externalism is correct andthought content consists in the systematic dependencyof internal states on relational properties, we cannotknow non-empirically whether or not we havepropositional attitudes. Self-knowledge (apropositional attitude) is consistent with us lackingthe ability to rule out, via introspection, thepossibility that we don't have any propositionalattitudes. Self-knowledge provides us with knowledgeof what is in our minds, but not that we haveminds. Hence, the combination of externalism with thedoctrine of privileged self-knowledge does not allowfor an a priori refutation of skepticism and istherefore unproblematic.