 But using the 2D framework to characterize the subject’s epistemic perspective is not beholden to this internalist project. Semantic externalists reject the traditional view that our purely internal states afford apriori access to reference-fixing conditions for our words and thoughts. According to externalists, the basic assignments in a compositional semantics relate the subject’s words and thoughts to objective features of her environment—objects, kinds and properties whose nature is captured by standard (1D) possible world semantics. Even externalists, however, can define 2D matrices that reflect the subject’s epistemic perspective on the reference of her words and thoughts. For the externalist, however, these 2D matrices will not represent meanings—a specific aspect of understanding that is required for linguistic or conceptual competence and which figures in a compositional semantic theory that determines truth-conditions for sentences. On an externalist interpretation, 2D matrices merely reflect one aspect of a subject’s partial semantic understanding of what her words and thoughts represent. Because externalist 2D matrices don’t represent meanings, moreover, the externalist is free to use the 2D framework strategically to focus on different aspects of the subject’s understanding for different explanatory purposes.