Linguistic theories offer empirical hypotheses about the architecture of human language, which provide the basis for neurobiological investigations into the study of language use. Unfortunately, progress in linking the two fields of inquiry is hampered because core concepts and ideas from linguistics are not seldom misunderstood, making them controversial and seemingly irrelevant to the neurobiology of language. Here we identify three such proposals: the distinction between competence and performance, the autonomy of syntax, and the abstract nature of syntactic representations. In our view, confusion about these concepts stems from the fact that they are interpreted at a level of analysis different from the level at which they were originally described. We clarify the intended interpretation of these concepts and discuss how they might be contextualized in the cognitive neuroscience of language. By doing so, the discussion about the integration of linguistics and neurobiology of language can move toward a fruitful exploration of linking hypotheses within a multi-level theory of syntax in the brain.