Intentionality, or the property of minds and representations whereby they are “about” things real or unreal, such as chairs, ghosts, colors, or words. Although intentionality seems to play a crucial role in psychology and in Chomskyan linguistics, its reality has been contested by philosophers such as Quine and, surprisingly, by Chomsky himself. On behalf of Chomsky, John Collins has defended a “Scientific Eliminativism,” endorsing what I call a “Platonist-algebraic” reading of Chomsky’s core theory. I argue that this reading will fall short of satisfying “explanatory adequacy,” failing to provide an account of how a child could be perceptually sensitive to linguistic phenomena. As argued in Chapter 7, this latter requires intentionalist representations, even of phenomena such as words (and colors) that do not exist, what Brentano called “intentional inexistents,” a category this chapter argues is not as problematic as naturalistic philosophers have feared.