The extent to which the linguistic system—its architecture, the representations it operates on, the constraints it is subject to—is specific to language has broad implications for cognitive science and its relation to evolutionary biology. Importantly, a given property of the linguistic system can be “specific” to the domain of language in several ways. For example, if the property evolved by natural selection under the pressure of the linguistic function it serves then the property is domain-specific in the sense that its design is tailored for language. Equally though, if that property evolved to serve a different function or if that property is domain-general, it may nevertheless interact with the linguistic system in a way that is unique. This gives a second sense in which a property can be thought of as specific to language. An evolutionary approach to the language faculty might at first blush appear to favor domain-specificity in the first sense, with individual properties of the language faculty being specifically linguistic adaptations. However, we argue that interactions between learning, culture, and biological evolution mean any domain-specific adaptations that evolve will take the form of weak biases rather than hard constraints. Turning to the latter sense of domain-specificity, we highlight a very general bias, simplicity, which operates widely in cognition and yet interacts with linguistic representations in domain-specific ways.