Is there a notion of domain specificity which affords genuine insight in the context of the highly modular mind, i.e. a mind which has not only input modules, but also central ‘conceptual’ modules? Our answer to this question is no. The main argument is simple enough: we lay out some constraints that a theoretically useful notion of domain specificity, in the context of the highly modular mind, would need to meet. We then survey a host of accounts of what domain specificity is, based on the intuitive idea that a domain specific mechanism is restricted in the kind of information that it processes, and show that each fails at least one of those constraints.