The dream of cognitive neuroscience has always been a seamless integration of cognitive representations with neural machinery, but---despite decades of work---fundamental gaps remain. Part of the problem is that many contemporary theories of cognition are formulated in terms of representations and computations that are quite different from those used in computational neuroscience. Bridging this gap requires more than simply a translation between theoretical concepts in the two fields; what is needed is a more radical updating of neuroscience's theoretical vocabulary