In this talk we will address the discontinuities between formal systems and their physiological underpinnings: what are grammars, such that they can be represented in brains, and what are brains, such that they can host grammars? We will examine the main properties of formal grammars and neurocognitive processes, and propose a novel approach to bridging the gap between syntax and brains, which avoids reductionism and preserves the methodological boundaries between grammar and neuroscience. Complexity in syntax and neurocognition will be argued to arise, to a great extent, from a fundamental property of certain dynamical systems which are subjected to mutually incompatible external requirements.