How does meaning come about, given the nature of our brains? Taking up this question, the book unites two so far disjoint perspectives on how humans represent and process information: In philosophy, linguistics, and large parts of psychology informational processes are commonly regarded as transformations over semantically composed structures of concepts. Mental concepts are regarded as the ultimate bearers of intentional content and the providers of linguistic meaning. In neuroscience, in contrast, the interactions of neurons – forming an apparently very different structure – are viewed as fundamental for the flow of information. 'The Compositional Brain' makes a provoking claim that, nevertheless, is underpinned with cogent argumentation. It proposes a structural identity theory that identifies the mechanisms of concept composition with patterns of synchronous neural activity. It combines philosophical analysis with most recent neurobiological findings on the time-dependent nature of neural mechanisms. Using oscillatory networks as a biologically well-grounded model of cortical activity, simulations of brain activity are studied and re-described by refined algebraic and model-theoretic methods. So a link between neuroscience and semantics is established.