There is no doubt that cognition and intelligence are the results of neural activity - but how, exactly? How do molecules, neurons, and synapses give rise to reasoning, language, plans, stories, art, math? Despite dazzling progress in experimental neuroscience, as well as in cognitive science, we do not seem to be making progress on the overarching question. As Richard Axel recently put it in an interview: "We don't have a logic for the transformation of neuronal activity to thought and action. I view discerning [this] logic as the most important future direction of neuroscience". What kind of formal system would qualify as this "logic"? I will introduce a mathematical model of the brain, which arguably captures the basic tenets of neuroscience and can be simulated efficiently; its main emergent behavior are assemblies of neurons, representations of stimuli, concepts, words, etc.  Using this framework a Parser was constructed which (a) can handle reasonably complex sentences in English and other languages; and (b) works exclusively through the firing of biologically realistic neurons.  I will discuss ongoing work aiming to reproduce language acquisition in a biologically plausible way.