We consider three hypotheses concerning the primate neocortex which have influenced computational neuroscience in recent years. Is the mind modular in terms of its being profitably described as a collection of relatively independent functional units? Does the regular structure of the cortex imply a single algorithm at work, operating on many different inputs in parallel? Can the cognitive differences between humans and our closest primate relatives be explained in terms of a scalable cortical architecture? We bring to bear diverse sources of evidence to argue that the answers to each of these questions - with some judicious qualifications - are in the affirmative. In particular, we argue that while our higher cognitive functions may interact in a complicated fashion, many of the component functions operate through well-defined interfaces and, perhaps more important, are built on a neural substrate that scales easily under the control of a modular genetic architecture. Processing in the primary sensory cortices seem amenable to similar algorithmic principles, and, even for those cases where alternative principles are at play, the regular structure of cortex allows the same or greater advantages as the architecture scales. Similar genetic machinery to that used by nature to scale body plans has apparently been applied to scale cortical computations. The resulting replicated computing units can be used to build larger working memory and support deeper recursions needed to qualitatively improve our abilities to handle language, abstraction and social interaction.