Theories about the neural bases of semantic knowledge tend between two poles, one proposing that distinct brain regions are innately dedicated to different conceptual domains and the other suggesting that all concepts are encoded within a single network. Category-sensitive functional activations in the fusiform cortex of the congenitally blind have been taken to support the former view but also raise several puzzles. We use neural network models to assess a hypothesis that spans the two poles: The interesting functional activation patterns reflect the base connectivity of a domain-general semantic network. Both similarities and differences between sighted and congenitally blind groups can emerge through learning in a neural network, but only in architectures adopting real anatomical constraints. Surprisingly, the same constraints suggest a novel account of a quite different phenomenon: the dyspraxia observed in patients with semantic impairments from anterior temporal pathology. From this work, we suggest that the cortical semantic network is wired not to encode knowledge of distinct conceptual domains but to promote learning about both conceptual and affordance structure in the environment.