The ability to attribute properties to objects and events based on one's general knowledge about the world is an important aspect of cognition. To explain this capacity, traditional theories of semantic memory have posited that objects in the world belong to categories, which organize the storage and retrieval of general world knowledge. This position begs several controversial questions, which have constrained the research agenda in semantic cognition for several years. In the current work, we put forward a connectionist theory of semantic memory which does not assume that semantic knowledge is stored in representations of categories. We show how the principles of parallel distributed processing can account for ten empirical phenomena in development, adult cognition, and dementia, in a computational model that learns to represent instances in a multidimensional semantic space. The theory reconciles several seemingly contradictory findings in the literature, and provides a framework for understanding semantic representation throughout development and in dementia. Among other things, the model accounts for progressive differentiation of conceptual knowledge during development, progressive loss of differentiation during dementia, and the priority of the so-called "basic" level in child and adult cognition.