We present a model of symbol manipulation implemented using spiking neurons and closely tied to the anatomy of the cortex, basal ganglia, and thalamus. The model is a general-purpose neural controller which plays a role analogous to a production system. Information stored in cortex is used by the basal ganglia as the basis for selecting between a set of inferences. When an inference rule is selected, it commands the thalamus to modify and transmit information between areas of the cortex. The system supports special-case and general-purpose inferences, including the ability to remember complex statements and answer questions about them. The resulting model suggests modifications to the standard structure of production system rules, and offers a neurological explanation for the 50 millisecond cognitive cycle time.