Logic is widely considered the basis of rationality. Logical choices, however, are often influenced by emotional responses, sometimes to our detriment, sometimes to our advantage. To understand the neural basis of emotionally neutral ("cold") and emotionally salient ("hot") reasoning we studied 19 volunteers using event-related fMRI, as they made logical judgments about arguments that varied in emotional saliency. Despite identical logical form and content categories across "hot" and "cold" reasoning conditions, lateral and ventral medial prefrontal cortex showed reciprocal response patterns as a function of emotional saliency of content. "Cold" reasoning trials resulted in enhanced activity in lateral/dorsal lateral prefrontal cortex (L/DLPFC) and suppression of activity in ventral medial prefrontal cortex (VMPFC). By contrast, "hot" reasoning trials resulted in enhanced activation in VMPFC and suppression of activation in L/DLPFC. This reciprocal engagement of L/DLPFC and VMPFC provides evidence for a dynamic neural system for reasoning, the configuration of which is strongly influenced by emotional saliency.