Converging lines of evidence from diverse research domains suggest that the left and right hemispheres play distinct, yet complementary, roles in inferential reasoning. Here, we review research on split-brain patients, brain-damaged patients, delusional patients, and healthy individuals that suggests that the left hemisphere tends to create explanations, make inferences, and bridge gaps in information, while the right hemisphere tends to detect conflict, update beliefs, support mental set-shifts, and monitor and inhibit behavior. Based on this evidence, we propose that the left hemisphere specializes in creating hypotheses and representing causality, while the right hemisphere specializes in evaluating hypotheses, and rejecting those that are implausible or inconsistent with other evidence. In sum, we suggest that, in the domain of inferential reasoning, the left hemisphere strives to reduce uncertainty while the right hemisphere strives to resolve inconsistency. The hemispheres’ divergent inferential reasoning strategies may contribute to flexible, complex reasoning in the healthy brain, and disruption in these systems may explain reasoning deficits in the unhealthy brain.