Deductive reasoning is fundamental to science, human culture, and the solution of problems in daily life. It starts with premises and yields a logically necessary conclusion that is not explicit in the premises. Here we investigated the neurocognitive processes underlying logical thinking with event-related functional magnetic resonance imaging. We specifically focused on three temporally separable phases: (1) the premise processing phase, (2) the premise integration phase, and (3) the validation phase in which reasoners decide whether a conclusion logically follows from the premises. We found distinct patterns of cortical activity during these phases, with initial temporo-occipital activation shifting to the prefrontal cortex and then to the parietal cortex during the reasoning process. Activity in these latter regions was specific to reasoning, as it was significantly decreased during matched working memory problems with identical premises and equal working memory load.