Various cognitive theories aim to explain human deductive reasoning: (1) mental logic theories claim syntactic language-based proofs of derivation, (2) the mental model theory proposes cognitive processes of constructing and manipulating spatially organized mental models, and (3) imagery theories postulate that such abilities are based on visual mental images. To explore the neural substrates of human deductive reasoning, we examined BOLD (blood oxygen level dependent) contrasts of twelve healthy participants during relational and conditional reasoning with whole-brain functional magnetic resonance imaging (fMRI). The results indicate that, in the absence of any correlated visual input, reasoning activated an occipitoparietal–frontal network, including parts of the prefrontal cortex (Brodmann’s area, BA, 6, 9) and the cingulate gyrus (BA 32), the superior and inferior parietal cortex (BA 7, 40), the precuneus (BA 7), and the visual association cortex (BA 19). In the discussion, we first focus on the activated occipito-parietal pathway that is well known to be involved in spatial perception and spatial working memory. Second, we briefly relate the activation in the prefrontal cortical areas and in the anterior cingulate gyrus to other imaging studies on higher cognitive functions. Finally, we draw some general conclusions and argue that reasoners envisage and inspect spatially organized mental models to solve deductive inference problems.