The ability to think logically is a hallmark of human intelligence, yet our innate inferential abilities are marked by implicit biases that often lead to illogical inference. For example, given AB (“if A then B”), people frequently but fallaciously infer the inverse, BA. This mode of inference, called symmetry, is logically invalid because, although it may be true, it is not necessarily true. Given pairs of conditional relations, such as AB and BC, humans reflexively perform two additional modes of inference: transitivity, whereby one (validly) infers AC; and equivalence, whereby one (invalidly) infers CA. In sharp contrast, nonhuman animals can handle transitivity but can rarely be made to acquire symmetry or equivalence. In the present study, human subjects performed logical and illogical inferences about the relations between abstract, visually presented figures while their brain activation was monitored with fMRI. The prefrontal, medial frontal, and intraparietal cortices were activated during all modes of inference. Additional activation in the precuneus and posterior parietal cortex was observed during transitivity and equivalence, which may reflect the need to retrieve the intermediate stimulus (B) from memory. Surprisingly, the patterns of brain activation in illogical and logical inference were very similar. We conclude that the observed inference-related fronto-parietal network is adapted for processing categorical, but not logical, structures of association among stimuli. Humans might prefer categorization over the memorization of logical structures in order to minimize the cognitive working memory load when processing large volumes of information.