Our human cognitive skills trump those of our primate relatives in many domains, ranging from logical reasoning to managing complex social lives and from tool-use to language. A basic yet powerful faculty might underlie many of these characteristic functions of the human mind: instant conceptual inference. Humans can quickly infer high-order abstract relationships, even between physically separate objects and across sensory modalities. Interestingly, other primates need to learn these relationships by gradual reinforcement over hundreds of trials while they have no problem learning relationships between physically linked objects. I will test the hypothesis that conceptual inference has evolved as a critical and uniquely human cognitive faculty, building upon neural mechanisms of physical inference and multi-sensory integration that we share with other primates.