Our genotype is so similar to those of the African apes, and our last common ancestor with them so recent, that it seems impossible that human and non-human cognition should differ qualitatively. But the outputs of human cognition are unique in their limitless creativity and adaptability. Exaption resolves the apparent paradox. Assume that the power to create symbols emerges from stimulus-stimulus linkages and is latent in many animals, and that the structural side of language emerges from the argument structures inherent in the social calculus associated with reciprocal altruism. These adaptations confer the potential for language. However, creating complex messages requires uniquely long-lasting coherence of neural signals, which depends in turn on the large quantities of neurons unique to Homo. The only difference between human and non-human minds is that we can sustain longer and more complex trains of thought. All else (emotions, rational processes, even consciousness) could be exactly the same.