Human beings’ capacity for cooperation vastly outstrips that of other great apes. The shared intentionality hypothesis explains this difference in terms of motivational and representational discontinuities, particularly the capacity to represent joint goals. In this paper, I first present an argument as to why we should reject the shared intentionality hypothesis’ hyper-competitive characterization of chimpanzees’ social cognitive abilities, and provide reasons to be skeptical of the generalizability of experimental findings from captive chimpanzees. Next, I outline an alternative account of the contrast between human and great ape social cognition that emphasizes gradual differences in domain-general reasoning rather than novel domain-specific representational abilities. Lastly, I review further cognitive and motivational factors that might affect human beings’ capacity for cooperation.