The automatic translation of folk psychology into newly formed brainmodules specifically dedicated to mind-reading and other social cognitive abilities should be carefully scrutinized. Searching for the brain location of intentions, beliefs and desires as such might not be the best epistemic strategy to disclose what social cognition really is. The results of neurocognitive research suggest that in the brain of primates, mirror neurons, and more generally the premotor system, play a major role in several aspects of social cognition, from action and intention understanding to language processing. This evidence is presented and discussed within the theoretical frame of an embodied simulation account of social cognition. Embodied simulation and the mirror neuron system underpinning it provide the means to share communicative intentions, meaning and reference, thus granting the parity requirements of social communication.