Cognitive neuroscience provides new insights on cognition and intersubjectivity by emphasizing the crucial role of the body, the constitutive source of the pre-reflective consciousness of the self and of the other. The naturalization of cognition and intersubjectivity implies a first attempt to deconstruct the concepts we use when referring to these aspects of human nature by literally investigating what they are made of at the level of description of the brain-body system. This neurocognitive approach reveals the tight relationship between a core notion of the bodily self, namely its potentiality for action, and motor simulation at the level of the cortical motor system. The brain level of description is necessary but not sufficient to study intersubjectivity and the human self, unless coupled with a full appreciation of the tight relationship the brain entertains with the body and the world. I introduce the mirror mechanism (MM) and embodied simulation (ES), discuss their relevance for a new account of basic aspects of perception and cognition, which privileges the body as the transcendental foundation of both. Finally, I answer some criticisms raised by Shaun Gallagher on ES.