In this paper, I draw a distinction between weak and strong versions of the "embodiment thesis". The weak version claims that mental states are grounded in a body that moves and acts in the environment, i.e., a functional body. The strong version claims that mental states are grounded in a body that is not only functional but also sentient, i.e., a body that is the locus of sensibility or phenomenal consciousness. I argue that some approaches within the "new embodied cognitive science" - Brooks' robotics, Noe's and O'Regan's sensorimotor enactivism, Hutto's and Myin's radical enactivism - imply a weak version of the embodiment thesis. In contrast, by drawing on a phenomenological analysis of living and lived corporeality, I argue for the strong version, which claims that the mind is essentially grounded in the functional and sentient body.