I examine the phenomenological philosophies of Merleau-Ponty and Sartre as possible responses to contemporary studies of interpersonal relatedness in cognitive science, especially the experimental studies of infant's imitating simple facial gestures of adults. I discuss the implications and the challenges raised by the experimental studies to the dominant phenomenological accounts of intersubjectivity, but also envision how phenomenology may help to interpret the findings about infantile imitation in ways that favor the embodied perceptual connectedness between the self and the other, without recourse to the inner private mind postulate endorsed by the theory of mind and shared by the experimental researchers of imitation.