Research into intimacy must grapple with its ambiguity while attempting to place it within a contemporary technological and political context. I argue for a metaphysics of intimacy that provides a ground for research. Through a critical reading of the philosophy of Peter Sloterdijk, I suggest a formal dialectic between intimacy and cosmopolitanism. Intimacy is an enclosure over time, while cosmopolitanism is an opening through an event. These ideal forms become actual in digital media, which often reveal the dark side of intimacy, as they withhold the cosmopolitan event and hence the possibility of diverse yet cohesive collectives. I outline various fields of research where the contradiction between intimacy and cosmopolitanism can be explored and potentially resolved through methodologies that critically imagine alternative designs.