The confusion surrounding the early philosophical reception of Relativity theory can be traced back to a misconception regarding the status of ‘time’ in philosophical—and possibly scientific—discourse. For all its empirical grounding in actual perception and measurement, time is neither an empirical object, nor a category in the ordinary sense. As Aristotle first acknowledged, time is not some abstract or idealized motion; as such, it cannot be reduced to a generic representation of becoming. Kant underscored that time itself is immune to change, suggesting that it is best characterized as a form whose function for understanding is to coordinate a cluster of ideas and problems pertaining to persistence and change, as well as coexistence, in accordance with the most general principles of experience. The vindication of the unity and universality of time by philosophers as far apart as Russell and Bergson stems from the conviction that such basic temporal ideas cannot easily be taken apart. The fact that time comprises a subjective or psychological element is, in that respect, a peripheral issue. Thus, Bergson’s ‘quarrel’ with Einstein revolves around the possibility of apprehending simultaneity at a distance as a sheaf or envelope of durations unfolding in ‘real time’. Neither ‘proper’ time (invariant, local) nor ‘coordinate’ time (frame-dependent, global) can properly reflect the intuition of that thick present. While Bergson strives to incorporate it back into the relativistic framework based on the experience of lived simultaneity, Whitehead formalizes it in terms of ‘contemporaneous’ extended events. Yet both seek a regional understanding of the matter, in line with some contemporary philosophers of spacetime. The (in)famous twin paradox is examined in this light, along with certain critical concepts in Bergson’s philosophy of time. The challenge is to unpack the meaning of coexistence beyond the immediate phenomenological features of proximal co-presence.