Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)