Under the eternalist hypothesis that objects or events exist independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in time, and persisting objects perdure if they are singly located by having numerically different temporal parts. Recently, several authors have argued that special relativity favours perdurantism over its endurantist rival. In my talk, I want to show that in fact the purported arguments are only those against endurantism, and that with similar ones we should argue against perdurantism, as well: Enduring and perduring entities are both in conflict with SR which undermines the eternalist hypothesis. For arguing in favour of perdurantism Yuri Balashov, on the one hand, considers spatially unextended objects in Minkowski space-time and claims that for the endurantists there are unwelcome consequences from an adequate concept of their coexistence. On the other hand, spacelike extended objects are under investigation. Concerning point-like objects, Cody Gilmore has convincingly shown that Balashov’s arguments fail and, therefore, I will confine me to extended object. My paper has two parts following the two different strategies – namely, concerning the problem of the endurantist “explanatory deficiency” according to Balashov, and the problem of criss-crossing hyperplanes according to Gilmore
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