 A first argument from STR to perdurantism goes as follows: STR shows space to be much like time, objects extend in space by having spatial parts, so objects persist through time by having temporal parts.  But this argument is weak: although STR does show space to be like time in some respects, the theory does still differentiate between spatial and temporal dimensions. Even if it did not, we would need some further reason to believe that persistence must be just like spatial extension.