 While presentism and eternalism are alternative theories in the philosophy of time, their respective technical manifestations are interreducible. On the one hand, the constant domain semantics with eternalist quantification can be obtained from the varying domain semantics with presentist quantification by imposing the constraint that the Past and Future Barcan Formula schemata and their converses be valid. On the other hand, the varying domain semantics can be simulated in the constant domain semantics by adding to the language of FOTL an existence predicate for ‘existence at the current time instant’, which can be defined in the varying domain semantics by \(E(\tau) := \exists x (x=\tau)\).