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Abstract

A-theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A-theorists. It is commonly thought that A-theories can only be formally expressed in a tense logic: a logic with operators like P (“it was the case that”) and F (“it will be the case that”). And it seems natural to think that we live in a world where objects come to exist and cease to exist as time passes. Indeed, this is typically a key component of the most prominent kind of A-theory, presentism. But the temporary existence assumption cannot be upheld in any tense logic with a standard quantification theory. I will explain the problem and outline the philosophical and logical considerations that generate it. I will then consider two possible solutions to the problem – one that targets our logic of quantification and one that targets our assumptions about change. I survey the costs of each solution.