The Impossibility of an Infinite Future: Backward Traversal and Temporal Coherence

Arguments against an infinite past often rely on the impossibility of traversing an actual infinite. This paper develops a parallel argument against an actually infinite future by introducing a backward-traversal consideration: if the future were actually infinite, the present could neither be reached nor coherently located within a completed temporal structure. The paper examines whether an actually infinite future is compatible with coherent temporal structure and locatability. It challenges the view that temporal positions are fully given by purely relational descriptions, arguing instead that temporal reality involves a directed structure of asymmetric dependence requiring grounded determination. Starting from the foundational claim that the future is impossible to be infinite, the paper distinguishes two consequences often drawn from it—that the future cannot become actually infinite and that the future is finite—and argues that these are not independent, but context-sensitive outcomes depending on whether the future is conceived as growing or already existing. Addressing the objection that locatability does not require traversal (as illustrated by mathematical analogies), the paper distinguishes abstract mathematical ordering from temporal ordering, arguing that only temporal structure involves asymmetric dependence relations constituting a history. Temporal locatability therefore requires grounding, not merely relational description. Reformulating traversal as a grounding condition, the paper argues that an actually infinite future generates a non-terminating regress of temporal relations, preventing full determination within a completed temporal totality. It concludes that an actually infinite future is incoherent under conditions of grounded temporal structure, and that the future must be finite.