The Impossibility of an Actually Infinite Future: Grounding, Traversal, and Temporal Structure

Arguments against an infinite past typically rely on the impossibility of traversing an actual infinite. This paper develops a parallel argument against an infinite future. I introduce a backward traversal argument: if the future were infinite, the present could neither be reached nor located within the temporal structure. This paper examines whether an actually infinite future is compatible with coherent temporal structure and locatability. It challenges the view that temporal positions can be fully captured by purely relational descriptions, arguing instead that temporal reality involves a directed structure of dependence requiring grounded determination. Starting from the 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. It argues that these are not independent premises but context-sensitive outcomes of a single constraint, depending on how the future is conceived (as growing or as already existing). A central focus is the objection that locatability does not require traversal, as illustrated by mathematical structures where elements are fully determinate without sequential access. The paper responds by distinguishing abstract mathematical ordering from temporal ordering, arguing that only the latter involves asymmetric dependence relations constituting a history. Temporal locatability, therefore, requires grounded determination rather than physical movement. 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 of positions within a completed temporal totality. It concludes that an actually infinite future is incoherent under conditions of grounded temporal determination, and that the future must be finite within a structured temporal order.