The Scope of the Denial of an Actually Infinite Future: Interpretive Neutrality as a Burden-Shifting Norm

Arguments against an actually infinite past have traditionally occupied a central place in metaphysics and philosophy of religion, especially in discussions surrounding the Kalam Cosmological Argument. These arguments typically maintain that an actually infinite sequence of past events is impossible because such a sequence could never be traversed to arrive at the present. Yet an important asymmetry is almost universally assumed throughout this literature: the past is treated as a completed totality subject to constraints on actual infinity, while the future is treated as open and therefore exempt from analogous difficulties. This paper challenges that asymmetry and argues that an actually infinite future is likewise structurally incoherent across the major theories of time.

The argument proceeds in a theory-neutral manner and does not rely on controversial grounding principles, strong forms of metaphysical dependence, or the assumption that temporal ordering itself constitutes ontological grounding. Instead, it appeals only to a minimal coherence requirement shared by any adequate temporal ontology: a theory of time must remain internally consistent in the way it characterizes the structure of temporal reality.

The paper develops a dilemma across the two dominant families of temporal theory. On dynamic theories of time, such as presentism and the growing-block theory, the denial of an actually infinite future generates two competing interpretations. Under a totality interpretation, denying an actually infinite future entails that the future, considered as a totality, must be finite. Under a process interpretation, the future cannot become actually infinite, even if it extends indefinitely through temporal becoming. The paper argues that dynamic theories implicitly rely on both interpretations simultaneously: the totality interpretation to reject actual infinity and the process interpretation to preserve temporal openness. However, these interpretations impose incompatible structural descriptions of temporal reality — boundedness and indefinite extensibility — without a principled basis for privileging one over the other. The contradiction can be resolved only by abandoning the dynamic framework that generates the tension.

On static theories, including eternalism and block-universe models, the asymmetry between past and future collapses entirely. Since all temporal moments equally exist within a four-dimensional structure, there is no privileged ontological direction capable of exempting the future from the same difficulties often raised against an actually infinite past. An actually infinite future therefore constitutes a completed actual infinite totality and inherits the same structural paradoxes associated with completed infinities more generally.

The paper further argues that potential infinity does not provide a stable middle position. Although frequently invoked as a solution, potential infinity fails to reconcile the competing consequences generated by denying an actually infinite future and remains dependent on the same unresolved structural tension. The conclusion is that an actually infinite future is incoherent across the principal theories of time and that a finite temporal totality emerges as the only fully consistent resolution.