Grounding, Traversal, and Temporal Structure: A Response to S. C. Sayles’ Refutation and Criticism of “The Impossibility of an Actually Infinite Future”

This paper replies to S. C. Sayles’ Refutation of “The Impossibility of an Actually Infinite Future” and argues that the critique fails to overturn the central thesis that an actually infinite future is metaphysically incoherent. The response clarifies that backward traversal is not literal motion through infinity but the tracing of explanatory dependence within temporal structure. It further argues that temporal reality cannot be reduced to purely abstract mathematical ordering because temporal events are asymmetrically dependence structured and historically grounded. The paper defends the distinction between the two consequences arising from the foundational principle that the future is impossible to be infinite—that the future cannot become actually infinite and that the future is finite—and argues that growing-future interpretations generate tension between indefinite extension and boundedness. This tension disappears only if the future is understood as an already existing and finite temporal totality. The paper concludes that the objections fail to demonstrate the coherence of an actually infinite future or to undermine the requirement of a finite and fully grounded temporal structure.