Logical-Time Incompletability: A Structural Boundary of Artificial Intelligence

This paper examines the limits of artificial intelligence by distinguishing two dimensions that are frequently conflated in contemporary discussions: machine realization and task completion. While advances in AI are often understood as improvements in realization—better architectures, larger models, or more efficient learning—such advances do not necessarily imply that a task, as specified, is completable at all. The paper argues that this assumption obscures a class of structural limits that are independent of computational power or intelligence. To make this distinction precise, a task-relative framework based on logical time is introduced. Logical time characterizes the organization of conceptually required transitions leading toward a task’s completion conditions, abstracting away from implementation details. Within this framework, the notion of logical-time incompletability is defined as a property of tasks whose completion conditions cannot be reached along any logically bounded trajectory. Several general structural sources of incompletability are identified. On this basis, the paper formulates the AI Boundary Thesis: if a task is logically-time incompletable under its own specification, then no machine—regardless of realization—can fully complete it as specified. This perspective helps explain persistent phenomena in AI, including reliance on approximation, the appearance of pseudo-completion, and the contrast between superhuman performance on formal tasks and fragility in everyday reasoning.