Information Completeness and Incompleteness

This paper orthogonalizes information symmetry (who holds information) from information completeness (whether available information suffices for a target decision or inference). We formalize two dimensions of completeness: static (relative to a finite time window) and dynamic (absolute, intertemporal). Static incompleteness arises when currently admissible signals are insufficient to identify the target; dynamic incompleteness arises when further, in-scope and decision-relevant information is foreseeably forthcoming. Within a measurable "scope" and an information filtration, we define probabilistic relevance as primitive, relate it to decision relevance via Blackwell monotonicity, and characterize static completeness as (approximate) point identification while dynamic completeness requires the absence of any future relevant arrivals. We distinguish institutional regimes—closed versus expandable scope—and show non-confirmability results in expandable scopes: finite evidence cannot certify either the absence of omitted relevant variables (static) or the absence of future relevant information (dynamic). We provide audit-style certificates (sufficient conditions) and falsifiers (stop-tests) for both notions, and connect the framework to partial identification, robust decision-making, rational inattention, and optimal stopping. The key implication is normative and methodological: in open environments, "best" actions are conditional and time-indexed rather than absolutely correct, so governance and empirical practice should report identification-set diameters, treat scope as a policy lever, and prefer falsifiable, continuous disclosure over once-and-for-all attestations.