Laws of Nature: Between Empirical Openness and Theoretical Closure

Why do some well-confirmed empirical regularities appear to support necessity while others remain merely contingent? This paper argues that attributing necessity to any regularity requires a closure condition—treating the space of relevant alternatives as exhausted—that purely empirical sequences cannot secure on their own. The Incisive Lemma formalizes this structural constraint: no finite empirical sequence can justify the transition from “no further instances observed” to “no further instances admissible.” Apparent necessity therefore arises from the imposition of coherence-based closure onto open descriptive domains, rather than from empirical structure itself. The paper develops this diagnosis through the classic gold/uranium spheres contrast and explores its consequences for lawhood, counterfactual support, and scientific explanation. It shows that both Humean and necessitarian accounts share a common blind spot: the presupposition that necessity can be grounded (or denied) solely within empirical resources. The result reframes scientific explanation as requiring the preservation of empirical openness rather than its premature closure through coherence constraints.