Under what conditions is statistical inference epistemically justified? This paper argues thatthe answer depends on the dynamical structure of the system under study—a dependencythat current philosophy of statistics has not adequately examined. Drawing on attractordynamics and complex systems theory, we propose a three-domain framework. In Domain A(deterministic basin interiors), statistics is unnecessary. In Domain B (partially observed basininteriors), the foundational assumptions of statistical inference—stationarity, independence,identical distribution—are satisfied, and statistical methods are legitimately powerful. InDomain C (inter-basin transitions at bifurcation points), these assumptions fail simultaneouslyand in principle, rendering statistical inference structurally invalid. The framework revealsthat the Bayesian-versus-frequentist debate operates within Domain B; the prior question ofwhether Domain B conditions obtain cannot be answered by either tradition. We demonstratethe framework through structural reinterpretation of canonical failures—the 2008 financialcrisis, COVID-19forecasting, climatetippingpoints—andthroughanalysisofhowstatistically-designed institutions can deform the social phenomena they model. The paper engages recentwork on deterministic chance, philosophy of statistical testing, dynamical systems approachesto causation, and the ergodicity problem in economics, arguing that these independentlydeveloped insights converge on a single structural conclusion: the validity of statisticalinference is domain-dependent, and the concept of randomness foundational to statisticaltheory is a reification of the observer’s ignorance about attractor basin structure. We sketchan attractor-informed epistemology that explicitly assesses domain conditions before selectinganalytical methods.
Sophia Franny Philos (Wed,) studied this question.