The Regress of Uncertainty and the Forecasting Paradox

We show that epistemic uncertainty–our iterated ignorance about our own ignorance–inevitably thickens statistical tails, even under perceived thin-tailed environments from past realizations. Any claim of precise risk carries a margin of error, and that margin itself is uncertain, in an infinite regress of doubt. This “errors-on-errors” mechanism rules out thin-tailed certainty: predictive laws must be heavier-tailed than their in-sample counterparts. The result is the Forecasting Paradox: the future is structurally more extreme than the past. This insight collapses branching scenarios into a single heavy-tailed forecast, with direct implications for risk management, scientific modeling, and AI safety.