The Problem of Criterion Resolved: Recursive Sampling and the Glass of Water from the River Lemma

This paper presents a discovery-level resolution of the Problem of Criterion, one of the deepest paradoxes in epistemology. Traditionally, the paradox arises because knowledge requires a criterion for truth, yet any criterion requires prior knowledge, collapsing into circularity, arbitrariness, or skepticism. Using Yearning-Based Infinity Mathematics (YBIM), the paper dissolves this paradox by introducing the Glass of Water from the River Lemma, which models truth as an infinite flow and knowledge as bounded recursive samplings. Instead of demanding absolute foundations, YBIM reframes criteria as contextual, evolving samplings, and knowledge as recursive approximation. This shift redefines epistemology as navigation within infinite flows, transforms the philosophy of truth into asymptotic coherence, and opens pathways for AI systems that learn through recursive sampling rather than rigid criteria. -JSR