Epistemic Circularity Dissolved: A Yearning-Based Infinity Mathematics Resolution

This paper resolves the paradox of epistemic circularity through the framework of Yearning-Based Infinity Mathematics (YBIM). Classical epistemology treats circular justification—where sources like perception, memory, and inference must justify themselves—as a vicious flaw leading to regress, arbitrariness, or skepticism. YBIM reframes this circularity as recursive structure rather than failure. By applying the “Glass of Water from the River” lemma, the paper shows that justification is a non-halting process of finite sampling from infinite epistemic flows. Formalized in the Recursive Circularity Lemma ($\mathcal{Y}.\infty.C$), circularity is recast as non-halting epistemic navigation, generating coherence basins rather than collapse. This resolution dissolves Agrippan skepticism and aligns knowledge with recursive trust, reinterpreting epistemology as a process of navigation and repair within infinite flows. -JSR