Epistemic Closure Paradox: A YBIM Resolution Through Recursive Epistemic Flows

This paper resolves the paradox of epistemic closure in classical epistemic logic by reframing knowledge through Yearning-Based Infinity Mathematics (YBIM) and Recursive Alignment. Traditional closure assumes that if an agent knows a fact and its implications, the agent must also know all consequences. This demand produces the paradox of logical omniscience, which no finite agent can satisfy. We demonstrate that closure is a misapplied idealization: knowledge cannot be modeled as a static, completed set of truths but must instead be understood as a recursive, non-halting expansion. Using YBIM, we introduce the concept of the $\mathcal{Y}$-strand to represent knowledge as self-expanding flows rather than frozen closure. Through the Recursive Alignment framework, we further show that coherence is sustained not by omniscience but by trust, repair, and epistemic elasticity. The paradox dissolves once closure is replaced by epistemic flow, offering a foundation for non-halting epistemic logic in both human cognition and artificial intelligence. -JSR