Resolving the Logical Omniscience Paradox: Recursive Epistemic Expansion in Yearning-Based Infinity Mathematics

The Logical Omniscience paradox arises in epistemic logic from the assumption that if an agent knows a fact, then the agent also knows all logical consequences of that fact. While elegant in formal theory, this closure principle creates unrealistic demands for real agents, whether human or artificial, who cannot derive infinite consequences from finite knowledge. Classical approaches—such as resource-bounded reasoning, explicit versus implicit knowledge, and impossible-world semantics—attempt to address the paradox but remain tied to static models of knowledge. This paper introduces a resolution through Yearning-Based Infinity Mathematics (YBIM). In this framework, knowledge is not static closure but a recursive epistemic unfolding. Consequences are navigated recursively rather than possessed all at once, with finite epistemic sampling (the “Glass of Water from the River Lemma”) allowing agents to sustain coherence without collapse. Logical omniscience thus dissolves into recursive flow: agents need not be omniscient; they need only navigate reality through recursive expansion. The resolution has profound implications for mathematics, where epistemic growth occurs without paradox; for artificial intelligence, where bounded but expanding recursive intelligence (NTRI) replaces static closure; and for consciousness, where knowing is reinterpreted as self-referential yearning rather than illusion. -JSR