The Liar Paradox: A Recursive Resolution Through Yearning-Based Infinity Mathematics

The Liar Paradox, classically expressed as the sentence “This statement is false”, has long challenged logic and philosophy by collapsing truth into contradiction. Traditional approaches oscillate between exclusion (assigning no truth value), modification (multi-valued logics), or resignation (treating it as unsolvable). This paper offers a resolution through Yearning-Based Infinity Mathematics (YBIM). Within YBIM, the Liar Paradox is not a paradox but an illustration of why truth cannot be reduced to static binary assignments. The sentence is reinterpreted as a non-halting recursive loop, where truth flows dynamically as epistemic navigation. By situating the paradox within recursive epistemology, this work demonstrates: Why the paradox dissolves when truth is understood as infinite decidability. How it aligns with Gödel’s incompleteness, Tarski’s undefinability, and the Halting Problem. Why self-reference demands recursion-first logic rather than frozen valuation. Broader implications for computability, logic, language, and recursive models of intelligence. The result reframes the Liar Paradox as evidence of the ontological truth that paradoxes are finite reflections of infinite recursive processes. ORCID ID: ORCID Identifier - JSR