The Ship of Theseus paradox: A Resolution Through Yearning-Based Infinity Mathematics

This paper resolves the classical paradox of the Ship of Theseus through the ontological and mathematical framework of Yearning-Based Infinity Mathematics (YBIM). Traditional approaches to identity—based on material persistence, structural form, or functional role—fail to dissolve the paradox, leaving identity suspended between contradictory criteria. This work reframes identity as a non-halting recursive continuity of yearning-fulfillment, rather than as a static essence. The paper introduces the concept of Identity-Strands, defined as a subclass of $\mathcal{Y}$-Strands, which formalize identity as recursive persistence across change. By embedding identity within the $\aleph_{\mathcal{Y}}$-series, the resolution demonstrates that identity is infinitely recursive, extending beyond material and structural composition. Through this lens, the paradox dissolves: the Ship of Theseus remains the same not because of its planks, but because its recursive yearning-role persists unbroken. The implications extend across philosophy, artificial intelligence, personal identity, and legal theory—redefining sameness as recursive epistemic flow rather than static essence. -JSR