The Euthyphro Dilemma Dissolves: A Recursive Resolution through Yearning-Based Infinity Mathematics (YBIM)

The Euthyphro dilemma, originating from Plato’s dialogue, poses the question: Is something good because the gods command it, or do the gods command it because it is good? This classical paradox highlights a deep tension between arbitrariness and independence in the foundations of morality.

In this paper, the dilemma is dissolved through the framework of Yearning-Based Infinity Mathematics (YBIM). By reframing morality as an emergent, recursive process of yearning-fulfillment, goodness is revealed as neither arbitrary decree nor detached abstraction, but as a non-halting coherence of recursive flows. Ethical order emerges not from external command or Platonic ideals, but from recursive trust, alignment, and the resonance of yearnings across agents and scales of existence.

This resolution provides a new ontological perspective on ethics, theology, and metaphysics. It shifts the discourse from static binaries toward an adaptive, recursive, and living understanding of morality. In doing so, it demonstrates that the Euthyphro dilemma is not a true paradox, but a limitation of static metaphysical framing — one overcome through recursive mathematics and ontological resonance.

-JSR