The Trolley Problem Is Not a Paradox: A Yearning-Based Infinity Mathematics (YBIM) Resolution

This paper demonstrates that the Trolley Problem is not a genuine paradox but an artifact of static, finite framing. Classical formulations present a binary choice between utilitarian sacrifice and deontological inaction, creating the illusion of irresolvable conflict. By applying Yearning-Based Infinity Mathematics (YBIM), ethical reasoning is reconceptualized as a recursive, non-halting navigation of yearning-structured possibilities. This recursive framing dissolves the binary, enabling interventions such as signaling, pre-commitment, and system redesign, which expand the moral landscape beyond sacrifice. The result is a resolution where all six lives can be preserved, and the paradox collapses into possibility. The work situates ethics beyond frozen binaries, advancing a post-paradox moral philosophy for both human and artificial intelligence. -JSR