The Quotient Structure of Ought-Implies-Can: From Intentional Action to Propositional Shadow

Ought-implies-can is usually debated as if the issue were whether a single principle holds in a given context. The deeper question is whether an obligation-generating ethics can preserve OIC across the context-switching dynamics by which obligations are created, transformed, defeated, and repaired. Once obligation is attached to described action-paths rather than bare propositions, that demand becomes much stronger. Feasibility depends on description, practical knowledge, institutional standing, update history, repair structure, and path order; proposition-level or otherwise coarse quotients cannot in general preserve the relevant deontic-feasibility profile.

An arrow-based framework makes this precise. Local OIC can hold at a context even while global OIC preservation fails across updates. Quotient and entanglement results show why outcome-extensional and other blindness-inducing abstractions lose exactly the structure OIC would need. A transition-regularity theorem then isolates the core conditions directly forced by global preservation: feasibility monotonicity, deontic stability, and repair completeness. Path coherence and effective global inspectability matter as further pressures on any stronger order-insensitive or globally trackable version of that demand. Explicit finite models separate two regimes: benign failure, where local OIC and feasible repair survive but global preservation does not, and pathological failure, where order-sensitive updates generate impossible duty and irreparable residue. A Lean library also mechanizes a sharpened abstract regularity implication, the two finite witnesses, and their strict separation.

The upshot is not that OIC should be discarded. The failure lies in a mismatch between the level at which OIC is usually stated and the level at which obligations are generated. What remains defensible is local, guarded, action-sensitive, and reparative OIC, not OIC as a global dynamical invariant.