Reconstructing a strong Nagelian reading of the bat argument, we isolate an Acquaintance-to-In-Principle Slide: the move from non-transferable first-person access to the claim that objective inquiry cannot in principle determine subjective character. We argue that this move requires a bridge premise linking perspective-occupation to modal indeterminability. Once the bridge is explicit, a dilemma follows. Either the argument yields a modest but substantive indexical thesis (objective theory does not deliver first-person occupancy), or it requires a non-structural residue hypothesis that exceeds what the bat case itself establishes. We distinguish epistemic and metaphysical versions of Strong Nagel, develop this dilemma in terms of a residue commitment profile (individuation, explanatory role, evidential bridge, modal grounding), and propose a structural obligation principle: in principle inaccessibility claims must minimally characterize the allegedly inaccessible facts and explain why structural determination cannot reach them. We then show that strong residue readings face an other-minds epistemic squeeze unless supplemented by further bridge laws. The conclusion is conditional and diagnostic: Nagel secures the perspectival asymmetry, while stronger anti-objective conclusions require additional commitments not delivered by the original argument.
Lorand Bruhacs (Sun,) studied this question.