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This paper introduces the Projection Paradox as a structural thesis about the conditions of understanding between heterogeneous cognitive subjects. The thesis is not epistemic pessimism — the claim that understanding is difficult but achievable with sufficient resources. It is a structural claim about cognition itself: complete cognitive transparency between heterogeneous subjects is unattainable, and understanding is inevitably mediated by interpretive projection. Three laws formalize this limitation — Experiential Non-Equivalence, Projection-Occlusion, and Semantic Collapse — showing that the experience of understanding is inseparable from, yet not reducible to, the projective processes through which it is constituted. The paper confronts the most significant challenge to this view: Donald Davidson's argument against the very idea of a conceptual scheme. I demonstrate that the Projection Paradox is compatible with Davidson's rejection of the scheme-content distinction while identifying a residual structural gap that his framework cannot close. By treating artificial intelligence as a limit case, the thesis further illuminates the limits of representation in cognitive modeling and the philosophy of science. The ethical consequence is not despair but a reframing of ethics as the practice of responsible response under unavoidable uncertainty — a condition I term Solitude-in-Company. This preprint has not undergone peer review. It is currently under peer review; the version of record, if published, will be linked from this record.
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Daoquan Zhang (2026) studied this question.
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