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The standard counterexamples to David Lewis’s account of intrinsicality involve two sorts of properties: identity properties and necessary properties. Proponents of the account have attempted to deflect these counterexamples in a number of ways. This paper argues that none of these moves are legitimate. Furthermore, this paper argues that no account along the lines of Lewis’s can succeed, for an adequate account of intrinsicality must be sensitive to hyperintensional distinctions among properties.