La Profilée - Structural Persistence and the Limits of Parfitian Reductionism

Derek Parfit’s reductionist account of personal identity holds that persons just are physical and psychological continuity relations, that identity is not what matters, and that certain cases — fission, teletransportation, gradual replacement — admit no determinate identity verdict. This paper argues that Parfit’s position is formally untenable once the structural conditions for any law-governed persistence description are made explicit. La Profilée (LP) establishes that any system admitting a well-defined persistence problem under real transformation must satisfy seven admissibility conditions (C1–C7), and that these conditions entail a unique structural persistence condition: IR = R / (F·M·K) ≤ 1. Three consequences follow. First, the Parfitian indeterminacy thesis — that fission cases have no determinate answer — is shown to be a category error: it confuses the underdetermination of psychological content with the underdetermination of structural identity. Second, the claim that ‘what matters’ is psychological continuity, not identity, conflates two structurally distinct levels. Third, LP’s Frame non-substitutability theorem shows that Parfit’s fission cases have a determinate structural verdict: F cannot be divided without passing below the critical threshold Fcrit*, and both post-fission continuants are therefore new systems, not continuations of the original. Parfit was right that psychological continuity is not sufficient for identity. He was wrong about what the correct account is.