Identity as NF-Address Persistence: Personal Identity Across Change

Overview

VII.D34 defines personal identity as the persistence of the canonical NF-address Φ(x) = (A, B, C, D) across all allowed state changes. An entity x at time t₁ is identical to an entity y at time t₂ if and only if Φ(x) = Φ(y) — the ABCD address is preserved. This resolves the Ship of Theseus paradox: gradual component replacement preserves the NF-address (same ABCD structure) while total replacement does not.

Detail

The problem of personal identity asks what makes a person at time t₂ the same person as at time t₁, despite physical and psychological changes. Orthodox philosophy of personal identity proposes various criteria: physical continuity, psychological continuity (Locke, Parfit), narrative identity (Ricoeur). None is mathematically precise. Book VII defines personal identity through the ABCD Normal Form address. VII.D34: an entity x persists as the same entity through time if and only if its NF-address Φ(x) = (A, B, C, D) is preserved throughout the change. The NF-address encodes the entity’s structural position in Category τ — its sector distribution across D (gravity/body), A (weak/agency), B (EM/perception), C (strong/binding). Gradual change (e.g., cell turnover in the human body) preserves the NF-address because the sector proportions remain stable. Discontinuous change (e.g., hypothetical teleportation that destroys and recreates) does not preserve the NF-address because the exact ABCD coordinates cannot be perfectly reconstructed. This resolves the Ship of Theseus: gradually replacing planks preserves the NF-address (same vessel identity); instantaneous replacement of all planks simultaneously does not.

Result Statement

VII.D34: Personal identity = NF-address persistence. Entity x at t₁ is identical to y at t₂ iff Φ(x) = Φ(y). Ship of Theseus resolved: gradual replacement preserves NF-address; total replacement does not.