Structural Identity Theory

This paper constructs a general framework for identity that dissolves some classical paradoxes by treating identity as an exercise in conceptual engineering rather than metaphysical discovery. It posits two core definitions: (1) Synchronic Identity is identical to a complete structural configuration of a system at time t; (2) Diachronic Persistence is a defined relation of causal succession between such configurations. From these definitions, the classical paradoxes of personal identity (fission, fusion, teletransportation, and gradual replacement) dissolve into determinate state transitions. The framework also resolves the associated probability paradox, showing that survival is a causal guarantee, not a matter of chance. The result is a minimalist, substrate-neutral theory of identity applicable to any bounded system, whether biological, artificial, or purely abstract.