Property-Specific Continuity of Identity: Why "the Same" Needs to Say the Same in What Respect

This conceptual paper introduces Property-Specific Continuity of Identity, the distinction between an object’s continuity under a stated identity criterion and its continuity in a property on which someone relies. A stable name, address, or interface can coexist with changes in behavior relevant to a task. The paper assesses claims of sameness by specifying what the identity criterion tracks and whether the evidence concerns the property relied on. Visible resemblance alone does not establish continuity in that property. The account does not treat every change as consequential or prescribe one identity criterion for every setting. The discussion relates the distinction to the ship of Theseus and examines Chen, Zaharia, and Zou’s comparison of March and June 2023 GPT-3.5 and GPT-4 versions. The study compared distinguishable API versions under continuing broader model names and documented task-specific behavioral differences. It did not establish the causes of those differences or measure their effects on users. Part of the Possibility and Counterfactual Structure series within On Human Modeling, the paper offers questions about what continuity claims establish and what users are relying on. It connects human judgments of sameness and trust with AI evaluation, versioning, and the monitoring of behavior relevant to particular uses.