Rigid Designation

In the [YOU] on AI Field Guide

The cycle asks about the conditions under which it is safe to trust an AI system’s outputs in consequential domains. Rigid designation is a condition on coherent reasoning about individuals: a system that cannot hold an individual fixed across a chain of inference cannot reliably reason about that individual’s situation, their obligations, their rights, or the consequences of actions taken on their behalf. In medicine, law, and finance—domains the cycle treats as among the first places AI will be deployed at scale and at high stakes—identity stability is not an edge case. The patient must remain the same patient across the reasoning chain; the defendant must remain the same defendant across the analysis of evidence; the counterparty must remain the same counterparty across the construction of the contract. A system whose representations of persons drift with context introduces a structural unreliability at exactly the point where the reliability question is most consequential.

The concept connects to the fluency-authority decorrelation the cycle treats as the signature hazard of the era: the model’s outputs are fluent and confident throughout the drift, so the loss of the referential grip is invisible in the prose. Rigid designation failure is often a hallucination failure in disguise—the model did not fabricate an entity so much as imperceptibly substitute one entity for another, maintaining the surface form of reference while the underlying grip changed. The rule-following paradox and rigid designation failure are, in this sense, the same structural problem seen from different angles.

Origin

Kripke introduced the concept in his three Princeton lectures of January 1970, published as Naming and Necessity in 1980. The context was an attack on the descriptivism of Frege and Russell—the view that a name like “Gödel” abbreviates a description (“the man who proved the incompleteness of arithmetic”) that the speaker associates with it. Kripke’s counterexamples are elegant: suppose it turned out that Gödel did not prove the theorem, that a man named Schmidt did, and that Gödel stole it. On the descriptivist view, “Gödel” would then refer to Schmidt, since Schmidt fits the description. But that is clearly wrong: we have been talking about Gödel, whatever he did or did not do. The name is not the description.

In place of descriptivism Kripke offered the causal-historical theory: the name was introduced at a baptism, passed from speaker to speaker through chains of communication in which each link intended to use the name as the previous link did, and refers now to whatever it referred to at the point of introduction. This picture locates reference in a chain of events in the world, not in descriptions in heads—which is exactly what a text-trained model lacks. The rigidity of names is a consequence of this picture: if the name was introduced to designate this individual, it continues to designate this individual in every possible world, regardless of what that individual might have done otherwise.

Key Ideas

Names versus descriptions. A definite description like “the inventor of bifocals” is non-rigid: in a possible world where someone other than Franklin invented bifocals, the description picks out that person. A proper name like “Benjamin Franklin” is rigid: in any counterfactual scenario we consider, “Benjamin Franklin” still refers to that same man, even a scenario in which he became a farmer and invented nothing. The distinction is not about whether we can describe the referent but about whether the reference tracks descriptions or individuals.

The precondition of counterfactual reasoning. Rigid designation is the device that makes coherent modal reasoning possible. To ask what would have happened if a person had acted differently, you must hold that person fixed while varying their circumstances—otherwise you are reasoning about whoever else might have occupied those circumstances, not about the original person. A system that cannot hold individuals fixed across counterfactual reasoning cannot reliably perform causal inference, plan from an agent’s perspective, or reason about obligations and consequences. These are exactly the capacities that distinguish competent reasoning in high-stakes domains from fluent but unreliable prose.

Context-sensitive embeddings as non-rigid designators. The transformer architecture that underlies modern large language models computes representations dynamically from context, so that the vector for a person’s name shifts as the surrounding text shifts. This is a feature for handling ambiguity and anaphora—the model needs “bank” to mean different things in different contexts. But for proper names, where rigidity is the requirement, the same contextual sensitivity becomes a structural liability: the model’s grip on an individual loosens whenever the context changes, and entity-tracking across long passages requires the model to maintain a stability that its architecture does not guarantee.