Saul Kripke

In the [YOU] on AI Field Guide

The cycle that began with [YOU] on AI asks what it would mean to see the machine clearly—to take neither the triumphalist position that it understands everything nor the dismissive position that it understands nothing, but to hold the harder question: which capacities does it have and which does it lack, and what follows from that distinction for how we use it? Kripke is the cycle’s logician of that question. He supplies, with the precision of a completeness proof, the instruments that measure the gap between behaving as if one understands and actually understanding. His rule-following paradox shows that behavioral evidence cannot, in principle, settle which rule a system learned—a theorem, not a mood, about the limits of evaluation. His causal theory of reference shows that the words a system produces may have no referent in the sense that makes reference possible—the causal chain that runs back through human use to the things themselves simply does not exist for a text-trained model. His possible-worlds semantics supplies the formal anatomy of the counterfactual and modal reasoning that robust planning and causal inference require, and identifies, precisely, what a next-token predictor is missing.

He sits in the cycle’s gallery as the philosopher who refuses both easy exits. The “stochastic parrot” position says the machines merely recombine statistics without understanding; the rival camp points to emergent capabilities as evidence of genuine comprehension. Kripke shows that the debate, staged in behavioral terms, has no resolution, because understanding-the-rule and conforming-to-the-rule produce the same outputs over any test we can run. The honest position is not to declare for either side but to see that the question of machine understanding inherits all the depth of his paradox. And his most disquieting move applies the same skeptical argument to us: there may be no inner fact that constitutes our understanding either, so the difference between humans and machines is not a private glow of comprehension we possess but our membership in the corrective practice—the community that holds us to the rule—that the machine stands outside.

The cycle thus uses Kripke the way you would use a calibrated lens: not to deliver a verdict but to enforce a discipline. The discipline is the refusal to slide from “behaves as if it understands” to “understands,” from “says it refers” to “refers,” from “applies the rule consistently” to “follows the rule.” That discipline is the rarest thing in the discourse around AI, and it is exactly the thing the systems’ fluency is engineered to erode. Symbol grounding is the engineering name for the problem his causal theory of reference identifies. The rule-following paradox is the philosophical name for the problem that out-of-distribution generalization identifies in machine learning. The names are different; the structure is the same.

Origin

Born in Bay Shore, New York, and raised in Omaha, Nebraska, where his father was a rabbi, Kripke was a prodigy in the precise and non-metaphorical sense: he proved a completeness result for modal logic as a teenager, and the paper appeared in the Journal of Symbolic Logic when he was eighteen. He was an undergraduate at Harvard when MIT invited him to lecture to graduate students in logic. He completed a bachelor’s degree in mathematics in 1962, then held positions at Harvard and Rockefeller before becoming McCosh Professor of Philosophy at Princeton, where he delivered the 1970 lectures that became Naming and Necessity. He later moved to the CUNY Graduate Center, where he taught until late in his life. He published almost nothing in the conventional academic sense—his most important works were either transcribed lectures or short papers—and treated the analytic philosophy of his century as a structure to be rebuilt from the foundations rather than decorated at the margins. He received the Schock Prize in Logic and Philosophy in 2001, widely regarded as the nearest equivalent to a Nobel Prize for philosophy.

The origin of the rule-following work is itself instructive. Kripke had been thinking about Wittgenstein’s Philosophical Investigations for years when he began lecturing on what he called the “Kripkenstein” reading in the late 1970s—a reading he acknowledged was his own reconstruction rather than a settled interpretation of the historical Wittgenstein, and which he offered as the strongest and most radical version of the skeptical argument the text contained. The candor is characteristic: Kripke distrusted the easy slide from “this is what the text says” to “this is what it means,” and he applied to the history of philosophy the same critical discipline he applied to everything else. The result was a book that transformed philosophy of language and philosophy of mind, drew on a close reading of a canonical text, and simultaneously disclaimed being a piece of Wittgenstein scholarship.

Key Ideas

The rule-following paradox. For any finite sequence of behavior, infinitely many rules are consistent with it. A child who has always added correctly has a track record equally consistent with the deviant function “quus,” which agrees with addition on all inputs tried so far and returns five on all larger ones. No fact about the child’s history or mental states can settle which function she actually meant, because every candidate fact is also finite and equally consistent with the deviant function. This is not a limiting result about our instruments; it is a structural theorem about the underdetermination of rules by finite evidence. It is, almost word for word, the problem of out-of-distribution generalization in machine learning: the model agreed with us on the training set; which rule did it learn? Kripke proved, decades early, why the question is so hard.

The causal theory of reference. Names reach their objects not through descriptions in the speaker’s head but through a causal-historical chain—an initial baptism, when someone pointed and dubbed, and a long relay of use in which each speaker intends to use the name as those who taught it to them did. A speaker can refer to Aristotle while knowing almost nothing true about him, because the chain of use runs back through teachers and books to the man himself. A text-trained language model has exactly the descriptions—the statistical patterns in which “Aristotle” appears near “Plato” and “logic”—and none of the chain. On Kripke’s account, this is not a thin version of reference; it is the absence of the relation that reference is. The symbol grounding problem is the engineering name for this absence.

Rigid designation. A name is a rigid designator if it picks out the same object in every possible world—if “Nixon” refers to that same man in every counterfactual scenario we describe, even one in which he became a concert pianist. Definite descriptions are not rigid; “the President of the United States in 1970” picks out different people in different possible worlds. Rigid designation is the device that lets thought hold an object fixed while rotating the world around it—the precondition of coherent counterfactual reasoning. A language model’s context-sensitive embeddings are the architecture of the non-rigid designator raised to a principle: the representation of a name shifts with context, so the system’s grip on an object drifts as the prompt changes, which predicts the entity-tracking and coreference failures these systems display.

Plato

The necessary a posteriori. Kripke pried apart two distinctions that the tradition had treated as the same line drawn twice—necessary/contingent and a priori/a posteriori—by showing that some truths are both necessary and empirical. “Hesperus is Phosphorus” (both names designate Venus rigidly) is necessarily true, yet it was discovered by astronomy. “Water is H2O” is necessarily true of water in every world, yet it was discovered by chemistry. A system that flattens necessary truths into the same statistical space as contingent regularities cannot distinguish a deep structural fact that constrains every possibility from a pattern that merely held in its training data—a foundational limit for any system reasoning about science, law, or engineering.