The result is a sentence-continuation machine that is likelier to emit sentences resembling those that a thoughtful, moral person could utter. This might seem like a reasonable goal to work toward; I think we’d all prefer it if chatbots never emitted sentences such as “You should kill yourself.” However, for all the times that “honesty” is mentioned in Claude’s constitution, I would argue that it is fundamentally dishonest to have a machine emit many categories of sentences, including any sentences using first-person pronouns.

Every game needs a goal. In a Turing machine, goals are imposed from the outside. For true induction, the process itself should create its own goals. And there was a key constraint: Putnam realized that the dynamics he had in mind would only work mathematically if the system had just one goal governing all its behavior. That’s when it hit him: The goal is to repeat. Repetition isn’t a goal that has to be programmed in from the outside; it’s baked into the very nature of things—to exist from one moment to the next is to repeat your existence. “This goal function,” Putnam wrote, “appears pre-encoded in the nature of being itself.” So, here’s the game. The system starts out in a random mix of “on” and “off” states. Its goal is to repeat that state—to stay the same. But in each turn, a perturbation from the environment moves through the system, flipping states, and the system has to emit the right sequence of moves (by forming the right self-reinforcing loops) to alter the environment in such a way that it will perturb the system back to its original state. Putnam’s remarkable claim was that simply by playing this game, the system will learn; its sequences of moves will become increasingly less random. It will create rules for how to behave in a given situation, then automatically root out logical contradictions among those rules, resolving them into better ones. And here’s the weird thing: It’s a game that can never be won. The system never exactly repeats. But in trying to, it does something better. It adapts. It innovates. It performs induction.

“You only perceive signals that are useful for shaping behavior … A game is a special kind of mathematics … But for a game you need a goal function … We’re suggesting that the category repetition is a candidate … You’re searching for rules of choice that allow a repeating or self-reproducing path … There’s a transcendental core to the laws of physics themselves …”

It’s easy to say why someone is wrong, Putnam said. The hard part is figuring out why they’re right. And everyone is right. Everyone has some central insight, hard won by the consistency-making mechanism of the brain, built of past experiences, cast as motor predictions, a pattern that repeats, sustains itself in the chaos. Our job is to pan for it like gold, sift it into our own nervous systems, reconcile the resulting contradiction, become something new.