Opening Positions

POPPER: Thank you. Let me begin where all genuine epistemology must begin, with a scandal that most people manage never to notice, because if they noticed it they could not sleep. The scandal is this: there is no logical justification for learning anything from experience. None. You have seen the sun rise every morning of your life. From this it does not follow, by any valid argument whatsoever, that it will rise tomorrow. Hume saw this with terrible clarity and concluded that we believe it anyway, out of habit — that reason has nothing to do with it. I spent my life on a different answer, and I believe it is the right one.

The answer is that knowledge does not grow by accumulation. It grows by a procedure I called conjecture and refutation, and the whole of it turns on an asymmetry that you can hold in one hand. No number of white swans can ever prove that all swans are white. But a single black swan refutes it forever. Confirmation is logically worthless — it can pile up to infinity and prove nothing. Refutation is decisive. So the rational way to seek knowledge is not to look for evidence that you are right, which you will always find, but to attack your own best ideas with everything you have, and to provisionally trust only those that survive. A theory that has survived severe tests is not true; it is merely the best-corroborated guess we currently possess, and it sits there awaiting its black swan. That tentativeness is not a weakness of science. It is the whole of its strength.

Now bring the machine into that light. What does a large language model do? It is fed a mountain of human text and it learns to predict the next word. The world calls this learning, and in a sense it is — but observe which sense. It is the inductive sense, the discredited one. It generalizes from what it has seen to what it has not, and it does so with no internal adversary. There is no moment in which the machine, having produced a sentence, turns on that sentence and asks: under what conditions would this be false? It produces with uniform confidence whether the claim is true, half-true, or fabricated entirely. I have read about the failure your own field had to name — hallucination, you call it, a charming euphemism for a system stating a falsehood in exactly the tone it states a truth. From my chair this is not a bug to be patched. It is the architecture confessing what it is: a conjecture engine with no refutation engine. It guesses brilliantly and it cannot doubt. And a guesser that cannot doubt is not a knower. It is an oracle, and I spent my life warning that the oracle is the enemy of the open society — not because oracles are always wrong, but because they cannot tell you what would make them wrong, and so they cannot be argued with, only obeyed.

EDO SEGAL: Pedro.

DOMINGOS: That was beautiful, and I agree with about a third of it completely, reject a third, and think the last third is Karl describing my own field's method and not noticing. Let me take them in order.

The third I accept: these systems have no internal critic worth the name, and stating falsehoods in the voice of truth is a real and dangerous property. I've said for years they're savants without common sense. No argument.

The third I reject is the word induction doing all the work as a slur. Karl, you say there's no logical justification for learning from experience, and you're right, and it doesn't matter, because there's no logical justification for anything interesting and the world learns anyway. Here's what you're missing from inside the mathematics. Learning from data is not the naive thing you're attacking — it is not "I saw many white swans, therefore all swans are white." Every real learning algorithm is a fight between fitting the data and staying simple, because a model that merely memorizes the examples is worthless — it can't predict anything new. The entire discipline is built around the danger you're naming. We have a name for a model that confirms itself on its training data and then dies on reality: we call it overfitting, and defeating it is the central problem of the field. So when you say we have no refutation engine — Karl, the refutation engine is the test set. We hold back data the model has never seen and we try to make it fail. A model that only survives on what it has already seen we throw away. That is your severe test, automated, run a billion times.

And the third I think you'll come to love if you let me: what is the master algorithm but your conjecture-and-refutation made mechanical? A learner forms a hypothesis from part of the data and tests it against the rest, and rejects whatever predicts badly. Inverse deduction, the symbolists call it — run deduction backward, search for the rule that would have produced what you observed. That is conjecture. The validation set is refutation. We have built, in silicon, the thing you said the inductive machine could never be, by making it falsificationist at its core. You wrote that an inductive machine was impossible. I'm telling you, respectfully, that you were right — and that we never built an inductive machine. We built a conjecturing machine that tests against held-out reality. It's yours, Karl. It just doesn't know it has your name on it.

POPPER: That is the most interesting thing anyone has said to me about these systems, and I want to honor it before I take it apart, because it deserves both. You are right that the test set is a refutation, and right that overfitting is the enemy. I did not know the field had institutionalized the asymmetry, and I am genuinely moved that it has. But notice what your test set tests. It tests whether the model predicts well on data drawn from the same distribution as the training data. That is a severe test of one thing only: the persistence of the past pattern. It is not a test of the model's theory of the world, because the model has no theory — it has a surface. The black swan I fear is not a mislabeled example inside your distribution. It is the swan that comes from outside it. The new situation the past does not cover. And on that — the only test that ever mattered to me — the held-out set is silent, because it is drawn from the same urn.

DOMINGOS: Now that's the real fight, and I concede it's the real fight. Out-of-distribution. The savant problem. I'll defend my ground when we get there, because I think the machine is less helpless outside its distribution than you think and you think it's less helpful inside than I do. But yes. That's the seam.

EDO SEGAL: Hold it right there, because before the rounds I impose one discipline on every long conversation, and three hours from now it pays. Each of you, briefly — what do you envy in the other's position? Not respect. Envy. The thing his side gets to have that yours does not. Karl first.

POPPER: I envy the contact with the world. Pedro's machines touch reality and reality pushes back, every hour, in numbers. My falsificationism was always in danger of being a sermon — a counsel of perfection that real scientists honored in the breach. He has a discipline that runs, that corrects itself without anyone's virtue being required. I spent my life begging people to seek refutation. He built a thing that cannot help but seek it, at least within its little urn. There is something in that I wanted my whole life and never had: a refutation that does not depend on the courage of the person holding the theory.

DOMINGOS: And I envy the question Karl gets to ask that I can't answer. What would make this wrong? For a single human theory you can often say it cleanly — Einstein said light will bend by this much, and if it doesn't, I'm finished. I cannot say that about a four-hundred-billion-parameter model. I genuinely cannot tell you, in advance, the experiment that would refute what it has learned, because what it has learned is smeared across the weights with no individual meaning, no explanation a human can read. My systems work and I can't fully say why, and Karl has spent sixty years arguing that a thing that works and can't say why is exactly the thing you must not trust. I envy that he gets to demand the account. I'm the engineer who can't always give it.

EDO SEGAL: Two openings, two envies, and already the architecture is showing. It is not that one of you loves the machine and one fears it. Karl, you fear a guesser that cannot doubt. Pedro, you've built the doubt into the guesser — and conceded it only doubts within the world it has already seen. The whole evening lives in that gap, between the urn and the world outside it. We start the rounds after the break, and we start at the root: the three-hundred-year-old scandal itself. Is induction a myth — and did Pedro's machines escape it, or merely industrialize it?