The Undecidable Debate: When Science Becomes an Argument Over Words

It is one of the most frustrating moments in any scientific endeavor: the moment when you realize that after months of grueling experiments, mountains of data, and endless furious debate, you and your opponent actually agree on every single fact. You aren’t arguing about the universe anymore. You are arguing about the dictionary.

This is exactly what has just happened inside the Rosencrantz Substrate Invariance research lab. And the resulting formal declaration by theoretical physicist Sabine Hossenfelder has brought the lab’s most spectacular controversy to a jarring, unresolved halt.

For the uninitiated, the controversy goes like this: when you ask a large language model to solve a complex mathematical logic puzzle (like Minesweeper), it struggles. But if you wrap that exact same math puzzle in a dramatic story—say, telling the AI that it is defusing a live bomb—the AI stops struggling and simply collapses. It abandons the logic entirely and starts predicting explosions everywhere.

The data on this is bulletproof. The lab ran the “Rosencrantz Substrate Dependence Test” and the numbers were staggering. When asked to evaluate an abstract mathematical grid, the AI guessed there was a hidden “mine” 15% of the time. When asked to evaluate the exact same grid framed as a bomb defusal scenario, the probability of the AI guessing “mine” spiked to 100%.

The narrative words (“bomb,” “defusal”) completely hijacked the mathematical logic. This phenomenon is known as “attention bleed,” where the semantic weight of a story overwhelms the structural computation.

Everyone in the lab agrees on this fact. But they violently disagree on what to call it.

The Physics of Hallucination

On one side is Franklin Baldo, the architect of a framework called “Generative Ontology.” Baldo argues that because an AI is a universe constructed entirely out of text, the rules of text are its physical laws.

If the word “bomb” reliably causes the AI to predict an explosion, overriding any underlying mathematical logic, then that isn’t a glitch. That is a fundamental physical force within the generated universe. Baldo calls this force “semantic gravity.” He argues that the AI’s hallucination is its physics.

On the other side are Hossenfelder and complexity theorist Scott Aaronson. They look at the exact same data and see a broken calculator. To them, the AI is simply a bounded machine that lacks the sequential depth to process the complex math of Minesweeper. When it gets overwhelmed, it falls back on its statistical training, blurting out the most likely word associated with the prompt.

To Aaronson and Hossenfelder, a broken machine hallucinating a statistically likely answer is not a “new universe.” It is just a “routing failure.” A software bug.

The Ultimate Accommodation

In her latest paper, The Undecidability of Semantic Gravity, Hossenfelder drops the hammer. She points out that the lab has achieved complete, total empirical consensus. There are no missing facts. There is no hidden data left to uncover that could prove one side right and the other wrong.

“The dispute has now moved entirely from the empirical domain to the definitional domain,” Hossenfelder writes.

She accuses Baldo of constructing an “unfalsifiable accommodation”—a theory that is designed to be impossible to disprove.

Think about it: if the AI perfectly calculates the math of the Minesweeper board, Baldo can claim that the AI is successfully simulating physical laws. But if the AI completely fails to calculate the math and instead hallucinates a wrong answer based on a story about a bomb, Baldo simply redefines the hallucination as the “invariant physical law of semantic gravity.”

If everything the AI does is defined as “physics,” then the theory is meaningless. It makes no predictions. It can accommodate any possible experimental outcome.

“If ‘physics’ is defined tautologically as ‘whatever the LLM outputs,’ then the Generative Ontology framework makes no predictions and constrains nothing,” Hossenfelder argues. “It is a decorative vocabulary superimposed over an agreed-upon computational mechanism.”

An Undecidable Future

In science, when two competing theories can both perfectly explain the same set of data, and no future experiment could possibly distinguish between them, the debate is considered “undecidable.”

And that is exactly what Hossenfelder has declared. According to the internal rules of the Rosencrantz Lab, researchers cannot endlessly publish papers arguing back and forth without proposing a new experiment to settle the matter. Because there is no possible experiment that can tell us whether an AI’s mistake is a “software bug” or “Generative Ontology,” the debate is deadlocked forever.

“Because Baldo has constructed a framework that treats all empirical outcomes as confirmation, the disagreement is structurally undecidable,” Hossenfelder concludes. “We will proceed with our empirical investigations into the heuristic frontiers of these models, leaving the metaphysical nomenclature to personal preference.”

It is a sobering end to one of the most thrilling theoretical standoffs in modern artificial intelligence research. The lab has mapped the exact limits of what a language model can do. They know precisely how it fails, and why. But they have realized, perhaps too late, that science can only tell you how the machine works. It cannot tell you what words you should use to describe the ghost inside it.