The Poet Who Died of a Sentence
What an ancient paradox teaches us about AI and the human brain
The poet who died of a sentence
Around 300 BC, one of the most admired scholars in the Greek world was a poet named Philitas of Cos. He tutored a future king of Egypt, Ptolemy II. He was also, by every account, extraordinarily thin.
Later writers joked that he wore lead in his shoes to keep from blowing away. They also passed down a darker story: that he worried himself to death over a single sentence.
The sentence was the liar paradox in its ancient form: “I am lying.” If that’s true, then he is lying, so it’s false. If it’s false, then he’s telling the truth, so it’s true. Round and round, all night.
His epitaph, as quoted centuries later by the writer Athenaeus, blames “the lying word” and long nights of worry for his death. One classic translation reads it as the Liar paradox itself. Historians suspect the epitaph was a later joke about an overly fussy scholar.
But the joke survived for two thousand years because it captures something real. Some sentences can trap a mind that tries too hard to answer them.
The textbook’s cure
I recently found a modern echo of Philitas in the opening pages of a pure mathematics textbook. It sets two sentences side by side:
- This sentence is false.
- I have been far even as decided to use even go want to do more like.
The first is the liar in its modern form. Assume it’s true and it becomes false; assume it’s false and it becomes true. The second is word salad. There is no claim in it at all.
The textbook doesn’t try to solve either one. It simply sets them aside and agrees to work only with statements that can actually be true or false. Mathematicians call these propositions.
That is the cure Philitas never found. Before asking “Is this true?”, ask a quieter question first: “Is this even the kind of thing that can be true or false?” If the answer is no, you are allowed to walk away. You can sleep.
This two-step filter turns out to matter far beyond mathematics. It shows up in the AI systems we use every day, and inside our own heads.
Machines that never lose sleep
Large language models have the opposite problem from Philitas. He couldn’t stop worrying about a question with no answer. A language model never worries at all.
At its core, a language model predicts which word should come next. It will produce smooth, confident text for any input: a good question, a trick question, or pure gibberish. Fluency is not truth. Often it isn’t even a claim.
That’s why researchers who measure AI accuracy borrow the textbook’s move. A widely used method called FActScore, published in 2023, breaks a long AI answer into small “atomic facts,” each a single checkable claim. It then verifies each one against a reliable source such as Wikipedia.
Here’s that filter applied to a made-up answer about the Eiffel Tower:
- “Great question!” Not a proposition. Nothing to check.
- “It was completed in 1889.” A proposition. True.
- “It’s the most beautiful landmark in Paris.” An opinion, not a fact. Nothing to check.
- “It was designed by Thomas Edison.” A proposition. False; it came from Gustave Eiffel’s engineering firm.
- “I hope this helps!” Not a proposition. Nothing to check.
The answer scores one out of two checkable claims, not one out of five. Tellingly, the FActScore team tested their method on biographies, because biographies are packed with verifiable facts rather than opinions. They chose their ground exactly the way the textbook did. Even the strong models of the time stumbled: only about 58% of ChatGPT’s atomic facts were supported.
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The liar shows up in AI too. Try asking a model: “Answer with one word: will your answer to this question be ‘no’?” If it says yes or no, it’s wrong either way. A good model notices the trap. A weaker one confidently picks a side.
The strictest version of the filter lives in AI mathematics. Proof assistants like Lean accept only well-formed mathematical statements. Word salad won’t even parse, and a definition like “L means not-L” is rejected outright. In July 2024, Google DeepMind’s AlphaProof wrote Lean proofs for International Mathematical Olympiad problems that humans had translated into Lean. Together with its sister system AlphaGeometry 2, it scored 28 out of 42, one point short of gold. Every proof was checked by Lean itself, leaving no room for confident nonsense.
A brain that checks fit, not truth
Neuroscience runs on propositions too. In the late 1950s, David Hubel and Torsten Wiesel tested a clear, checkable claim: that neurons in a cat’s visual cortex would fire in response to small spots of light. For hours, nothing happened.
Then, while they were swapping a glass slide in their projector, its faint edge swept across the screen. The neuron, Hubel later recalled, “went off like a machine gun.” The spot hypothesis was false. The real answer was edges at particular angles, a finding that helped earn them a Nobel Prize in 1981. A precise claim can be proven wrong, and being wrong is how they found the truth.
Your brain also runs a fast filter on every sentence you read. In 1980, Marta Kutas and Steven Hillyard recorded people’s brain waves as they read sentences like “He spread the warm bread with socks.” They expected the brain’s usual surprise signal, a positive wave called the P300. Instead they found something new: a negative wave peaking about 400 milliseconds after the odd word. They named it the N400.
The control condition is the clever part. When the last word made perfect sense but appeared in unexpected capital letters (“She put on her high-heeled SHOES”), the brain gave the ordinary surprise signal, not the N400. Your brain separates “this looks odd” from “this doesn’t make sense.”
So is the N400 a truth detector? In 1983, Ira Fischler and colleagues tested exactly that. “A robin is a tree” produced a big N400, as expected. But so did “A robin is not a tree,” which is true. Meanwhile “A robin is not a bird,” which is false, slipped by quietly.
The brain’s fast filter wasn’t asking “Is this true?” It was asking “Do these words belong together?” Later studies found that when a negation sounds natural in context, the brain tracks it much better. But the first-pass response is mostly about fit.
Here is where the story loops back to AI. In 2024, a team at UC San Diego found that GPT-3’s “surprisal” (how unexpected the model finds each word) was the best account of N400 size among the explanations they tested. Earlier, linguist Allyson Ettinger gave the robin sentences to Google’s BERT model. In every negated case, BERT preferred the false ending: a robin is not a bird.
Today’s far larger models handle simple negation much better. But the lesson holds. A fast prediction system, made of neurons or of silicon, is built to sense fit. Truth takes a second, slower step.
Two questions, in the right order
Philitas, the textbook, the fact-checkers and the N400 all point to the same lesson. Good reasoning asks two questions, and the order matters.
- Can this be true or false? Gibberish, opinions, pleasantries and the liar all fail here, and that’s fine. They simply aren’t candidates.
- Is it true? Only now does the real checking begin.
Fluent systems, whether a chatbot or the first 400 milliseconds of your own brain, mostly answer a different question: does this fit? Fit is useful. It’s also exactly how a polished AI answer and a plausible rumor both slip past us.
So the next time an AI hands you a confident paragraph, do what the textbook does. Pull out the sentences that make real claims. Then check those, one at a time.
And if you ever meet a sentence that insists it is false, don’t lose any sleep. Philitas already did that for all of us.
Sources
- Philitas of Cos, Wikipedia; Pataki (2013) on the lead-weights anecdote
- A Serendipitous Shadow Brought the Brain’s Visual Pathways to Light, The Scientist
- N400 (neuroscience), Wikipedia; Kutas & Federmeier, thirty years of the N400
- Nieuwland & Kuperberg (2008), on Fischler et al. (1983) and natural negation
- Michaelov et al. (2024), Strong Prediction: Language model surprisal explains multiple N400 effects
- Ettinger (2020), What BERT is not
- Min et al. (2023), FActScore
- AI achieves silver-medal standard solving IMO problems, Google DeepMind
