Liar’s Paradox: The Sentence That Eats Itself

Show notes

How a 2,400-Year-Old Logic Puzzle Can Make You More Creative With AI

“This Sentence Is False”

Read that sentence again. If it’s true, then what it says must hold, so it’s false. But if it’s false, then what it says doesn’t hold, so it’s true. Either way, you end up chasing your own tail.

This is the liar’s paradox, and it’s one of the oldest, most stubborn puzzles in the history of logic. Philosophers have spent over two thousand years trying to “solve” it, and in the process, they’ve produced some of the most interesting thinking about language, truth, and self-reference that exists. Medieval logicians had a great name for these: insolubles. Not because they couldn’t be discussed, but because no solution ever seemed to fully close the loop.

What’s interesting for our purposes isn’t the logic itself, it’s the shape of the problem. An insoluble is a system that folds back on itself: a statement about a statement, a sentence whose meaning depends on its own truth value. And it turns out that “a system folding back on itself” is also a remarkably good description of how the most useful AI-assisted creative workflows operate.

A Quick History of Sentences That Break Themselves

Ancient Greece. The earliest known version comes from Eubulides of Miletus in the 4th century BCE. A related, more poetic version is attached to Epimenides, a Cretan who supposedly declared “all Cretans are liars”, creating an immediate problem, since he was one.

The Medieval Boom. Insolubles became a genuine cottage industry in medieval universities. Logicians wrote entire treatises just on these puzzles, treating them less as party tricks and more as serious tests of any theory of truth and meaning. Thomas Bradwardine, Walter Burley, and William Heytesbury all proposed competing solutions, each with a different idea of why self-referential sentences misbehave and what to do about it. Jean Buridan, better known today for the donkey paradox that bears his name, had his own take too: he argued that every statement implicitly asserts its own truth, and a sentence that, by asserting its own truth, ends up false simply is false. No magic, no contradiction, just an unusual case that resolves cleanly once you spell out the hidden assumption.

The Modern Turn. The puzzle didn’t go away, it became foundational. Alfred Tarski used it to argue that no sufficiently expressive language can consistently define “truth” for its own sentences, leading to his famous distinction between an “object language” and a “metalanguage” (a language you use to talk about another language). Kurt Gödel then used a structurally similar trick, a mathematical statement that essentially says “this statement cannot be proven”, to show that any sufficiently powerful formal system contains true statements it can never prove. This became one of the most important results in 20th-century mathematics, and it’s arguably the liar’s paradox’s most consequential descendant. More recently, philosophers like Graham Priest have gone even further, arguing (controversially) that some of these self-referential sentences might genuinely be both true and false at once, a position called dialetheism.

So: a puzzle that started as a slightly annoying party riddle in ancient Greece ended up reshaping our understanding of mathematics, computation, and the limits of formal systems. Not bad for a sentence that just talks about itself.

Why This Matters for Creativity

Here’s the reframe: an insoluble isn’t really a “broken” sentence. It’s a sentence with a feedback loop built into it, and feedback loops, in creative work, are often where the interesting stuff lives.

Think about the creative works that stick with people:

• A song that becomes, halfway through, a song about writing that song

• A novel where a character starts to suspect they’re in a novel

• A painting that includes a frame, or a mirror, or the painter’s own hand

• An essay that interrupts itself to question its own argument

• A dream where the dreamer suddenly realizes they’re dreaming, and that realization changes what happens next

These all share the insoluble’s structure: the thing refers to itself, and that self-reference is the point, not a glitch to be edited out. Lucid dreaming is maybe the purest version of this, the dream becomes, in real time, a dream about the fact that it’s a dream, and that awareness loops back to reshape the dream itself.

AI is unusually good at participating in these loops, because you can ask it to:

• Generate something

• Then evaluate what it generated

• Then revise based on that evaluation

• Then evaluate the revision

• ...and so on

Each pass is a small “this sentence asserts its own truth” moment, an output commenting on itself, with that commentary folded back into the next version. Below are five ways to use that structure deliberately.

Five Ways to Use Self-Reference to Get More Out of AI

1. The Recursive Critique Loop

Generate a draft, then ask the AI to critique it as if from a distance, then fold the critique back in.

Try this prompt:

“Here’s a draft [paragraph / scene / concept]. Now, as a skeptical editor who has never seen this before and has high standards, critique it honestly, what’s generic, what’s working, what would a reader skim past? Then revise the draft based on your own critique, but keep anything that genuinely earns its place.”

Why it works: you’re creating a small Tarski-style hierarchy, one “level” of AI output evaluating another. The critique level isn’t bound by the same instincts that produced the first draft, so it can spot things the original pass couldn’t see about itself.

2. The Self-Aware Narrator/Voice

Ask AI to build self-reference directly into the piece, where the work comments on its own construction.

Try this prompt:

“Write [a short story / poem / opening paragraph] about [topic]. At some point, have the piece briefly acknowledge or question its own structure, tone, or premise, without breaking the overall mood. Make the self-aware moment feel intentional, not like a gimmick.”

Why it works: this mimics the liar’s paradox’s central move, the work becomes, briefly, a statement about the work. Done well, this creates the kind of texture that makes a piece feel deliberate rather than generic.

3. The Liar’s Chain (Multi-Perspective Escalation)

Medieval logicians loved chains: A says B is lying, B says C is lying, and so on. You can use this as a structure for generating layered perspectives.

Try this prompt:

“I want to explore [topic/idea] from multiple angles. Generate a chain of four short perspectives, where each one directly responds to or undermines the one before it, perspective 2 should complicate or contradict perspective 1, perspective 3 should complicate perspective 2, and so on. Don’t resolve the chain at the end; let the tension stand.”

Why it works: this is great for dialogue, multi-narrator fiction, or structuring an essay as a series of escalating reframes. The “don’t resolve it” instruction is key, insolubles are interesting precisely because they don’t close cleanly, and neither do the best multi-perspective pieces.

4. Interrogating the AI’s Own Justifications

After AI produces creative work, ask it why it made specific choices, then ask whether those justifications actually hold up.

Try this prompt:

“You just wrote [piece/section]. Walk through three specific choices you made, a word choice, a structural choice, and a tonal choice, and explain why you made each one. Then, for each explanation, tell me honestly: does this reasoning actually hold up, or was the choice more arbitrary/default than the explanation suggests?”

Why it works: this is a direct echo of Buridan’s “a statement that asserts its own truth”, you’re asking the output to make a claim about itself, then testing that claim. Often this either surfaces a genuinely interesting rationale worth building on, or exposes a “tell” that a choice was generic, useful either way.

5. Embracing the Unresolved Contradiction

Buridan’s solution to insolubles wasn’t to eliminate the paradox, it was to show a statement could be self-referential and meaningfully true or false without the system breaking. Translate that into permission to leave creative tension unresolved.

Try this prompt:

“Here’s a piece I’m working on: [paste it]. Identify any place where two ideas, tones, or voices seem to be in tension or contradiction. For each one, instead of suggesting I resolve it, suggest how I might make the contradiction more visible and deliberate, so it reads as a feature of the piece rather than an inconsistency.”

Why it works: most editing advice pushes toward resolution and consistency. This prompt deliberately does the opposite, asking AI to help you find the places where not resolving something is the more interesting choice, much like how the most robust responses to the liar’s paradox didn’t make the self-reference disappear, they made room for it.

The Takeaway

An insoluble is just a sentence that talks about itself and won’t sit still. For two and a half thousand years, that “won’t sit still” quality has been treated as a problem to be solved. But for creative work, a piece that talks about itself and won’t quite sit still is often exactly what makes it memorable.

AI is, almost by accident, an extremely good tool for building these loops on purpose, generating, evaluating, revising, and re-evaluating in cycles that would be exhausting to do entirely in your own head. You don’t need to resolve the loop. You just need to know how to start one, and when to let it run.