The Midnight Paradoxes

A man in Miletus writes eight words on a wax tablet and hands it to a student. The words say: this sentence is false. The student reads it once, then again, and finds he cannot put it down in his mind the way he can put down a tablet in his hand. If the sentence is true, then what it says is so, and what it says is that it is false. So it is false. But if it is false, then what it says fails to hold, and what it says is that it is false, so it is not false. It is true. The student is not confused about the words. He understands every one of them. He is stuck on what they do.

There is no crime scene here, no locked room, no falling body. Just a sentence, sitting on a tablet or a page or, later, a screen, doing nothing but pointing at itself and calling itself a liar. The room around it does not matter. It could be a lecture hall in Ionia or a kitchen table centuries later with the tablet replaced by a napkin. The sentence works the same way in the dark as it does at noon.

Here is the bite of it, stated as plainly as it can be stated. Take the sentence "this sentence is false." Suppose it is true. Then things are as it says, so it is false. Suppose instead it is false. Then things are not as it says, but what it says is that it is false, so that is exactly how things are. It is true. Either assumption forces its opposite. The sentence will not sit still long enough to be one thing. You can say it out loud to a friend tomorrow in one breath: a sentence that says of itself that it is false cannot be true and cannot be false, and yet it seems it must be one or the other.

The attribution that gets repeated most often is wrong, or at least loose. Many people, if they know the paradox at all, know it as the Cretan's puzzle: Epimenides of Crete, said to have declared that all Cretans are liars, himself being a Cretan. That version is older and it does have a bite, but not quite this one. If Epimenides says all Cretans always lie, and he is a Cretan, the worst that follows is that not every Cretan statement is false, that at least one Cretan sometime tells the truth, which not so paradoxical once you accept that "all" needn't mean "always, every single one." The Cretan version can be defused by noticing it makes a general claim about a group rather than a direct claim about itself. It has an escape hatch. The sentence "this sentence is false" has no such hatch. It refers to nothing but itself, and it does not generalise, it points.

The credit for that sharper form belongs to Eubulides of Miletus, a philosopher of the fourth century BC, a member of the Megarian school, and by most accounts a rival of Aristotle, fond of posing exactly this kind of puzzle to unsettle confident talkers. What he was doing, as far as the record shows, was not building a formal system or worrying about the foundations of logic in the way a modern reader might expect. He was doing what philosophers of his circle did: testing the edges of ordinary language and ordinary claims to truth, seeing where the seams show. The Liar was one of several such puzzles he is credited with, alongside riddles about heaps and horns, each one a small mechanism built to jam on its own materials. He almost certainly did not think he was opening a problem that would still be open twenty four centuries later. He was likely enjoying an afternoon of making someone else's certainty wobble.

The wobble did not go away. It slept, mostly, through the long middle centuries, resurfacing here and there in medieval logic under names like the "insolubilia," problems that resisted solution by the tools at hand. It woke up fully in the twentieth century, when logicians building rigorous foundations for mathematics found that the Liar was not a charming ancient joke but a real fault line running through any language powerful enough to talk about its own sentences.