Can a sentence contradict itself without ever mentioning itself?
The classic liar paradox ('this sentence is false') relies on a single sentence pointing directly at itself. Now imagine an infinite list of sentences, where sentence 1 says 'every sentence below this one is false,' sentence 2 says the same about everything below it, and so on forever, with no sentence ever referring to itself or to anything above it. Can this list still produce a contradiction, even though nothing in it is self-referential?
Reveal the answer
Yes. Suppose any sentence on the list were true; then every sentence after it would have to be false, including ones that themselves claim everything below them is false, forcing a contradiction. Suppose instead that every sentence is false; then each one has correctly described the sentences below it, making it true after all. Philosopher Stephen Yablo published this puzzle in 1993 to show paradox can arise from an infinite chain of reference, without any single sentence looping back on itself.
— Stephen Yablo, Paradox Without Self-Reference — Analysis, 1993