Curry's Paradox
Consider the sentence: 'If this sentence is true, then Germany borders China.' Assume for a moment that the sentence is true. Then, by what it says, its own truth lets you conclude Germany borders China. Using only ordinary rules of logical deduction, can you really prove an absurd, unrelated claim just from a sentence that refers to itself?
Reveal the answer
Yes — and that's the unsettling part. Because the sentence's truth implies the consequent whenever the antecedent (the sentence's own truth) holds, and you can independently show the antecedent must hold, standard logical rules let you detach the consequent and 'prove' Germany borders China, or absolutely anything else substituted in. Logician Haskell Curry described the paradox in 1942; unlike the classic Liar Paradox, it doesn't even need negation to break a naive logical system, part of why it's considered a much deeper problem for formal logic and set theory than it first appears.
— Haskell Curry, The Inconsistency of Certain Formal Logics — The Journal of Symbolic Logic, 1942