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The Liar Paradox
A statement that contradicts itself.
Consider the following simple sentence: 'This statement is false.' Is the sentence true or false? If it's true, then what it says must be correct, which means it must be false. But if it's false, then it's not a false statement, which must make it true.
What philosophers say
This self-referential paradox has fascinated logicians for centuries. There's no easy solution. Some, like Alfred Tarski, proposed that 'true' and 'false' must operate in different language levels to avoid this loop. You can't use a language to assess the truth of its own sentences. The paradox reveals deep issues in logic and language about how truth works.