More commonly known as the Liar Paradox. Developed by Epimenides, the best and most basic version of it says, "This sentence is false." The paradox of it is, of course, that if it is true, it therefore must be false, and thus it negates its truth. If it is false, its falsehood affirms its truth.

It can be expanded by going

The following sentence is false.
The preceding sentence is true.

And then, of course, each sentence is harmless by itself or with another sentence coupled with it. However, when taken together, they produce a paradox. Therefore, there is no intrinsic fault with either sentence there, and so if you are looking to eliminate paradox from a system, one must consider not just individual statements, but also the relationship of statements to one another.

Kurt Gödel translated it to mathematics in the form of Gödel's incompleteness theorem.

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