statement of a liar who states that they are lying: for instance, declaring that "I am lying" or "everything I say is false"
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.
Assume that "this sentence is false" is true, then we can trust its content, which states the opposite and thus causes a contradiction. Similarly, we get a contradiction when we assume the opposite.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).