Renard's paradox

Renard's paradox illustrates a logical inconsistency when trying to define the concept of "truth" based solely on its linguistic or logical properties. It involves a statement that claims, "This statement is unprovable," creating a paradox similar to the famous Liar Paradox. If the statement is true, then it is indeed unprovable, which aligns with its claim. But if it's false, then it must be provable, contradicting its assertion. This paradox highlights limits in certain formal systems and shows that some statements about provability or truth cannot be definitively resolved within those systems, revealing complexities in understanding self-reference and formal logic.