Why did the liar paradox remain difficult for logical theories of truth until the 20th century?

The liar paradox, which centers on self-referential statements like "This sentence is false," remained a significant challenge for logical theories of truth until the 20th century because it exposed the dangers of unrestricted self-reference within formal systems.123

Early logicians struggled to develop systems of mathematical reasoning that could avoid such paradoxes without inadvertently rendering legitimate proof procedures impossible. The core difficulty lay in the lack of a generally agreed-upon principle to distinguish between "good" self-reference and "bad" self-reference.3

This issue was addressed in the 20th century, most notably by Alfred Tarski, who demonstrated that a language cannot consistently contain a complete semantic theory of its own sentences. Tarski resolved this by distinguishing between an object language—the language being analyzed—and a metalanguage—the language used to describe the truth conditions of the object language. By separating these levels, Tarski provided a framework to define truth for formal languages without falling into the circularity of the liar paradox.13