The “Liar’s Paradox” of the ancient Cretan philosopher Epimenidis led to two major breakthroughs about the limitation of “mechanistic” systems such as Logic (Gödel) and Computation (Turing). We explore here both and see in particular how the connection with computation tells us that many problems will never receive a computational solution. Some such are of high practical interest, e.g., the problem of checking the correctness of a computer program.