The Nature of Paradox

If you ask most modern logicians why there can be no true contradictions, they will probably tell you that everything follows logically from a contradiction, so if even one contradiction were true, everything would be true. Clearly, everything is too much! … But the fact that it is rational to accept some contradictions does not mean that it is rational to accept any contradiction. If the principle of noncontradiction fails, then contradictions cannot be ruled out by logic alone. But many things cannot be ruled out by logic alone, though it would be quite irrational to believe them.