 However, the move from the importance of classical logic in mathematics to the truth of classical logic is much too fast. It is one thing to say that classical logic, including say, instances of the principles of Double Negation Elimination (DNE) and ex falso quodlibet (EFQ), are widely used in mathematics. But mathematics does not require any principles with the full strength and generality of classical logic’s (DNE) and (EFQ)—it only uses some of the instances of those principles, the instances that employ mathematical language. When we say that (DNE) and (LEM) are logically valid we are saying that they are valid no matter what expressions we substitute for the non-logical expressions in them—including extra-mathematical vague predicates like ‘heap’ or ‘red’ and notoriously troublesome metalinguistic predicates like ‘true’ and ‘heterological’.