Just as we can describe ‘likes’ as a predicate satisfied by ordered pairs \(\langle x, y \rangle\) such that \(x\) likes \(y\), so we can think about ‘every’ as a predicate satisfied by ordered pairs \(\langle X, Y \rangle\) such that the extension of \(X\) includes the extension of \(Y\). (This is compatible with thinking about ‘every boy’ as a restricted quantifier that combines with a predicate to form a sentence that is true iff every boy satisfies that predicate.) One virtue of this notatio