 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 notational scheme is that it lets us represent relations between predicates that cannot be captured with ‘\(\forall\)’, ‘\(\exists\)’, and the sentential connectives; see Rescher (1962), Wiggins (1980). For example, most boys sang iff the boys who sang outnumber the boys who did not sing. So we can say that ‘most’ indicates a function that maps \(\langle X, Y \rangle\) to T iff the number of things that both \(Y\) and \(X\) map to T exceeds the number of things that \(Y\) but not \(X\) maps to T.