 Kreisel (1967) has pointed out that second-order set theory in a sense decides the CH, i.e., decides whether it is true or not, even if we do not know which way the decision goes. More exactly \(\ZFC^2\models CH\) or \(\ZFC^2\models \neg CH\), because \(CH\) is true if and only if \(V_\kappa\models CH\) for inaccessible \(\kappa\), i.e., if and only if \(\ZFC^2\models CH\). Of course we can express CH in first order set theory, too, so the situation is not really different from first order set theory. Many set theorists think that the concept of set is definitive enough to decide eventually also CH even if ZFC does not decide it. Likewise, we may argue that the concept of second-order semantics is definitive enough to decide CH even if the current axioms of second-order logic cannot do it.