 König also observed that the argument extends to the second number class and a similar paradox could be obtained by considering the collection \(\mathbf{FOD}\) of finitely definable countable ordinals. In this case, taking inspiration from Cantor, König’s solution is that Cantor’s second number class is not a set in a proper sense (a completed totality). To define a set, according to König, one should provide not only a rule for defining its elements, but also a means for distinguishing them.