 As to the proposed solutions of the paradoxes, Hessenberg was inspired by a Kantian idea. Just as in the natural sciences antinomies arise if Nature is conceived as a closed whole, similarly the collection \(\mathbf{ON}\) and the set of all sets cannot be conceived as completed totalities. Hence the distinction ‘ultrafinite’/‘transfinite’ is apparently in accord with a theoretical approach which is close to Russell’s limitation of size doctrine.