 The earliest modern paradoxes concerned the notions of ordinal and cardinal number. Burali-Forti, a mathematician of Peano’s school, attempted to prove that the ordinal numbers are not linearly ordered. Assuming by contradiction that the class \(\mathbf{ON}\) of all ordinals could be linearly ordered, he observed that then \(\mathbf{ON}\) itself would be well-ordered and it would possess an ordinal \(\Omega \in \mathbf{ON}\). Thus \(\mathbf{ON}\) would be similar (order-isomorphic) to a proper initial segment of itself, the one determined by \(\Omega\), contradicting a well-known theorem about well-ordered sets. The result was published in 1897 and, though Burali-Forti’s original aim is impossible to achieve, his argument showed that the collection \(\mathbf{ON}\) is problematic at best (Moore-Garciadiego 1981).