 On the other hand, in Mirimanoff’s 1917a there is a remarkable use of Burali-Forti’s paradox which suggests a necessary condition for set-hood in terms of size, viz., if a collection is in bijection with the set of all ordinals, then it does not exist as a set. In Mirimanoff 1917a,b, one can also find the idea of von Neumann ordinal (von Neumann 1923, 1925) and a form of the replacement axiom is present.