 For the history of paradoxes, it is important to emphasize that Mirimanoff 1917a gave a generalization of the Burali-Forti antinomy, the paradox of grounded sets. This paradox actually proves that the collection \(\mathbf{W}\mathbf{F}\) of ordinary sets (on a given set of atoms) is not itself a set. Indeed, let \(\mathbf{W}\mathbf{F}\) be the set of grounded (= ordinary = wellfounded) sets; then \(\mathbf{W}\mathbf{F}\) itself is grounded, for were \(\mathbf{W}\mathbf{F} \ni x_0 \ni x_1 \ni x_2\ldots\), then \(x_0\) would be an ungrounded member of \(\mathbf{W}\mathbf{F}\), which is absurd. Hence \(\mathbf{W}\mathbf{F} \in \mathbf{W}\mathbf{F}\), so \(\mathbf{W}\mathbf{F}\) is ungrounded, contradiction (the same paradox will also appear in Shen-Yuting 1953).