 Russell succeeded in developing a theory that respects his principle, the ramified type theory. In Poincaré, we find nothing that is comparable, for he believed that the principle guarded against the definitional mistakes that he denounced. He did not seriously take up the question and only formulated successively different variants of the principle when he learned from Ernst Zermelo that the proof, proposed by Argand and Cauchy, of the fundamental theorem of algebra makes an appeal precisely to the rejected, non-predicative definitions. Hence, only when the measures taken against the logical antinomies affected “real mathematics” did he try to modify the principle. The discussion between Poincaré, Russell, Peano, and Zermelo on the measures to take lasted for six years. The difficulty consisted in the obligation to formulate a principle that is neither too restrictive for the important results in analysis, nor too liberal with respect to the formations of concept to be excluded by reason of Poincaré’s philosophical position. The absence of a truly convincing solution shows that the analysis of the concept of predicativity with the help of informal methods appeared to have reached its limits.