 We know that Poincaré hoped to avoid the known antinomies by limiting himself to predicative definitions (see Heinzmann 1985). It was Russell who introduced the terms “predicative” and “non-predicative” to highlight the difference between two kinds of propositional functions, those that determine and those that do not determine a class. He called the first “predicative” and the second “non-predicative.” Poincaré attributed the mistake of non-predicative definitions to a vicious circle: a definition is “non-predicative” if the definiens contains or relates to a totality of which the definiendum is a part. He formulated a principle to avoid circularity, which leads directly to Russell’s famous vicious circle principle: