Original sentence: "A definition may very well rely upon notions that are equivalent to the one being defined; indeed in every definition definiens and definiendum are equivalent notions, and the strict observance of Poincaré's demand whould make every definition, hence all of science, impossible."According to Poincaré (1906, p.307) a definition is "predicative" and logically admissible only if it excludes all objects that are "dependent" upon the notion defined, that is, that can in any way be determined by it".A detailed analysis of the failure of the Russell theory of types, Russell's attempt to skirt the issue with a ramified theory of types, and the axiom of reducibility can be found in W.Modern mathematicians agree with Zermelo (indeed Kleene 1952 presents a few examples similar to Zermelo's).Quine's commentary before Russell's 1908 in van Heijenoort 1967:150-152.Such a prohibition was roundly criticised by Zermelo 1908, stung as he was by a similar demand coming from Poincaré:.Zermelo countered: