 Russell argued that such definitions involve a subtle kind of vicious circle. The definiens of the first definition invokes, Russell thought, the totality of all propositions, but the definition, if legitimate, would result in propositions that can only be defined by reference to this totality. Similarly, the second definition attempts to define the class \(\mathbf{N}\) by reference to all classes, which includes the class \(\mathbf{N}\) that is being defined. Russell maintained that such definitions are illegitimate. And he imposed the following requirement—called, the “Vicious-Circle Principle”—on definitions and concepts. (Henri Poincaré had also proposed a similar idea.)