sentences:  Kleene, however, parenthetically observes that "the logicistic definition of natural number now becomes predicative when the [property] P in it is specified to range only over properties of a given order; in [this] case the property of being a natural number is of the next higher order".But this separation into orders makes it impossible to construct the familiar analysis, which [see Kleene's example at Impredicativity] contains impredicative definitions.To escape this outcome, Russell postulated his "axiom of reducibility".