 The propositional function \(x\) is self-identical maps the Moon to the true proposition that the Moon is self-identical, it maps the Sun to the true proposition that the Sun is self-identical, etc. The thrust of (5) is the proposition that no matter what object we supply as argument, the propositional function \(x\) is self-identical will map it into a true proposition. The only salient difference between Frege and Russell’s account of quantification lies in the choice of concepts and propositional functions, respectively, as the objects of predication; while Frege takes each quantifier to correspond broadly to a second-level concept, Russell analyzes them in terms of certain properties of propositional functions.