 Principia does not analyze relations (or mathematical functions) in terms of sets of ordered pairs, but rather takes the notion of propositional function as primitive and defines relations and functions in terms of them. The upper case letters \({R}, {S}\) and \({T}\), etc., are used after ∗21 to stand for these “relations in extension”, and are distinguished from propositional functions by being written between the arguments. Thus it is \(\psi(x,y)\) with arguments after the propositional function symbol, but \(xRy\). From ∗21 functions “\(\phi\) and \(\psi\)”, etc., disappear and only relations in extension, \({R}\), \({S}\) and \({T}\), etc., appear in the pages of  Principia. While propositional functions might be “intensional”, that is two functions may be true of the same objects yet not be identical, no distinct relations in extension are true of all the same objects. The logic of Principia is thus “extensional”, from page 200 in volume I, through to the end in Volume III. 