In the Principles, the quantifier ‘all’ is analyzed as a part of referring phrases that pick out classes (1903, 72). This, we can see, is a hold-over from the 19th Century extensional logicians (see Section 1). But in slightly later works, such as ‘On Denoting’ (1905), propositional functions are said to be constituents of universal propositions. According to this analysis the proposition expressed by sentences such as ‘All dogs bark’ is made up of the propositional function x is a dog ⊃ x barks and a function (of propositional functions) that is represented by the quantifier phrase ‘all’. Quantified propositions are interesting for us because they contain propositional functions as constituents.