Russell discovered his paradox while writing The Principles of Mathematics. When this book appeared in 1903, it contained a discussion of his paradox but no more than a sketch of a solution. He then began to work on a second volume, in which the formal development of mathematics from logic was to be presented. When it eventually appeared almost ten years later, this second volume had metamorphosed into a separate three-volume work called Principia Mathematica, which was intended to provide the complete logical derivation promised in the Principles of the foundations, not just of arithmetic, but of the whole of pure mathematics. The programme Russell was engaged in was thus in a sense a direct continuation of Frege's: his task was to repair the error in Frege's system and hence establish the logicist thesis.
Keywords: Principia Mathematica, theory of denoting, substitutional theory, propositional paradox, Frege, mathematical logic, propositional functions, reducibility