Oracular philosophy contented neither Russell nor Ramsey. “The philosopher must drag beliefs into the light of day,” Russell once wrote, “and see whether they still survive. Often it will be found that they die on exposure.” The Tractatus promises solutions for the problems of philosophy. It is a disappointment that it offers only programmatic gestures toward solutions. It was left to Russell in the 1925 second edition of Principia and Ramsey in “The Foundations of Mathematics” (1925) and “Mathematical Logic” (1926) to develop and assess the viability of some of Wittgenstein's ideas for rectifying Principia.

To evaluate Wittgenstein's idea that Reducibility would not be needed in a system in which there has been a complete analysis and reconceptualization of all nonextensional contexts, Principia's second edition offers a new introduction and three new appendices A, B, and C. The new introduction and appendixes of the second edition were written by Russell alone. Whitehead resoundingly disowned the new introduction, publishing a note in Mind that Russell alone was responsible for it. Interpretations typically portray Russell's new introduction as abandoning the system of the first edition and endorsing Wittgenstein's Tractarian ideas. For example, Monk writes: