 Section ∗10 formulates quantificational logic as it is currently formulated, namely the axioms and theorems of propositional logic are assumed to hold for all formulas, and not just the elementary propositions of ∗1–5. It appears that Russell became concerned about this assumption, and so a new section ∗9 was introduced to derive the principles of quantification theory from elementary propositions alone. While of interest to scholars of PM, the upshot is the same for later uses of quantificational logic in PM.