 What follows in PM up to ∗12 is a presentation of quantificational logic in the ramified theory of types. The complications are due to the decision of the authors (surely on Russell’s insistence) to add a new section ∗9 which allows the earlier theory of propositional logic to be incorporated directly into a quantificational logic as is done in contemporary logic. This shows the extent to which the earlier theory is indeed a theory of propositions, not an account of a fragment of quantificational logic allowing open sentences containing free variables.