 The theory of types in the initial chapters of PM is ramified, so that within a given type, of propositions, or of functions of individuals, and functions of functions of individuals, there will be finer subdivisions. This ramification is necessary for the application of the logic of PM to what what are called “epistemological” paradoxes in the Introduction to PM. The most prominent of these is the (propositional) Liar paradox created by the proposition that all propositions of a certain sort, say asserted by Epimenides, are false, when that very proposition is of that sort, that is the only proposition that Epimenides asserted. The solution in the ramified theory of types requires that a proposition about a sort of first level propositions, say that they are all false, will itself be of the next order.