 Despite such concerns, PM proved to be remarkably influential in at least three ways. First, it popularized modern mathematical logic to an extent undreamt of by its authors. By using a notation more accessible than that used by Frege, Whitehead, and Russell managed to convey the remarkable expressive power of modern predicate logic in a way that previous writers had been unable to achieve. Second, by exhibiting so clearly the deductive power of the new logic, Whitehead and Russell were able to show how powerful the idea of a modern formal system could be, thus opening up new work in what soon was to be called metalogic. Third, Principia Mathematica re-affirmed clear and interesting connections between logicism and two of the main branches of traditional philosophy, namely  metaphysics   and epistemology, thereby initiating new and interesting work in both of these areas.