In The Principles of Mathematics, published in 1903, Bertrand Russell (1872–1970) set out to establish the logicist view that "all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of logical principles" (2nd ed., p. xv) and also to explain "the fundamental concepts which mathematics accepts as indefinable" (ibid.). In the Principles this program is pursued with minimal recourse to symbolism, the systematic formal presentation being reserved for a proposed second volume. What in fact appeared as the sequel was the classic Principia Mathematica (3 vols., Cambridge, U.K., 1910–1913), written in collaboration with Alfred North Whitehead. The subject matter of Principia Mathematica considerably overlaps that covered by Frege in his Grundgesetze der Arithmetik, a work to which the authors acknowledge their chief debt on questions of...