ABSTRACT
There was a revolution within mathematics that maintained that mathematicians are studying relational structures when they do mathematics. Whitehead and Russell’s Principia Mathematica was intended to be its flagship—with an agenda to free every branch of mathematics (including the Euclidean and non-Euclidian geometries) from the indispensability arguments of metaphysicians that impose abstract particulars (numbers, sets/classes, triangles, points, lines, and planes, etc.) onto its branches. In this very important respect, the logicism of Principia was quite antithetical to the logicism of Frege, who never doubted that numbers are abstract particulars ("objects" in his technical sense). It is time for a Principia revival—and in hope of kindling such a movement, I offer a Principia Redux.
