 The need for some sort of account of the logical features of matter, what he called “the problem of matter”, had already occupied Russell much earlier. While we distinguish the certain knowledge we may have of mathematical entities from the contingent knowledge of material objects, Russell says that there are certain “neat” features of matter that are just too tidy to have turned out by accident. Examples include the most general spatiotemporal properties of objects, that no two can occupy the same place at the same time, which he calls “impenetrability”, and so on. In The Principles of Mathematics (Russell 1903, §453) there is a list of these features of matter including “indestructibility”, “ingenerability” and “impenetrability”, which were all characteristic of the atomic theory of the day. Russell followed the progression through the exact sciences from logic through arithmetic, and then real numbers and then to infinite cardinals. There followed a discussion of space and time, with the book ending with a last part (VII) on Matter and Motion, chapters §53 to §59. In them Russell discusses what he calls “rational Dynamics as a branch of pure mathematics” (Russell 1903, §437). This rational Dynamics, would involve justifying many of the fundamental principles of physics with pure mathematics alone, from definitions that yield the geometry of space and time and the formal properties of its occupants, quantities of matter and energy. In this respect the construction of matter most resembles the construction of numbers as classes as an effort to replace the “theft” of postulating axioms with the “honest toil” of devising definitions that will validate those postulates. 