  The later portions of PM should thus be studied for a hint of how the real numbers and the use of mathematics in measurement can be developed with this rival foundation on the theory of relations. Gandon (2008, 2012) argues that the the application of mathematics is better explained using this logicist account than by rivals.    In ∗300–∗314, positive and negative integers, ratios and real numbers all defined. The goal of the section is to begin the study of how these numbers are used in the measurement of quantities in geometry and physics.