ABSTRACT
This chapter examines Whitehead's ideas about mathematics both from a general, pedagogical perspective and more specifically as an instrument of philosophical investigation. It involves some direct application of these ideas as it examines the role of one particular thread of mathematical/relational thinking as a "bridge" between logic, broadly construed, and metaphysics. The three mathematical ideas he describes are congruence, similarity, and the relations of trigonometry. It is important to understand that the algebraic approach to problems—whether in the direct application to mathematics or as an analogical technique in other areas—is particularly relational. Rather than speaking directly to the issue of spatial reasoning and metaphysics, the authors want to close this chapter with a few words on ontology. Clearly metaphysics and ontology are related; the authors tend to view the connection as one between relational structures (metaphysics) and their various relata (ontology).
