Abstract

This dissertation explores the reasons why structured graphics have been largely ignored in the representation and reasoning components of contemporary theories of axiomatic systems. In particular, it demonstrates that for the case of modern logic and geometry, there are systematic forces in the intellectual history of these disciplines which have driven the adoption of sentential representational styles over diagrammatic ones. These forces include: the changing views of the role of intuition in the procedures and formalisms of formal proof; the historical contrast between the universalist subject matter of logic and the specific subject matter of geometry; and the ways in which both logic and geometry were affected by the changes that swept through mathematics during the nineteenth century. This dissertation traces the effects of each of these influences in the evolution of logic and geometry from antiquity to the early twentieth-century work of David Hilbert. For each discipline, it examines the historical factors impacting the creation and development of important diagrammatic systems, the reasons for the adoption or abandonment of these systems, and the philosophical context and debates surrounding the use of these systems. It concludes by arguing that the history of diagrammatic representations in logic and geometry cannot be adequately understood without essential reference to their philosophical background