Abstract

The central aim of this dissertation is to clarify, defend and develop a realist field ontology of the causal-inertial structure of spacetime forcefully advanced by Hermann Weyl. Weyl's field ontology of spacetime structure may roughly be described as follows. The Special and General as well as the non-relativistic spacetime theories are principle theories of spacetime structure. They all postulate various structural constraints, and events within spacetime are held to satisfy these constraints. When interpreted physically, these mathematical structures correspond to physical structural fields on spacetime. ;The thesis begins with a discussion of the significance of Riemann's Dynamical Hypothesis within the context of the debate between geometrical realism and conventionalism. In particular, Grunbaum's unyielding insistence that Riemann's work must be seen as the immediate progenitor of his brand of geometrical conventionalism is challenged and shown to be unsupported by a textual analysis of the relevant works by Riemann. The first two chapters provide a historical/exegetical analysis of Riemann's Habilitationsvortrag. Chapter 3 presents a general account of geometrical conventionalism apart from issues of its alleged historical ancestry as seen by Grunbaum. This is followed by a critical examination of Grunbaum's interpretation of Riemann. ;Grunbaum has repeatedly argued that Weyl's interpretation of Riemann accords with his. It is shown, however, that Weyl's understanding of Riemann is the direct opposite of that of Grunbaum. Chapter 4 provides an examination of Weyl's philosophy of geometry and his interpretation of Riemann. It is shown that Weyl considers Riemann's work to be essentially progenitorial of his version of geometrical realism. . . . UMI.