A New Taxonomy Beyond Substantivalism and Relationism I: Early Modern Spatial Ontologies

Abstract

This chapter will forge a new third-way taxonomy or classificational system for spatial ontologies based on the many themes, both historical and conceptual, that have been featured in our investigation. After an introduction to the limitations of the standard dichotomy in a quantum gravity setting (§9.1), the new classificational scheme will be developed (§9.2) and then applied to Newton, Leibniz, and a host of other natural philosophers from the sixteenth through eighteenth centuries (§9.3). Next, the lessons gathered from our analysis will be juxtaposed with rival assessments of spatial ontologies and employed to resolve various perplexities relating to seventeenth century theories (§9.4 and §9.5). The new taxonomy will then be applied, in Chap. 10, to the strategies proposed among competing quantum gravity hypotheses and to examine various issues, such as background independence and nominalism. All told, the new taxonomy will be demonstrated to be in harmony with the property theory of spatial ontology, whether of the P(O-dep) or P(TL-dep) type.