The deep metaphysics of quantum gravity: The seventeenth century legacy and an alternative ontology beyond substantivalism and relationism

• A new and more successful analysis of space and spacetime theories is offered.
• Analogies among seventeenth century and quantum gravity theories are now fruitful.
• Geometric structures at the fundamental and emergent levels are now incorporated.
• Platonism and nominalism are more accurate than substantivalism and relationism.
• Mathematics and ontology aren't conflated as under substantivalism and relationism.

This essay presents an alternative to contemporary substantivalist and relationist interpretations of quantum gravity hypotheses by means of an historical comparison with the ontology of space in the seventeenth century. Utilizing differences in the spatial geometry between the foundational theory and the theory derived from the foundational, in conjunction with nominalism and platonism, it will be argued that there are crucial similarities between seventeenth century and contemporary theories of space, and that these similarities reveal a host of underlying conceptual issues that the substantival/relational dichotomy fails to distinguish.