The 'Space' at the Intersection of Platonism and Nominalism

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it also assists in critiquing alternative uses of nominalism (Field, Arntzenius), platonism (Psillos), and both ontic and epistemic structural realism (French).