Universal nature of structure.

Ontic Structural Realism (OSR) holds that structure is ontologically fundamental, yet it lacks a precise metaphysical account of structure. Returning to the insight that originally motivated structural realism, I develop a new basis for OSR grounded in the metaphysical foundations of mathematics. This approach draws on the principles of ante rem structuralism and their formal axiomatizations to define Structure Theory (ST), the view that structures exist sui generis and constitute the subject matter of mathematics. ST compels OSR to confront its “collapse problem” of distinguishing physical from mathematical structure. I argue for embracing the collapse by adopting the Mathematical Universe Hypothesis (MUH), which identifies our physical universe as an ante rem structure.