Colin Hamlin

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. This yields the Universal Theory of Structure (UTS), providing a fundamental ontology of structures for both mathematical and physical reality. The theory refines OSR’s fundamentality thesis from the vague “physical reality is structural” to the metaphysically substantive “physical reality is an ante rem structure,” thereby strengthening responses to criticisms concerning representation, objecthood, and causation. The UTS also illuminates important foundational problems concerning the applicability of mathematics, the particular form of our universe, and the nature of existence. I conclude that the theory’s unifying and explanatory virtues support an inference to the best explanation.

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. This yields the Universal Theory of Structure (UTS), providing a fundamental ontology of structures for both mathematical and physical reality. The theory refines OSR’s fundamentality thesis from the vague “physical reality is structural” to the metaphysically substantive “physical reality is an ante rem structure,” thereby strengthening responses to criticisms concerning representation, objecthood, and causation. The UTS also illuminates important foundational problems concerning the applicability of mathematics, the particular form of our universe, and the nature of existence. I conclude that the theory’s unifying and explanatory virtues support an inference to the best explanation.

The maturation of the physical image has made apparent the limits of our scientific understanding of fundamental reality. These limitations serve as motivation for a new form of metaphysical inquiry that restricts itself to broadly scientific methods. Contributing towards this goal we combine the mathematical universe hypothesis as developed by Max Tegmark with the axioms of Stewart Shapiro’s structure theory. The result is a theory we call the Theory of the Structural Multiverse (TSM). The focus is on informal theory development and constraint satisfaction. Some empirical consequences of the theory are worked out, in particular the feasibility of a predictive observer selection effect. The explanatory, unifying, and generative powers of the theory are found to substantially support the theory. The TSM is demonstrated to be an empirically significant scientific theory that is foundational to and continuous with the rest of the scientific image.