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Keith Elliott Peterson (Dec 11 2025 at 20:46):What is the role of mathematics in informing metaphysics? And what is the role of metaphysics in informing mathematics?
John Onstead (Dec 16 2025 at 21:46):The relation between math and metaphysics is probably similar, if less explored, compared to the relation between math and physics. There, math informs physics by allowing us to construct mathematical models of physical systems we can make empirical predictions from, and physics informs math by inspiring new mathematical definitions and axioms. For instance, Euclid's axioms were inspired by his observations of the world, and more recently there's been many new fields of interest opening in higher geometry inspired by string theory.
John Onstead (Dec 16 2025 at 21:46):For math and metaphysics, math might inform metaphysics by allowing us to construct logical models of the metaphysics that we can draw constrained logical deductions from, and metaphysics might inform math also by inspiring new mathematical points of view. For instance, a metaphysical theory about how the world is composed (a theory of compositionality) might lead one to adopting a certain set of set theoretic axioms that most correlate with that worldview.
Jonathan Beardsley (Jan 06 2026 at 04:40):Badiou's work is potentially relevant. He has a rather set-theoretic point of view on ontology https://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_ontology