Poincaré's conventionalism and Helmholtz's empirical geometry each supply frameworks where structural principles organize experience without reducing to either idealism or naive phenomenalism.

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Empirical geometry(as a theory of how we know geometry): The view that the rules of geometry (like whether parallel lines can meet) come from observing and experiencing the physical world, not from pure logical thinking alone.
Helmholtz, Hermann von(Credited with demonstrating what truly determines geometric properties): A 19th-century German physician and physicist who studied vision, perception, and the nature of space, and argued that geometry depends on physical properties of how objects can move.
Naive phenomenalism(as a theory of perception and reality): A simple or uncritical version of phenomenalism that assumes our immediate sensory experiences directly show us all of reality without any hidden structure.
Poincaré, Henri(as used in philosophy of mathematics and geometry): A famous French mathematician and philosopher (1854-1912) who argued that the rules of geometry are human conventions we choose, not absolute truths about the world.

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