Most of classical physics needs classical (not constructionist) mathematics, because it deals with emergent layers of description (like classical mechanics or GR) that are often not computable. But foundational physics must break with this and be constructionist, I think.
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hmm... sure there don't exist "sufficient constraints" to allow measurers of superpositions to deliver inconsistent possible results to comparers of their outputs, but that is true in QM too: consistency of measurement is what allows outcomes to be associated with universes.
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What happens when you try to measure something that does not exist, like a position in spacetime when your universe is not in space but in a graph, and a particular location is underconstrained to be projected into 3space?
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