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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Leibniz equivalence, which dissolves hole-type indeterminism by identifying diffeomorphic models, is compatible with retaining the manifold-metric distinction.

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    Reasons For

    1 perspective
    Reason for
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    • 1.If manifold and metric are truly distinct, diffeomorphisms that preserve metric structure may not preserve all physically meaningful properties of the manifold.
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    • 2.Leibniz equivalence assumes observational indistinguishability entails metaphysical identity, but this conflates epistemology with ontology illegitimately.
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    • 3.Retaining the manifold-metric distinction while eliminating diffeomorphic models creates tension: one entity (manifold) seems underdetermined by physics independently.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Diffeomorphic models represent identical physical possibilities, so identifying them preserves empirical content while eliminating spurious indeterminism.
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    • 2.The manifold provides the topological structure needed for physics; the metric encodes physical geometry. These are conceptually distinct but jointly necessary.
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    • 3.Leibniz equivalence respects the principle that unobservable differences shouldn't multiply ontological commitments or generate determinism failures.
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