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    The Likelihood Ratio Convergence Theorem presupposes a fi... — Carmelics
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    Part of a larger discussion

    Challenges→The inductive logic of probabilistic support functions satisfies the Criterion of Adequacy (CoA).

    The Likelihood Ratio Convergence Theorem presupposes a fixed, well-defined hypothesis space that persists through evidential accumulation.

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    Reasons For

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    Reason for
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    • 1.The theorem's mathematical proof requires hypothesis space to remain constant; changing it mid-analysis invalidates the convergence guarantee.
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    • 2.Scientific practice often treats hypothesis spaces as fixed within experimental design to ensure rational belief updating.
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    • 3.Without a stable space, we cannot distinguish between evidence against a hypothesis and evidence that requires reformulating hypotheses entirely.
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    Reasons Against

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    Reason against
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    • 1.Real inquiry involves discovering new hypothesis classes (paradigm shifts, novel frameworks) that weren't in the original space.
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    • 2.The theorem assumes idealized conditions rarely met in practice; actual evidence often suggests the hypothesis space itself was incomplete or misconstrued.
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    • 3.Requiring fixed hypothesis spaces privileges whatever initial space was proposed, potentially excluding better-framed alternatives discovered later.
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    Related

    Real inquiry involves discovering new hypothesis classes (paradigm shifts, novel...Requiring fixed hypothesis spaces privileges whatever initial space was proposed...Scientific practice often treats hypothesis spaces as fixed within experimental ...The inductive logic of probabilistic support functions satisfies the Criterion o...
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    The theorem assumes idealized conditions rarely met in practice; actual evidence...The theorem's mathematical proof requires hypothesis space to remain constant; c...Without a stable space, we cannot distinguish between evidence against a hypothe...

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    claim
    Perspectives
    2 (1 for, 1 against)
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