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    The inductive logic of probabilistic support functions sa... — Carmelics
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    The inductive logic of probabilistic support functions satisfies the Criterion of Adequacy (CoA).

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

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    • 1.The Criterion of Adequacy requires that a probabilistic inductive logic converge on the true hypothesis and away from false ones as evidence accumulates.
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    • 2.The Likelihood Ratio Convergence Theorem establishes that posterior probabilities of false competitors converge to 0 and posterior probability of the true hypothesis converges to 1.
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    Reasons Against

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    Reason against 1 of 2
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    • 1.The Likelihood Ratio Convergence Theorem assumes the true hypothesis has non-zero prior probability, but Bayesian priors are assigned before evidence.
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    • 2.If a prior probability of zero is assigned to the true hypothesis—as can occur with infinitely many competitors—convergence to truth is mathematically impossible.
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    • 3.Therefore, CoA satisfaction is conditional on prior assignment practices that the probabilistic framework itself cannot justify without circularity.
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    Reason against 2 of 2
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    • 1.Kuhn and Feyerabend demonstrate that hypothesis spaces are theory-laden, meaning what counts as a 'competitor' shifts across paradigms.
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    • 2.The Likelihood Ratio Convergence Theorem presupposes a fixed, well-defined hypothesis space that persists through evidential accumulation.
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    • 3.Because revolutionary science replaces rather than refines hypothesis spaces, convergence results apply only within paradigms, not to the scientific enterprise CoA is meant to vindicate.
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    Related

    Because revolutionary science replaces rather than refines hypothesis spaces, co...If a prior probability of zero is assigned to the true hypothesis—as can occur w...Kuhn and Feyerabend demonstrate that hypothesis spaces are theory-laden, meaning...The Criterion of Adequacy requires that a probabilistic inductive logic converge...
    +4 moreShow less
    The Likelihood Ratio Convergence Theorem assumes the true hypothesis has non-zer...The Likelihood Ratio Convergence Theorem establishes that posterior probabilitie...The Likelihood Ratio Convergence Theorem presupposes a fixed, well-defined hypot...Therefore, CoA satisfaction is conditional on prior assignment practices that th...

    Similar

    Any inductive logic that employs the same probability functions to rep...83%The Criterion of Adequacy requires that a probabilistic inductive logi...82%An inductive logic using the same probability functions for both direc...78%Convergent inductive evidence supports P ≠ NP77%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-inductive
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    The theorem itself does not require the full apparatus of Bayesian probability functions. It draws only on likelihoods. Neither the statement of the theorem nor its proof employ prior probabilities of any kind. So even likelihoodists, who eschew the use of Bayesian prior probabilities, may embrace this result. Given the forms of Bayes’ Theorem, 9*-11 from the previous section, the Likelihood Ratio Convergence Theorem further implies the likely convergence to 0 of the posterior probabilities of f
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    Validity: Extracted via Max plan + API grounding/validity checks

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