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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 Any inductive logic that employs the same probability functions to represent both the probabilities of evidence claims due to hypotheses and the probabilities of hypotheses due to evidence claims must be a Bayesian inductive logic.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Probability functions satisfying Kolmogorov's axioms can be interpreted frequentistically, propensity-wise, or logically without any prior probability assignments over hypotheses.
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    • 2.Bayesian inductive logic is constitutively defined by the use of prior probabilities over hypotheses updated via conditionalization, not merely by application of Bayes' theorem.
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    • 3.Using Bayes' theorem as a mathematical identity does not entail the epistemic commitments—priors, conditionalization, coherence—that define Bayesian inference as a normative framework.
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    Reason for 2 of 2
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    • 1.Halpern and colleagues have shown that probability-like functions satisfying weaker axiom sets (e.g., Dempster-Shafer belief functions) can coherently relate evidential support in both directions without collapsing into classical probability.
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    • 2.If non-Bayesian formalisms can represent both likelihoods and posterior-like degrees of support using the same formal apparatus, the alleged entailment from shared probability functions to Bayesianism is not logically necessary.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Bayes' theorem follows directly from the axioms that any probability function must satisfy.
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    • 2.Bayes' theorem expresses a necessary connection between the probabilities of evidence claims due to hypotheses and the probabilities of hypotheses due to those evidence claims.
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    • 3.An inductive logic using the same probability functions for both directions of inference necessarily invokes that necessary connection.
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