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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The Principle of Indifference leads to contradictory results when the partition in question is not held fixed.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.If Sophia is ignorant about the color of a marble, the Principle of Indifference requires her to assign equal probability to each color in the partition.
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    • 2.Under a partition of many colors, Sophia must assign low probability to Blue, making her nearly certain the marble is not Blue.
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    • 3.Yet under a binary partition of Blue vs. not-Blue, Sophia must assign probability 0.5 to Blue.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Bertrand's paradox demonstrates that continuous variables yield incompatible uniform distributions depending on geometric parameterization chosen.
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    • 2.If the Principle of Indifference were partition-invariant, Bertrand's chord problem would produce a unique probability, but it yields 1/2, 1/3, and 1/4 simultaneously.
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    • 3.A principle generating logically incompatible probability values for identical physical setups cannot be epistemically coherent.
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    Reason against 2 of 2
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    • 1.van Fraassen's cube factory problem shows that applying indifference to side-length, volume, and surface-area partitions yields mutually inconsistent priors over the same state space.
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    • 2.Jaynes acknowledged that invariance under transformation groups must constrain prior selection, implicitly conceding that indifference alone underdetermines the correct partition.
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    • 3.If resolving contradiction requires supplementing indifference with external constraints, then indifference by itself is insufficient and partition-dependence constitutes a genuine internal failure.
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