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    The Principle of Indifference leads to contradictory resu... — Carmelics
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    Home/Skepticism
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    The Principle of Indifference leads to contradictory results when the partition in question is not held fixed.

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    1 reason against

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 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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    Reasons Against

    1 perspective
    Reason against
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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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    Topics

    SkepticismTruth & Knowledge

    Related

    A principle generating logically incompatible probability values for identical p...Bertrand's paradox demonstrates that continuous variables yield incompatible uni...If Sophia is ignorant about the color of a marble, the Principle of Indifference...If resolving contradiction requires supplementing indifference with external con...
    +6 moreShow less
    If the Principle of Indifference were partition-invariant, Bertrand's chord prob...Jaynes acknowledged that invariance under transformation groups must constrain p...These two applications of the Principle of Indifference yield conflicting probab...Under a partition of many colors, Sophia must assign low probability to Blue, ma...Yet under a binary partition of Blue vs. not-Blue, Sophia must assign probabilit...van Fraassen's cube factory problem shows that applying indifference to side-len...

    Similar

    The Principle of Indifference requires uniform distribution but produc...86%These two applications of the Principle of Indifference yield conflict...83%The Fraenkel-Mostowski construction produces a Henkin (set-theoretic) ...76%The Thesis and Antithesis cannot both be true of a completed or comple...74%

    Source

    AI-extracted1/3 agreementValid
    SEP: formal-belief
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    Subjective probability theory models ignorance with respect to a proposition \(A\) by assigning probability of .5 to \(A\) and its complement \(\neg A\). More generally, an agent with subjective probability Pr is said to be ignorant with respect to the partition \(\{A_{1},\ldots,A_{n}\}\) if and only if \(\Pr(A_{i}) = 1/n\). The Principle of Indifference requires a doxastic agent to distribute her subjective probabilities in this fashion whenever, roughly, the agent lacks evidence of the relevan
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit