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    Jaynes acknowledged that invariance under transformation ... — Carmelics
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    Supports→The Principle of Indifference leads to contradictory results when the partition in question is not held fixed.

    Jaynes acknowledged that invariance under transformation groups must constrain prior selection, implicitly conceding that indifference alone underdetermines the correct partition.

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    1 reason for
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    Reasons For

    1 perspective
    Reason for
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    • 1.Pure indifference priors produce contradictions under reparameterization (e.g., uniform on θ vs uniform on θ²), proving logical inconsistency.
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    • 2.Transformation group invariance provides objective mathematical constraints that resolve partition ambiguity without arbitrary choices.
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    • 3.Jaynes's maximum entropy principle itself relies on invariance properties, so acknowledging this dependence is logically consistent.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Transformation groups themselves require prior selection—choosing which group to use reintroduces the underdetermination problem at a higher level.
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    • 2.Jaynes never fully conceded indifference alone fails; he argued proper application requires understanding the physical problem structure first.
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    • 3.Invariance constraints may eliminate some priors but don't uniquely determine a single prior, leaving substantive underdetermination unresolved.
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    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

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    Related

    Invariance constraints may eliminate some priors but don't uniquely determine a ...Jaynes never fully conceded indifference alone fails; he argued proper applicati...Jaynes's maximum entropy principle itself relies on invariance properties, so ac...Pure indifference priors produce contradictions under reparameterization (e.g., ...
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    The Principle of Indifference leads to contradictory results when the partition ...Transformation group invariance provides objective mathematical constraints that...

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    Transformation groups themselves require prior selection—choosing which group to...