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    Carmelics

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

    It is not the case that Therefore the conflict between regularity and uncountable sample spaces is an artifact of restricting probability values to the reals, not a necessary feature of probability theory.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Non-real probability values lack empirical interpretation; experiments yield finite frequencies, which require real-valued comparison.
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    • 2.Regularity itself may be the problematic assumption for uncountable spaces, not the real-number restriction masking a deeper issue.
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    • 3.Abandoning reals introduces computational and philosophical burdens without resolving which alternative system probability *should* use.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Hyperreal and surreal number systems coherently extend probability theory while preserving regularity and handling uncountable spaces.
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    • 2.Measure-theoretic probability already abandons countable additivity for uncountable cases; non-real extensions are a natural next step.
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    • 3.The conflict arises from imposing real-number constraints, not from probability's fundamental structure or interpretive foundations.
      ?

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