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    Regularity is only violated when undefined singletons are... — Carmelics
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    Challenges→Countably additive Kolmogorovian probability distributions must violate regularity when the sample space is uncountable

    Regularity is only violated when undefined singletons are illicitly treated as measurable events requiring positive probability assignment.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Regularity requires positive probability only for well-defined measurable events in sigma-algebras.
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    • 2.Undefined singletons lack the mathematical structure needed for coherent probability assignment.
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    • 3.Treating unmeasurable sets as probability-bearing prevents inconsistency in probability spaces.
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    Reasons Against

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    Reason against
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    • 1.Regularity's violation stems from logical properties of measure theory, not singleton definition status.
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    • 2.The claim conflates epistemological clarity with mathematical regularity, which are distinct problems.
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    • 3.Non-regular measures exist on well-defined spaces; the issue isn't undefined singletons per se.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Countably additive Kolmogorovian probability distributions must violate regulari...Non-regular measures exist on well-defined spaces; the issue isn't undefined sin...Regularity requires positive probability only for well-defined measurable events...Regularity's violation stems from logical properties of measure theory, not sing...
    +3 moreShow less
    The claim conflates epistemological clarity with mathematical regularity, which ...Treating unmeasurable sets as probability-bearing prevents inconsistency in prob...Undefined singletons lack the mathematical structure needed for coherent probabi...

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    claim
    Perspectives
    2 (1 for, 1 against)
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