Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    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 In continuous distributions, the probability of any event can be computed via integration of a probability density function

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Vitali sets and other non-measurable subsets of the real line cannot be assigned consistent probability values via Lebesgue integration.
      ?

      Think about whether this reason is strong or weak

    • 2.Any probability space over a continuous domain must exclude legitimate subsets, making 'any event' computability via integration demonstrably false under ZFC.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.De Finetti's constructivist approach shows that probability density functions presuppose a prior measure, making the claim circular for foundational purposes.
      ?

      Think about whether this reason is strong or weak

    • 2.Without an independently justified reference measure, the choice of density function is arbitrary, undermining the claim that probabilities are computed rather than stipulated.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.In common continuous distributions there is usually a way to define a probability density for each state
      ?

      Think about whether this reason is strong or weak

    • 2.The probability of any event is the integral of the density over the states that make up the event
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.