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
    Bertrand's paradox demonstrates that continuous variables... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→The Principle of Indifference leads to contradictory results when the partition in question is not held fixed.

    Bertrand's paradox demonstrates that continuous variables yield incompatible uniform distributions depending on geometric parameterization chosen.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Different parameterizations of the same geometric space (Cartesian vs. polar) produce genuinely distinct probability measures.
      ?

      Think about whether this reason is strong or weak

    • 2.Without additional justification, no parameterization has privileged status—making any choice of 'uniform' distribution arbitrary.
      ?

      Think about whether this reason is strong or weak

    • 3.This arbitrariness reveals that 'uniformity' lacks objective meaning independent of how we mathematically represent a problem.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The paradox conflates the question (selecting chords) with answers (parameterizations), not showing uniform distributions themselves are incompatible.
      ?

      Think about whether this reason is strong or weak

    • 2.Once a random process is precisely specified, it determines a unique distribution; multiple specifications yield different processes, not a logical contradiction.
      ?

      Think about whether this reason is strong or weak

    • 3.The paradox illustrates practical ambiguity in problem specification, not a fundamental defect in probability theory itself.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Connections

    2 topics

    Truth & Knowledge1 linkedSkepticism1 linked

    Related

    Different parameterizations of the same geometric space (Cartesian vs. polar) pr...Once a random process is precisely specified, it determines a unique distributio...The Principle of Indifference leads to contradictory results when the partition ...The paradox conflates the question (selecting chords) with answers (parameteriza...
    +3 moreShow less
    The paradox illustrates practical ambiguity in problem specification, not a fund...This arbitrariness reveals that 'uniformity' lacks objective meaning independent...Without additional justification, no parameterization has privileged status—maki...

    Details

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