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    Inverse View

    It is not the case that Bertrand's chord paradox shows that three geometrically valid but non-equivalent equipossibility partitions yield probabilities of 1/3, 1/4, and 1/2 for the same event, proving internal inconsistency.

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    Reasons For

    1 perspective
    Reason for
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    • 1.The three methods solve different problems (random endpoints vs. random radii vs. random midpoints), so disagreement reflects different questions, not internal inconsistency.
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    • 2.Inconsistency requires that the same setup yield contradictory probabilities; but different randomization procedures are not 'the same event' mathematically.
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    • 3.The paradox shows probability depends on *how* we generate randomness, not that equipossibility is incoherent—physics, not logic, determines the correct method.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The three methods produce mathematically correct results under their own definitions, yet contradict each other, demonstrating that probability requires external assumptions.
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    • 2.If equipossibility were a self-evident principle, identical geometric objects couldn't yield incompatible probability assignments without logical contradiction.
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    • 3.The paradox reveals that 'geometric validity' alone cannot determine probability—something non-geometric must specify which partition reflects reality.
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