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    The standard treatment of zero-probability events differs... — Carmelics
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    The standard treatment of zero-probability events differs between finite/discrete and continuous distributions

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.In finite and discrete distributions it is standard to treat events of probability 0 as if they do not happen
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    • 2.In continuous distributions there is always some event of probability 0 that actually occurs
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.The distinction between discrete and continuous distributions is a mathematical idealization; all physical measurements have finite precision and discrete outcomes.
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    • 2.If continuous distributions are merely approximations of underlying discrete processes, then zero-probability events in continuous models carry no genuine ontological weight.
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    • 3.Therefore the alleged asymmetry collapses: both cases reduce to the discrete treatment, where probability-zero events are treated as non-occurring.
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    Reason against 2 of 2
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    • 1.De Finetti's subjectivist framework replaces point-valued probabilities with interval-valued credences, dissolving the zero-probability problem entirely.
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    • 2.Under strict coherence conditions articulated by Shimony and later Skyrms, every logically possible event must receive positive credence, making genuine zero-probability assignments rationally impermissible regardless of distribution type.
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    • 3.If zero probabilities are never epistemically legitimate assignments in a well-formed credence function, the claimed discrete/continuous asymmetry rests on an artifact of an inadequate probability framework rather than a genuine conceptual difference.
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    Related

    De Finetti's subjectivist framework replaces point-valued probabilities with int...If continuous distributions are merely approximations of underlying discrete pro...If zero probabilities are never epistemically legitimate assignments in a well-f...In continuous distributions there is always some event of probability 0 that act...
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    In finite and discrete distributions it is standard to treat events of probabili...The distinction between discrete and continuous distributions is a mathematical ...Therefore the alleged asymmetry collapses: both cases reduce to the discrete tre...Under strict coherence conditions articulated by Shimony and later Skyrms, every...

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    However, many applications of probability require what are known as continuous distributions (such as the uniform/rectangular, normal, and beta distributions), and thus require a restriction to countable additivity. In a continuous distribution, there are uncountably many states, usually named by real numbers. Each individual state has probability 0, even though events containing uncountably many states often have non-zero probability. (This violates full additivity.) However, in the common cont
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    Details

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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit