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    The classical interpretation of probability yields implau... — Carmelics
    Home/Natural Theology
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    The classical interpretation of probability yields implausible and contradictory results when applied generally.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The classical interpretation requires an a priori principled basis for individuating possibilities, but no such basis exists independently of antecedent probability assignments.
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    • 2.Keynes demonstrated in his Treatise on Probability that the reference class of 'equipossible' outcomes changes with how the problem is described, yielding contradictory probability values for identical events.
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    • 3.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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    Reason for 2 of 2
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    • 1.Carnap's inductive logic program revealed that infinitely many confirmation functions satisfy the classical symmetry constraints, with no non-circular grounds for preferring one partition over another.
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    • 2.If the classical interpretation cannot adjudicate between competing equipossibility partitions without importing prior probability judgments, it is viciously circular as a foundational account of probability.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Under the classical interpretation, all possibilities receive equal weight.
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    • 2.A lottery ticket either wins or does not win, so each possibility would have probability 1/2.
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    • 3.Yet the actual probability of winning a lottery is one-in-a-million, not 1/2.
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    Natural Theology

    Related

    A lottery ticket either wins or does not win, so each possibility would have pro...Bertrand's chord paradox shows that three geometrically valid but non-equivalent...Carnap's inductive logic program revealed that infinitely many confirmation func...If the classical interpretation cannot adjudicate between competing equipossibil...
    +4 moreShow less
    Keynes demonstrated in his Treatise on Probability that the reference class of '...The classical interpretation requires an a priori principled basis for individua...Under the classical interpretation, all possibilities receive equal weight.Yet the actual probability of winning a lottery is one-in-a-million, not 1/2.

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    SEP: pascal-wager
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    Morris 1994 is sympathetic to (1), while Hacking 1972 finds it “a monstrous premiss” (189). One way to defend it is via the classical interpretation of probability, according to which all possibilities are given equal weight. The interpretation seems attractive for various gambling games, which by design involve an evidential symmetry with respect to their outcomes; and Pascal even likens God’s existence to a coin toss, evidentially speaking. However, unless more is said, the interpretation yiel
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    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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