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    Complete ignorance should not be modeled as equiprobability. — Carmelics
    Home/Natural Theology
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    Complete ignorance should not be modeled as equiprobability.

    Natural Theology
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    2 reasons for
    1 reason against

    Reasons For

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    Reason for 1 of 2
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    • 1.Jaynes's transformation group invariance shows equiprobability is justified only when a problem exhibits formal symmetry under permutation of outcomes.
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    • 2.Epistemic ignorance about God's existence lacks the structural symmetry required: the hypothesis space is not closed under any natural permutation group.
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    • 3.Therefore equiprobability under theological ignorance violates the very criterion that licenses the principle of indifference in well-posed cases.
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    Reason for 2 of 2
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    • 1.Keynes argued that probability is a logical relation between propositions, and where evidence is absent, the relation is indeterminate rather than uniform.
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    • 2.Indeterminate probability, as formalized in Walley's imprecise probability theory, permits a range [0,1] rather than the single value 0.5.
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    • 3.Modeling complete ignorance as the interval [0,1] is strictly more epistemically faithful than collapsing it to a point estimate of 0.5, which itself encodes a substantive belief.
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    Reasons Against

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    Reason against
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    • 1.Assigning equal probability to all outcomes under ignorance produces contradictions (e.g., lottery example).
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    • 2.The classical interpretation is only plausible in contexts of evidential symmetry by design, such as gambling games.
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    Natural Theology

    Related

    Assigning equal probability to all outcomes under ignorance produces contradicti...Epistemic ignorance about God's existence lacks the structural symmetry required...Indeterminate probability, as formalized in Walley's imprecise probability theor...Jaynes's transformation group invariance shows equiprobability is justified only...
    +4 moreShow less
    Keynes argued that probability is a logical relation between propositions, and w...Modeling complete ignorance as the interval [0,1] is strictly more epistemically...The classical interpretation is only plausible in contexts of evidential symmetr...Therefore equiprobability under theological ignorance violates the very criterio...

    Similar

    Assigning equal probability to all outcomes under ignorance produces c...80%Under the classical interpretation of probability, complete ignorance ...78%Pascal's equiprobability argument does not speak to those in his audie...76%An argument premised on equiprobability only applies to agents who acc...74%

    Source

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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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    Details

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