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    A reformulation of how prospects of infinite rewards are ... — Carmelics
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    A reformulation of how prospects of infinite rewards are compared can resolve both the mixed-strategies objection and the many Gods objection to Pascal's Wager

    Natural Theology
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    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.The mixed-strategies objection and the many Gods objection both arise from how infinite reward prospects are compared
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    • 2.A revised comparison method can accommodate rational preference among infinite goods
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Hájek's argument establishes that any mixed strategy assigning positive probability to wagering yields infinite expected utility, making dominance reasoning structurally unavailable for resolving mixed-strategy cases.
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    • 2.A reformulated comparison method that assigns lexical or hyperreal values to infinite prospects still cannot escape the result that infinitely many mixed strategies remain rationally equivalent to pure belief.
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    • 3.This equivalence is a feature of the mathematics of infinite utility aggregation itself, not a product of how prospects are compared, so no comparison-method revision can dissolve it.
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    Reason against 2 of 2
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    • 1.Any comparison method that ranks infinite reward prospects must impose an ordering on uncountably many possible theological configurations, which formal decision theory cannot uniquely determine.
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    • 2.Without a principled, non-arbitrary basis for comparing infinities across distinct theological hypotheses, a revised comparison method merely relocates rather than resolves the indeterminacy the many Gods objection exposes.
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    Natural Theology

    Related

    A reformulated comparison method that assigns lexical or hyperreal values to inf...A revised comparison method can accommodate rational preference among infinite g...Any comparison method that ranks infinite reward prospects must impose an orderi...Hájek's argument establishes that any mixed strategy assigning positive probabil...
    +3 moreShow less
    The mixed-strategies objection and the many Gods objection both arise from how i...This equivalence is a feature of the mathematics of infinite utility aggregation...Without a principled, non-arbitrary basis for comparing infinities across distin...

    Similar

    The mixed-strategies objection and the many Gods objection both arise ...90%If Pascal's decision problem is exactly as Pascal claims, then by the ...80%A revised comparison method can accommodate rational preference among ...74%Since the original mixed strategy was rational under those conditions,...74%

    Source

    AI-extracted1/3 agreementValid
    SEP: pascal-wager
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    Jackson and Rogers (2019), developing points in Jackson (2016), argue that the mixed-strategies objection is a “structural, but not substantive” (61) objection to Pascal's Wager. They provide cases in which it is clearly rational to prefer one infinite good to another. They suggest a reformulation of how prospects of infinite rewards should be compared. (This also provides a response to the many Gods objection.) Hájek (2003 and especially 2018) offers many valid reformulations of the Wager with
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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