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    If there are uncountably many times at which one implemen... — Carmelics
    Home/Natural Theology
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    If there are uncountably many times at which one implements a mixed strategy with non-zero probability of wagering for God, then with probability 1 one ends up wagering for God at one of those times.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.With a continuum of times available, Robertson's proposed sequence of rolls can be completed in an arbitrarily short period.
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    • 2.After completing that sequence, Monton's argument implies one should roll again.
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    • 3.A mathematical result shows that uncountably many independent trials each with non-zero probability of success yields success with probability 1.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Probability-1 convergence in infinite trials does not entail that any finite agent actually performs the requisite uncountably many actions.
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    • 2.Human deliberation and action are constrained to countable sequences, so the uncountable-trials model misrepresents the agent's actual decision situation.
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    • 3.Applying measure-theoretic results about uncountable probability spaces to discrete rational agency commits a category error between mathematical idealization and normative decision theory.
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    Reason against 2 of 2
    ?
    • 1.Zeno-style supertask completions presuppose a metaphysics of time permitting infinite divisibility of action, which is contested by both Aristotelian and quantum-discrete accounts.
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    • 2.If supertasks are metaphysically impossible, the premise that uncountably many trials can be completed collapses, and the probability-1 guarantee never applies to any realizable agent.
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    Topics

    Natural TheologyModality & Possibility

    Key Terms

    Pascal's Wager(Pascal's own framing of the Wager's role)
    An instrumental argument intended as a first step toward genuine religious faith, not as a substitute for it.
    Probability 1(as used in mathematics and probability theory)
    A certainty; something that is absolutely guaranteed to happen (as opposed to being merely likely).
    Uncountably many(as used in mathematics and logic)
    An infinite number of things so large that you couldn't list them all even with infinite time; larger than regular infinity (like comparing all real numbers to just whole numbers).
    Wager for God(a famous philosophical argument about faith and probability)
    A reference to Pascal's Wager, the idea of choosing to believe in and live as if God exists because the potential benefit (eternal reward) outweighs the cost of being wrong.
    mixed strategy(The uniform three-way randomization over bridges is the mixed strategy under analysis.)
    A strategy in which a player assigns probabilities over available actions and randomizes according to that distribution.

    Related

    A mathematical result shows that uncountably many independent trials each with n...After completing that sequence, Monton's argument implies one should roll again.Applying measure-theoretic results about uncountable probability spaces to discr...Human deliberation and action are constrained to countable sequences, so the unc...
    +4 moreShow less
    If supertasks are metaphysically impossible, the premise that uncountably many t...Probability-1 convergence in infinite trials does not entail that any finite age...

    Source

    AI-extracted1/3 agreementValid
    SEP: pascal-wager
    View source passageHide passage
    Monton 2011 defends Pascal’s Wager against this line of objection. He argues that an atheist or agnostic has more than one opportunity to follow a mixed strategy. Returning to the first example of one, suppose that the fair coin lands tails. Monton’s thought is that your expected utility now changes; it is no longer infinite, but rather that of an atheist or agnostic who has no prospect of the infinite reward for wagering for God. You are back to where you started. But since it was rational for
    Extraction notes

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

    Details

    With a continuum of times available, Robertson's proposed sequence of rolls can ...
    Zeno-style supertask completions presuppose a metaphysics of time permitting inf...

    Similar

    For a mixed strategy in which the probability of wagering for God decr...89%Repeatedly applying a mixed strategy based on an n-sided die (where n ...85%Any mixed strategy that assigns positive finite probability to wagerin...85%The 'coin toss' strategy (probability 1/2 of wagering for God) has the...84%
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit