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    Convergence to limiting frequencies constitutes a form of... — Carmelics
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    Challenges→Probabilistic reasoning does not yield a conclusion that the next ball will be a certain color, but rather that certain future observations are very likely given past observations

    Convergence to limiting frequencies constitutes a form of practical certainty that dissolves the epistemic gap between 'very likely' and 'guaranteed' for scientific purposes.

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    Reasons For

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    Reason for
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    • 1.Large-sample frequency convergence enables predictions accurate enough for all practical engineering, medicine, and policy decisions.
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    • 2.The distinction between 'extremely likely' and 'certain' becomes operationally meaningless when error rates fall below detection thresholds.
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    • 3.Scientific practice already treats converged frequencies as decision-basis, not merely as 'very likely' propositions requiring further justification.
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    Reasons Against

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    • 1.Convergence describes observed behavior in finite samples, not mathematical certainty; the gap between contingent and necessary remains philosophically distinct.
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    • 2.Finite-sample tail risks and black swan events retain non-zero probability; dissolving epistemic gaps requires proving impossibility, not high probability.
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    • 3.Pragmatic sufficiency for action does not eliminate the logical gap—practical needs and truth conditions are separate epistemological questions.
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    Related

    Convergence describes observed behavior in finite samples, not mathematical cert...Finite-sample tail risks and black swan events retain non-zero probability; diss...Large-sample frequency convergence enables predictions accurate enough for all p...Pragmatic sufficiency for action does not eliminate the logical gap—practical ne...
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    Probabilistic reasoning does not yield a conclusion that the next ball will be a...Scientific practice already treats converged frequencies as decision-basis, not ...The distinction between 'extremely likely' and 'certain' becomes operationally m...

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