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It is not the case that Any application of probability under the frequentist interpretation thus presupposes stable, law-governed regularities in nature.
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Reasons For
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1.
Frequentist probability can apply to finite, non-repeating events (elections, trials) without requiring eternal natural laws, only consistency within a bounded context.
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2.
The claim conflates a practical working assumption with a logical presupposition; we can use frequentist methods provisionally without believing in metaphysical stability.
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3.
Chaotic and quantum systems show that useful frequentist probabilities can emerge even where microscopic determinism or laws don't hold in classical senses.
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Reasons Against
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1.
Frequentist probability requires repeated trials under identical conditions to converge to stable frequencies, which only makes sense if nature exhibits consistent regularities.
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2.
Without assumption of law-governed stability, past frequency data provides no rational basis for predicting future outcomes or assigning probability values.
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3.
Empirical science has successfully applied frequentist methods only in domains where natural laws appear stable, suggesting this presupposition is necessary for the framework's applicability.
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