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It is not the case that C.D. Broad and later Elliott Sober showed that cumulative case arguments conflate correlated evidence with genuinely additive probabilistic support.
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Reasons For
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1.
Not all cumulative case arguments treat evidence as independent; sophisticated versions explicitly model evidential relationships and adjust accordingly.
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2.
Even correlated evidence can provide multiplicative support if each piece explains distinct phenomena or comes from independent sources, which Broad/Sober underaddressed.
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3.
The charge conflates a flaw in how some argue cumulatively with whether cumulative reasoning itself is invalid as a philosophical method.
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Reasons Against
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1.
Evidence for God's existence (fine-tuning, cosmological, moral arguments) often shares common explanatory targets, making them probabilistically dependent.
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2.
When evidence is correlated, multiplying probabilities as if independent artificially inflates cumulative support without accounting for this dependence.
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3.
Bayesian analysis requires explicit conditional probabilities; cumulative case arguments typically omit these calculations entirely.
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