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It is not the case that Mill's methods and Bayesian confirmation theory provide general frameworks for inductive reasoning without licensing all inductive arguments.
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Reasons For
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1.
Mill's methods presuppose causal closure and no hidden confounds, assumptions often violated in complex systems but never fully vindicated independently.
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2.
Bayesian theory merely transfers the problem: choosing priors is subjective, so it licenses inferences its users deem reasonable without principled discrimination.
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3.
Both frameworks remain silent on non-causal inductive patterns (analogical, abductive, statistical) that reasoning actually relies upon in practice.
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Reasons Against
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Reason against
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1.
Mill's methods (agreement, difference, etc.) identify causal relationships through systematic elimination, avoiding arbitrary inductive leaps.
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2.
Bayesian confirmation requires explicit prior probabilities and likelihood ratios, which constrains inference to rational, mathematically defensible arguments.
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3.
Both frameworks reject crude induction (all observed swans are white) by demanding either systematic variation or probabilistic updating against evidence.
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