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It is not the case that Hume demonstrated that the inference from 'every event we have examined has a cause' to 'every event has a cause' is an illegitimate ampliative leap.
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Reasons For
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Reason for
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1.
Hume's critique conflates logical validity with rational justification; we can rationally accept ampliative inferences without them being deductively valid.
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2.
Rejecting all induction as illegitimate leads to radical skepticism that undermines science, practical reasoning, and Hume's own empirical philosophy.
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3.
Causation may not require strict universality; acknowledging that causal principles hold contingently or probabilistically avoids the uniformity problem.
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Reasons Against
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Reason against
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1.
Finite observation can never logically entail universal claims; induction requires assuming nature's uniformity, which cannot itself be inductively justified.
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2.
Past regularities provide no logical guarantee about unobserved cases; we cannot derive necessity from contingent empirical patterns alone.
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3.
The leap assumes the unobserved future resembles the observed past, but this assumption itself needs justification independent of the induction being validated.
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