The Clustering Postulate's probabilistic co-occurrence metric conflates accidental correlations with law-like regularities, a distinction Hempel showed is essential to legitimate inductive support.

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Accidental correlations(as used in logic and statistics): When two things happen together by pure chance, with no deeper reason connecting them—like how ice cream sales and drowning rates both rise in summer, but neither causes the other.
Clustering Postulate(Hesse's a priori justification of analogical reasoning (1974)): Hesse's proposed assumption that the epistemic probability function has a built-in bias towards generalization, intended to support inductive and analogical inference along Carnapian lines
Hempel(as a historical reference): Carl Hempel (1905-1997) was a philosopher who created a famous theory about what counts as scientific explanation and confirmation.
Law-like regularities(as used in philosophy of science): Patterns in nature that are genuine scientific laws (like gravity always pulling objects down) that hold universally and necessarily.

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