Hesse's own positive analogy criterion requires that shared properties be causally or nomically connected to the inferred property, a condition irreducibly material and not capturable by co-occurrence statistics.
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A relationship where one thing is linked to another by a law of nature—meaning they're connected in a way that's always true, not just by accident.
Positive analogy criterion(in philosophy of science and reasoning by analogy)
A rule that decides whether a comparison between two things is actually useful for learning something new; it asks: what things do they share, and does that sharing actually matter?