army1987 comments on Causal Diagrams and Causal Models - Less Wrong
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Correlation does not imply causation,
but
causation implies correlation,
and therefore
no correlation implies no causation
...which permits the falsification of some causal theories based on the absence of certain correlations.
That only works if by correlation you mean any kind of statistic dependence -- Pearson's correlation coefficient does vanish for certain relationships if they're non-monotonic.