Whether Non-Correlation Implies Non-Causation

It has been well argued that correlation does not imply causation. Is the converse true: does non-correlation imply non-causation, or more plainly, does causation imply correlation? Here we argue that this is a useful intuition of the semantic essence of the faithfulness assumption of causal graphs. Although the statement is intuitively reasonable, it is not categorically true (but it is true with probability one), and this brings into question the validity of causal graphs. This work reviews Cartwright’s arguments against faithfulness and presents a philosophical case in favor of the faithfulness assumption. This work also shows how the causal graph formalism can be used to troubleshoot scenarios where faithfulness is violated.