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Even when there is causation, you still don't which is the cause and effect, or if both are effects of hidden common cause.

That doesn't make any sense.

There could be a causation link between alcohol and suicide, but whether suicidal thoughts lead to alcohol or alcohol leads to suicidal thoughts is unknown.

Alternatively, both alcohol and suicidal thoughts could be the result of a 'hidden common cause', such as drugs or unemployment.

> Correlation does imply causation.

Yeah, and maternities cause pregnancies.

In the terminology used to describe logic (i.e. used by logicians and mathematicians), implies = proves