> two things happening at the same time are correlated but what is not necessarily proven definitively is that its causation.
That part is incorrect: Correlation is defined as (A => B) AND (!A => !B). (I.e., that's a logical AND; both terms must be true.) Every morning, the rooster crows and the sun rises; that's not correlation because if the rooster doesn't crow, the sun still rises. (The actual definition of correlation is, IME, a very powerful tool for analysing through assertions.)
As you say, correlation does not mean causation, even using the proper definition. For example, two people completely unknown to each other may, over the course of an hour, laugh, cheer, and cry at the same time, in a highly correlated manner. But there is no causation between them; they are merely watching the same live TV show.
That part is incorrect: Correlation is defined as (A => B) AND (!A => !B). (I.e., that's a logical AND; both terms must be true.) Every morning, the rooster crows and the sun rises; that's not correlation because if the rooster doesn't crow, the sun still rises. (The actual definition of correlation is, IME, a very powerful tool for analysing through assertions.)
As you say, correlation does not mean causation, even using the proper definition. For example, two people completely unknown to each other may, over the course of an hour, laugh, cheer, and cry at the same time, in a highly correlated manner. But there is no causation between them; they are merely watching the same live TV show.