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Coscott comments on Open thread, 23-29 June 2014 - Less Wrong
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You are leaving out one type of causation. It is possible that you are conditioning on some common effect C of A and B.
You may argue that this does not actually give a correlation between A and B, it only give a correlation between A given C and B given C. However, in real life, there will always be things you condition on whenever you collect data, so you cannot completely remove this possibility.
This would be the same sort of selection-causing-pseudo-correlations that Yvain discusses in http://slatestarcodex.com/2014/03/01/searching-for-one-sided-tradeoffs/ ? Hm... I think I would lump that in with my response to Nancy ('yes, we rarely have huge ns and can wish away sampling error and yes our data collection is usually biased or conditioned in ways we don't know but let's ignore that to look at the underlying stuff').
Even if we promoted it to the level of the other 3 causation patterns, does that change any of my arguments? It seems like another way of producing correlations-which-aren't-due-to-direct-causation just emphasizes the point.
Yes, I am talking about the exact same thing that Yvain is talking about there.
So, I think any time you observe a correlation, it is because of one of those 4 causation patterns, so even if the fourth does not show up as regularly as the other 3, you should include it for completeness.