If correlation doesn’t imply causation, then what does?

I confess that I only skimmed the latter 75% of the article, but it seemed like the author is ignoring a more fundamental issue: what does it even mean for something to cause something else? In so many cases, we humans assume a rather trivial obvious definition: X causes Y if X happens before Y and Y is extremely likely given X. Other stipulations may be assumed, like X dramatically increases the chances of Y, or Y rarely happens without X happening previously.

All of these intuitive definitions are useful for everyday language (smoking causes lung cancer, drunk driving causes traffic accidents, exercise causes weight loss, etc.), but if you think a bit deeper it seems like something is missing. Why does it sound silly to say that marriage causes divorce, hospitals cause deaths, graduating from high school causes college dropouts, etc.?

I'm convinced that a precise definition of causality doesn't really exist, or at least that there isn't one that can be usefully applied both to everyday language and formal mathematical/scientific/philosophical language.

Correlation is a necessary, but not sufficient condition for causation. If a is correlated with b, it means a might causes b, but you don't know for sure. Some dum-dums think that if a is correlated with b, then it cannot cause b.

in order to show causation, you need to go back in time and change things. This is called a counter-factual. Obviously we cannot do this. the best we can do is to control everything as closely as possible, changing only one factor at a time, or at least thinking we do. This is called the scientific method.

Basically, you cannot really ever prove causation, but you can provide overwhelming evidence, along with isolated control over changing factors.

Related http://stats.stackexchange.com/questions/36/correlation-does...

I've always heard "correlation is not causation" which makes the title less clever. Understood the phrase to mean that while it does imply causation, fact is not necessarily so.

The article's great. Appreciate the 'Problems for the author' highlighting gaps for thought.

The article's title reminded me of this post on lesswrong - "timeless causality" - http://lesswrong.com/lw/qr/timeless_causality/ - also based on Judea Pearl's work.