From the NIST Engineer's Handbook:
"Generally, we first need to find and explore correlations and then try to establish causal relationships. It is much easier to find correlations as these are just properties of the data."
So I'm saying that correlation is often used (and misused) in an attempt to find good candidates for causation. This is how much science and engineering is practiced. If you disagree with this, you disagree with some fundamentals of how the scientific method is used (ie, hypothesis forming).
> To me correlation is more a way to reinforce a hypothesis of causality that is already suspected
It certainly can be used in this way, but that doesn't mean it's the only scientifically-valid way to use it.
The data may be flawed in many ways, so there is no automatic assumption that any conclusion is correct.
And - as this answer says - this is a completely different process to discovering a robust causal mechanism that can reliably explain a correlation and predict its persistence into the future.
> Corrleations are meaningful because they indicate how strongly variables can predict other variables.
This is not wrong per se, but may be wrongly interpreted.
1) I think it is important to stress that the reverse is not true. If a correlation is 0, it does not mean the variables are independent. It means they are linearly independent. There are a lot of things out there which are very much linked but not with a linear relationship.
2) This is only true if the correlation was done properly. For instance, correlating non-stationary variables will spuriously yield a high correlation, giving a false impression of link. The classic example is trying to correlate stock prices between themselves. An other example of spurious correlation is when not enough points are given to get an accurate result. Looking at tstat, r2, etc. is as important as looking at the actual correlation coefficient.
3) You use the word "predict" here, which I don't quite like. Correlation can predict outcomes only in the case where you have proven that past information will continue to occur. This is not always the case.
> A positive correlation between two variables means they tend to move in the same direction.
This is misleading also. The variables tend to move in the same direction _relatively to their mean_! I can plot you very different looking curves that are highly correlated just because their mean vary differently. Especially because of potential outliers.
> And it turns out that a strong positive correlation can be a good place to hunt for possible causality, such as hunting for something that causing both variables to change together.
I tend to dislike that thought process. It is very tempting to infer causality from correlation. Especially when automating correlation at scale is affordable, so generating spurious correlation is easy. To me correlation is more a way to reinforce a hypothesis of causality that is already suspected. It won't give you the direction, but may hint you that you are on the right track. I mean, correlation should not be a clue to discover causality, as there are too many false positives. Correlation should be an intermediary step in studying a potential causality.