Although causation necessarily implies correlation, correlation does not imply causation. — Mr Bee
One use of the concept, though, is to help us weed out spurious correlations. — Srap Tasmaner
In my work and in my play I have occasion to do many regressions - statistical analyses of the association between observed phenomena. In that context, for many years I have preached the gospel of 'correlation does not imply causation' and pointed to regressions that identify strong relationships between tea sales in Germany and rates of divorce in Canada as evidence of the difference.
What has changed in me is not that I think that there's no difference between useful correlations and spurious ones. It's that I think 'causality' is the wrong razor to use to make the distinction.
The most obvious reason for that is that a razor is - the etymology declaims it - something sharp, accurate, defined with excruciating precision. We have seen in this thread that nobody wants to define causality, and it has even been suggested that it's a mistake to try to do so. That's fine, but without a definition we cannot use it as a razor. We need a different concept - a clear, precise, well-defined one - to distinguish between spurious and non-spurious correlations.
My current thinking is that a good candidate for that razor is the
persistency of the correlation under different circumstances. That is what I was trying to elucidate with the pharmaceutical example. Most spurious correlations will disappear if we can conduct the experiment under different circumstances.
An even better razor is if we can identify a
mechanism that enables us to predict that if B occurs, C is likely to follow. We can't always do that, so we have to fall back on the first razor. Sometimes we can't even use that, so we remain in a state of ignorance as to whether the correlation is spurious or persistent. But we keep trying.
There's nothing illogical about saying 'the cause of your fever is that you have influenza'. It's just that I see it as an imprecise, slang statement that's great for everyday life but doesn't fit well in philosophy, or in law courts or other arguments about whose fault it was. Its meaning is usually something like 'you have influenza, and in the process of working through one's influenza, one usually develops a fever.' The latter statement has a precision that the former does not. If more detail is wanted, one can describe how the immune system typically reacts to its detection of the influenza virus, the rapid increase in the activity of T cells and white cells, the battles that take place in the blood stream, and so on. It's all about mechanism.
Another point - God I prattle on, don't I? The use of the word 'cause' as a substitute for mechanism seems to depend haphazardly on the history of the discipline. In physics we talk about 'light cones of causality' even though they are better described as 'light cones of predictability'.
Against that is the example of Credit Risk Analysis - the discipline of predicting how many borrowers are likely to default on (fail to repay) their debts. Poor credit risk analysis was a major factor in the global economic disaster that started in 2008 and whose effects are still being felt. In this field there are two types of mathematical models used to predict probability of default. They are called Statistical and Structural models respectively. Statistical models, as the name suggests, look solely at the characteristics of borrowers and do regressions to work out which characteristics are correlated with default. Structural models focus on the financial structure of the company - its assets and liabilities - and the movements of stock price indices and use an economic model to predict which companies are likely to default, based on the observation that default occurs when one's liabilities exceed one's assets. This type of model looks at what some would loosely describe as 'cause' of default whereas Statistical models do not. But interestingly, the word 'cause' is barely mentioned in the literature. The word 'Structural' is used instead, which has a natural similarity with Mechanism.